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tag:blogger.com,1999:blog-24338418806191718552020-07-14T09:47:16.247+01:00Pat'sBlogThe mathematical (and other) thoughts of a (now retired) math teacher,firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-29099235659101189802020-07-14T00:00:00.000+01:002020-07-14T00:00:06.913+01:00On This Day in Math - July 14

Antoine Caron: Astronomers Studying an Eclipse *TIA

 Nature is not embarrassed by difficulties of analysis.
~Augustin Fresnel

The 196th day of the year, A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its base 10 digits and adding the resulting numbers. 196 is the lowest number conjectured to be a Lychrel number; the process has been carried out for one billion iterations without finding a palindrome, but no one has ever proven that it will never produce one. The number produced on the one billionth iteration had 413,930,770 digits. The name "Lychrel" was coined by Wade VanLandingham—a rough anagram of his girlfriend's name Cheryl. No Lychrel numbers are known, though many numbers are suspected Lychrels, the smallest being 196. (Students might try finding the number of iterations of the process to find a palindrome for various n. 195, for example, takes four iterations :
195 + 591 = 786
786 + 687 = 1473
1473 + 3741 = 5214
5214 + 4125 = 9339)
DO not try the numbers 89 or 98. Harry J Saal used a computer to repeatedly iterate this process and finally did come up with a palindrome, the number 8,813,200,023,188 on the 24th iteration.

Jim Wilder noticed that 142 =196 and 132=169... are there other squares of consecutive numbers that share the same digits?

A number is said to be square-full if for every prime, p, that divides it, p2 also divides it. 196 is such a number. Are there cube-full numbers? (of course there are, but what are they?) Stay tuned, one is coming soon.

EVENTS
1686 On June 20th Halley Wrote to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton responded On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

1696 Construction of the Eddystone lighthouse began today by Henry Winstanley. Winstanley ...investing some of the money he had made from his work and commercial enterprises in five ships. Two of them were wrecked on the Eddystone Rocks near Plymouth, and he demanded to know why nothing was done to protect vessels from this hazard. Told that the reef was too treacherous to mark, he declared that he would build a lighthouse there himself, and the Admiralty agreed to support him with ships and men.
In the 1690s he opened a Mathematical Water Theatre known as "Winstanley's Water-works" in London's Piccadilly. This was a commercial visitor attraction which combined fireworks, perpetual fountains, automata and ingenious mechanisms of all kinds, including "The Wonderful Barrel" of 1696 which served visitors with hot and cold drinks from the same piece of equipment. It was a successful and profitable venture and continued to operate for some years after its creator's death.(*Today in History)

1776 The beginning of Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.*Wik

1791 A mob in Birmingham, England, rioted during festivities marking the anniversary of the fall of the Bastille on this date in 1789. The mob, which ran wild for three days, destroyed the house, laboratory and library of Joseph Priestley, discoverer of oxygen, because of his anti religious views and espousal of revolutionary causes.*VFR Within a few years, on 7 Apr 1794, he forever left England and traveled to the United States. Priestley discovered oxygen nearly 20 years earlier, on 1 Aug 1774.*TIS

1831 Evariste Galois again arrested, as a precautionary measure. He received a six months sentence. *VFR

In 1867, Alfred Nobel demonstrated dynamite for the first time at a quarry in Redhill, Surrey. In 1866 Nobel produced what he believed was a safe and manageable form of nitroglycerin called dynamite. He established his own factory to produce it but in 1864 an explosion at the plant killed Nobel's younger brother and four other workers. Deeply shocked by this event, he now worked on a safer explosive and in 1875 came up with gelignite. Other inventions followed including ballistite, a form of smokeless power, artificial gutta-percha and a mild steel for armour-plating.*TIS

*http://connecticuthistory.org

1868 Alvin J. Fellows of New Haven, Connecticut, received patent #79,965 for the first tape measure. It was enclosed in a circular case with a spring lock to hold the tape at any desired point. *VFR (for my son Robin, who seems to collect them as icons of his trade) Earlier, a machine to print ribbon for the supple sewing tape measures had already been patented on 3 Sep 1847, after four years of research by the French fashion designer, Lavigne. Further, however, Sheffield, England claims to be not just the home of stainless steel, but also where the spring tape measure was invented. *TIS (This was for the spring type tapes common today. Earlier tapes were produced with a brass fold-out clip to rewind them... One my grand-daughter just found for her dad at a boot-sale for 50 pence was an old Chesterman that was marked in links (.01 chains) and rods (1/4 of a chain) on one side. .... "James Chesterman moved to Sheffield from London in 1820. Nine years later he patented the spring tape measure. He also invented the self-winding window blind, produced the first long steel Measuring tape and the first Woven metallic tape. His business adopted the bow as its trademark, and he named his factory the bow works which moved to this site in 1864. James Chesterman & Co became synonymous with high quality measuring instruments, especially tapes, callipers and squares. In 1963 amalgamation with John Rabone & Sons created Rabone Chesterman, who were subsequently bought by Stanley Tools and transferred to Stanley's Woodside Plant. Bow Works was refurbished and extended for its new occupants, Norwich Union in 1993."

1887 The first textbook about the international language, Esperanto, was published by its inventor, Dr. Ludwig Zamenhof, a Pole. Esperanto means "one who hopes." The Italian mathemati¬cian, Giuseppi Peano, created an international language of his own, Latina sina flexione (Latin without inflections), but it was even less successful than Esperanto. *VFR

1897 The Dorabella Cipher is an enciphered letter written by composer Edward Elgar to Dora Penny, which was included with a "thank you" note from his wife dated July 14, 1897. Penny never deciphered it and its meaning remains unknown.

Elgar also named Variation 10 of his 1899 Variations on an Original Theme (Enigma) Dorabella as a dedication to Dora Penny. *Wik

1943 George Washington Carver was honored by U.S. President Franklin Delano Roosevelt dedicating $30,000 for a National Monument to his accomplishments. The area of Carver's childhood near Diamond Grove, in southwest Missouri has been preserved as a park, with a bust of the agricultural researcher, instructor, and chemical investigator. This park was the first designated national monument to an African American in the United States. In 1850-65, Diamond was a typical "crossroads village" near a diamond-shaped grove of trees not far from the Carver farm in Newton County. Also called Diamond Grove, it consisted of a general store, a combination blacksmith shop and post office, and a church that served as a schoolhouse during the week.*TIS

1954 At a Conference for California Teachers of Mathematics, a Los Angeles dentist named Leon Bankoff presented a talk proving that the 2000 year old proof of Archimedes that there were a pair of congruent "Archimedean Twin Circles" in the Arbelos was in fact false. He produced a third identical circle, now usually called the "Bankoff triplet circle".
Later (1979) Thomas Schoch discovered a dozen new Archimedean circles; and then in 1998, Peter Y. Woo of Biola University, generalized two of Schoch's circles, to discover an infinite family of Archimedean circles named the Woo circles in 1999 *Wik *Mathematics Magazine For more on the Archimedean Circles, see my blog on The Shoemaker's Knife Cuts Beautiful Math Across the Centuries

1965 In the Evening of July 14, the Mariner space craft sent back 22 minutes of imaging from a close pass of Mars. These first images came in in strips of 200 numbers, each representing a shade of black to white for one of 200 rows of such pixels to make an image of the surface of the Red Planet. Knowing that at their stage of image creation, it would be many hours before the images were prepared by the computer printers, the telecommunications engineers at JPL began to attach the numbered strips on a bulletin board, and hand color the pixels in red, brown, and yellow pastels. Too impatient to await the computer drawn images, the first press released photos were images of the hand drawn, paint by number image. *NASA

1977 Minor planet (2509) Chukotka 1977 NG. Discovered by N. S. Chernykh at Nauchnyj. Named for a National Area of the R.S.F.S.R., situated in the northeastern part of the U.S.S.R. The discoverer participated in an expedition there to observe the 1972 total solar eclipse. *NSEC

2004 A patent application by John St. Clair was filed for a training program to teach people to walk through walls:Publication number US20060014125 A1 (Ok, just think about it a minute. Someone had to say, "Yeah, we'll give them a patent for that.")

2015 The New Horizons probe, launched on Jan. 19, 2006, with Clyde Tombaugh's ashes on board, arrived at Pluto on July 14, 2015. *The Las Cruces Sun-New
Also on board was a 1991 US postage stamp which was a motivator for people in the project.

BIRTHS
1610 Ferdinand II  (9 July 1578 – 15 February 1637) Fifth grand duke (granduca) of Tuscany, a patron of sciences, whose rule was subservient to Rome. Ferdinand II de' Medici was Grand Duke from 1621. He encouraged scientific studies, and he protected Galileo and the Accademia del Cimento (1657 - 1667). He also devised a sealed thermometer which, unlike Galileo's open one, was not affected by changes in air pressure. It was to him that Galileo dedicated the lens with which he had discovered the satellites of Jupiter and he also made him a gift of the armed lodestone. J. W. Blaeu dedicated to him one of his globes of the fifth type. Ferdinand II was also a patron of Robert Dudley.*TIS

1671 Jacques Eugène d'Allonville, Chevalier de Louville par Fontenelle (July 14, 1671 – September, 1732) French astronomer and mathematician.
He was born in the Château de Louville, and studied mathematics before joining the navy. He achieved the rank of colonel before retiring from military service in 1713, following the peace of Utrecht. He thereafter took up the study of astronomy.
He is noted for determining a method for precisely calculating the occurrence of solar eclipses.
The crater Louville on the Moon is named in his honor. *TIA

1793 George Green baptized in Nottingham, England. The date of his birth is unknown. His most famous work, An Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism was published, by subscription, in March 1828. Most of the fifty-two subscribers were friends and patrons. The work lay unnoticed until William Thomson rediscovered it and showed it to Liouville and Sturm in Paris in 1845. The Theory of Potential it developed led to the modern mathematical theory of electicity. *VFR
George Green was an English mathematician, born near Nottingham, who was first to attempt to formulate a mathematical theory of electricity and magnetism. He was a baker while, remarkably, he became a self-taught mathematician. In March 1828 he published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. He became an undergraduate at Cambridge in October 1833 at the age of 40. Lord Kelvin (William Thomson) subsequently saw, was excited by the Essay. Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son heralded the beginning of modern mathematical theories of electricity.*TIS

1905 Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He is the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. The concept of Young measure is named after him. *Wik

1918 Jay W(right) Forrester (born July 14, 1918- ) is a U.S. electrical engineer and management expert. In 1944-51 he supervised the building of the Whirlwind computer at the Massachusetts Institute of Technology, for which he invented the random-access magnetic core memory, the information-storage device employed in most digital computers. He also studied the application of computers to management problems, developing methods for computer simulation.*TIS

DEATHS
1800 Lorenzo Mascheroni (May 13, 1750 – July 14, 1800) was a geometer who proved in 1797 that all Euclidean constructions can be made with compasses alone, so a straight edge in not needed. In fact this had been (unknown to Mascheroni) proved in 1672 by a little known Danish mathematician Georg Mohr. *SAU In his Adnotationes ad calculum integrale Euleri (1790) he published a calculation of what is now known as the Euler–Mascheroni constant, usually denoted as γ (gamma).*Wik

1827 Augustin Jean Fresnel (10 May 1788, Broglie (Eure)- 14 July 1827 (aged 39)
Ville-d'Avray (Hauts-de-Seine)) French physicist who first investigated the effect of interference of light, with results known as Fresnel fringes. This decisively work, together with further experiments with polarized light supported Thomas Young's wave theory of light Fresnel advanced the wave theory by identifying light as transverse waves rather than the longitudinal waves previously assumed by Young and Huygens. His pioneering work in optics included showing that white light is composed of a spectrum of innumerable wavelengths ranging from red to shorter violet wavelenths. In 1819, he improved the optical system of lighthouses by replacing metal reflectors with revolutionary stepped lenses of his design.*TIS

1865 Benjamin Gompertz (March 5, 1779 – July 14, 1865), was a self educated mathematician, denied admission to university because he was Jewish.[citation needed] Nevertheless he was made Fellow of the Royal Society in 1819. Gompertz is today mostly known for his Gompertz law (of mortality), a demographic model published in 1825. The model can be written in this way:

N(t) = N(0) e^{-c (e^{at}-1)},

where N(t) represents the number of individuals at time t, and c and a are constants.

This model is a refinement of the demographic model of Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.

1899 Sir Arthur Thomas Cotton (15 May 1803 – 24 July 1899) British engineer whose life-work was constructing irrigation, navigation canals and dams for water storage in Southern India, saving thousands from famine and promoting local economy. He joined the Madras engineers in 1819, fought in the first Burmese war (1824-26) and began his ambitious irrigation project (1826-62). He built dams on several rivers, transforming the drought-stricken Tanjore district into the richest part of the state of Madras. His ambitious masterplan was not completed in his lifetime, but his ideas anticipated projects that were subsequently taken up. In the present time, India's goal of a National Water Grid confronts the problem of increasingly scarce water. Cotton founded the Indian school of hydraulic engineering.*TIS

1953 Richard von Mises (19 April 1883, Lviv – 14 July 1953, Boston, Massachusetts) Austrian-American mathematician and aerodynamicist who notably advanced statistics and the theory of probability. Von Mises' contributions range widely, also including fluid mechanics, aerodynamics, and aeronautics. His early work centred on aerodynamics. He investigated turbulence, making fundamental advances in boundary-layer-flow theory and airfoil design. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. He introduced a stress tensor which was used in the study of the strength of materials.Von Mises' primary work in statistics concerned the theory of measure and applied mathematics. His most famous, yet controversial, work was in probability theory. *TIS He is often credited with the creation of the "Birthday Problem", but in this blog I suggest otherwise.

1956 John Miller studied at Glasgow and Göttingen. He returned to Glasgow to the Royal College of Science and Technology (the precursor to Strathclyde University). He became President of the EMS in 1913. *SAU

1960 Maurice de Broglie (27 April 1875–14 July 1960)(6th duke) (Louis-César-Victor-) Maurice de Broglie was a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His "method of the rotating crystal" was an application of Bragg's "focussing effect" to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of "corpuscular spectra." During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation. *TIS

2016 Maryam Mirzakhani, the first woman and first Iranian to win the Fields Medal,died of metastatic breast cancer at the age of 40. She had been a professor at Stanford University since 2008. *Sci Am

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-80266886245832840682020-07-13T00:00:00.000+01:002020-07-13T00:00:01.771+01:00On This Day in Math - July 13

There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences. ... Many ... arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical, unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.

~John Dee, The Mathematical Preface

The 195th day of the year..195 is the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 Students might wonder which numbers can (and cannot) be expressed as the sum of one or more consecutive Primes.

195 is also the third integer that is the sum of the squares of three consecutive primes.*Prime Curios

also, 1*95 = 19*5 Derek Orr tells me there are only four non-trivial 3-digit numbers with this property *@Derektionary

a Heronian triangle is a triangle that has side lengths and area that are all integers. There is an almost-equilateral, scalene triangle with one side of 195. The other sides are 194, and 193. Students can find the area using Heron's formula.

EVENTS
1672 Newton writes to John Collins, "...about the infinite series I am not yet resolved, not knowing when I shall proceed to finish it." *Correspondence of Scientific Men of the Seventeenth Century ..., Volume 2

1773 Gerolamo Saccheri, a Jesuit priest, received the imprimatur of the Inquisition for his Euclides ab Omni Naevo Vindicatus (Euclid Cleansed of Every Blemish), an important forerunner of non-Euclidean geometry. [George E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, p. 304]*VFR

1783 Astronomer William Bayly is paid 200 pounds by the Board of Longitude for "as a recompense for his troubles in reducing, compiling, and printing the astronomical observations of Captain Cooks last voyage, intended to be published with the historical account thereof." *Derek Howse, Britain's Board of Longitude, The Finances
In 1772 Bayly accompanied William Wales as an astronomer on Cook's second voyage of discovery to the southern hemisphere. The two ships employed in the expedition, the Resolution and the Adventure sailed on 13 June. He also sailed in Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.

2012 the third Friday-the-thirteenth of the year. Each Gregorian 400-year cycle contains 146,097 days (365 × 400 = 146,000 normal days, plus 97 leap days) and they equal 146,097 days, total. 146,097 ÷ 7 = 20,871 weeks. Thus, each cycle contains the same pattern of days of the week (and thus the same pattern of Fridays that are on the 13th).
The 13th day of the month is slightly more likely to be a Friday than any other day of the week. On average, there is a Friday the 13th once every 212.35 days (compared to Thursday the 13th, which occurs only once every 213.59 days).
2012 has had Friday-the-13ths in January, April and July . David Dickinson<s>@</s>Astroguyz pointed out that these three Fri-13ths occur in intervals of 13 weeks.
According to the Stress Management Center and Phobia Institute in Asheville, North Carolina, an estimated 17 to 21 million people in the United States are affected by a fear of this day. Some people are so paralyzed by fear that they avoid their normal routines in doing business, taking flights or even getting out of bed. "It's been estimated that \([US]$800 or $900\) million is lost in business on this day". Despite this, representatives for both Delta and Continental Airlines say that their airlines do not suffer from any noticeable drop in travel on those Fridays.
According to folklorists, there is no written evidence for a "Friday the 13th" superstition before the 19th century. The earliest known documented reference in English occurs in Henry Sutherland Edwards' 1869 biography of Gioachino Rossini. *Wik

2016 Jaime Escalante commemorative stamp was officially unveiled at the 87th conference of the League of United Latin American Citizens (LULAC) today in Washington, D.C. Escalante, a teacher in his native Bolivia who arrived in the states in 1963, became known for using innovative methods to teach inner-city students in East Los Angeles that some considered "unteachable," and many of whom went on to master calculus under his tutelage.
His story was the subject of the seminal 1988 movie "Stand and Deliver," which is one of the most viewed movies in U.S. film history. *NBC

2018 Next solar eclipse on a Friday the 13th. The last solar eclipse on a Friday 13th was in December 1974. Both are partial solar eclipses. There are 24 solar eclipses on a Friday the 13th between the years 0 and 3000; Of which 13 partial, 9 annular and 2
total solar eclipses. *NSEC

BIRTHS
1527 John Dee born in London, England (13 July 1527–1608 or 1609). In 1570 he wrote a "fruitfull Praeface" to the Billingsley translation of Euclid, which he edited. This was the first English Euclid.
*VFR
Dee was a noted English mathematician, astronomer, astrologer, occultist, navigator, imperialist and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.*Wik Aubrey's Brief Lives gives Dee credit for inventing the phrase, "The British Empire."

Thony Christie, The Renaissance Mathematicus has written a really interesting blog post on Dee.

1741 Carl Friedrich Hindenburg (13 July 1741– 17 March 1808) published a series of works on combinatorial mathematics.*SAU
Hindenburg co-founded the first German mathematical journals. He also influenced Christian Kramp's work in combinatorics. In 1796, he edited Sammlung combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was "the most important proposition in all of mathematical analysis"*Wik

1822 Heinrich Louis d'Arrest13 July 1822 – 14 June 1875) German astronomer who, while a student at the Berlin Observatory, hastened the discovery of Neptune by suggesting comparison of the sky, in the region indicated by Urbain Le Verrier's calculations, with a recently prepared star chart. The planet was found the same night. His father-in-law was A. F. Moebius (1790 - 1868). d'Arrest found several comets, the one of 1851 with a period of 6.6 years bears his name. One work he published was on the Asteroids between Mars and Jupiter, another work titled Siderum nebulosorum observationes Hafniensis contained 1942 nebula, 340 described for the first time.*TIS The crater D'Arrest on the Moon is named after him, as well as a crater on the Martian satellite Phobos and the asteroid 9133 d'Arrest.

1924 Donald Edward Osterbrock  (July 13, 1924 - January 11, 2007) was an American astronomer who was a leading authority on the history of astronomy, and director of the University of California's Lick Observatory. He applied physics to produce accurate models of stars. For example, treating the outer part of the sun as turbulent and convective, he explained the seemingly anomalous fact that the sun's corona is hotter than its surface. He investigated the nature of ionized gas around hot stars, and was a pioneer in the use of spectroscopic methods for the study of gaseous nebulae. He discovered new types of active galactic nuclei, which are powered by black holes in the centers of galaxies. He fostered the construction of the 10-meter Keck Telescopes in Hawaii. *TIS

1932 Hubert Reeves, CC OQ (born July 13, 1932) is a Canadian astrophysicist and popularizer of science. He attended Collège Jean-de-Brébeuf, a prestigious French-language college in Montreal. He has been a Director of Research at the Centre national de la recherche scientifique since 1965 and currently lives in Paris, France where he often speaks on television promoting science. *Wik

1944 Erno Rubik (July 13, 1944, ) Hungarian mathematician, educator and inventor of Rubik's Cube (1974), which became a popular toy of the 1980s. Rubik's Cube consists of 26 small cubes that rotate on a central axis; nine coloured cube faces, in three rows of three each, form each side of the cube. When the cube arrangement is randomized, the player must then return it to the original condition of faces with matching colours, which is one among 43 quintillion possible configurations.*TIS

DEATHS
1762 James Bradley (March 1693 – 13 July 1762) English astronomer, the third Astronomer Royal, who in 1728 announced his discovery of the aberration of starlight, an apparent slight change in the positions of stars caused by the the motion of the person looking at them with the yearly motion of the Earth. That finding provided the first direct evidence for the revolution of the Earth around the Sun. Bradley was one of the first post-Newtonian observational astronomers who led the quest for precision. From the aberration of starlight, Bradley was also able to make calculations giving the speed of light to be about 283,000 km/s. Further, Bradley discovered that the earth nods a little on its axis, which he named as nutation.*TIS

1794 James Lind FRSE FRCPE (4 October 1716 – 13 July 1794) was a Scottish physician. He was a pioneer of naval hygiene in the Royal Navy. He is of matheamtical interest because he conducted the first modern clinical trial. He developed the theory that citrus fruits cured scurvy. He argued for the health benefits of better ventilation aboard naval ships, the improved cleanliness of sailors' bodies, clothing and bedding, and below-deck fumigation with sulphur and arsenic. He also proposed that fresh water could be obtained by distilling sea water. His work advanced the practice of preventive medicine and improved nutrition.
The concepts behind clinical trials are ancient. The Book of Daniel chapter 1, verses 12 through 15, for instance, describes a planned experiment with both baseline and follow-up observations of two groups who either partook of, or did not partake of, "the King's meat" over a trial period of ten days. Persian physician Avicenna, in The Canon of Medicine (1025) gave similar advice for determining the efficacy of medical drugs and substances. In spite of this history, there seems to have been no clinical trials actually practiced in Western Europe. He blocked a group of twelve men suffering form the effects of scurvy after two months at sea into six different treatment groups of two each. He applied six different treatments, one group getting an issue of cider, one getting citrus, and four other possible alternatives. (The word placebo would not be used until 1772.) Both men in the citrus group showed considerable improvement, and one of the Cider subjects showed mild improvement after the study was stopped in six days. *Wik

1807 Johann(III) Bernoulli (4 Nov 1744 in Basel, Switzerland - 13 July 1807 in Berlin, Germany) wrote a number of works on astronomy and probability theory. Bernoulli wrote a number of works on astronomy, reporting on astronomical observations and calculations, but these are of little importance. Strangely his most important contributions were the accounts of his travels in Germany which were to have a historical impact.
In the field of mathematics he worked on probability, recurring decimals and the theory of equations. As in his astronomical work there was little of lasting importance. He did, however, publish the Leipzig Journal for Pure and Applied Mathematics between 1776 and 1789.
He was well aware of the famous mathematical line from which he was descended and he looked after the wealth of mathematical writings that had passed between members of the family. He sold the letters to the Stockholm Academy where they remained forgotten about until 1877. At that time when these treasures were examined, 2800 letters written by Johann(III) Bernoulli himself were found in the collection. *SAU (See "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1896 Friedrich August Kekulé von Stradonitz (7 September 1829–13 July 1896) Kekulé was a German theoretical chemist who figured out how carbon atoms could have a valence of four and join together to make long isomers or even rings. He was the first to discover the ring structure of benzene and greatly advanced the understanding of organic chemistry and aromatic compounds of the time.
Kekulé wrote about the method of his discovery where he was sitting by the fireplace and started to nod off. He dreamed of atoms arranging themselves in groups of ever increasing size until they became long chains. The chains started to wind and turn like snakes until one snake grabbed its own tail. He woke up suddenly and spent the rest of the nightworking out the structure.*This Day in Science History

1921 Gabriel Lippmann (16 August 1845 – 13 July 1921) French physicist, born Hollerich, Luxembourg, who received the Nobel Prize for Physics in 1908 for producing the first colour photographic plate. Lippmann was a giant of his day in classical physics research, especially in optics and electricity. He worked in Berlin with the famed Hermann von Helmholtz before settling in Paris to head (in 1886) the Sorbonne's Laboratories of Physical Research until his death. His inventions include an instrument for precisely measuring minute differences in electrical power and the "coleostat" for steady, long-exposure sky photography.*TIS

1941 Ivan Ivanovich Privalov (13 Feb 1891 in Nizhny Lomov, Penza guberniya (now oblast), Russia - 13 July 1941 in Moscow, USSR) Privalov, often in collaboration with Luzin, studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals. He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere. In 1934 he studied subharmonic functions, building on the work of Riesz. He published the monograph Subharmonic Functions in 1937 which gave the general theory of these functions and contained many results from his papers published between 1934 and 1937. *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-6719572625649399352020-07-12T00:00:00.000+01:002020-07-12T00:00:05.676+01:00On This Day In Math - July 12

Technical skill is mastery of complexity while creativity is mastery of simplicity.
Sir Christopher Zeeman

This is the 194th day of the year, 1944+1 = 1,416,468,497 is prime *Prime Curios

194 is also the smallest number that can be written as the sum of 3 squares (not all unique) in five ways. (There is a slightly larger number that is expressible as the sum of 3 unique squares in five ways. )

194 is the product of the largest and smallest prime less than 100.

194 is the sum of three consecutive squares, \( 194 = 7^2 + 8^2 + 9^2 \)

194 is the even base of the Largest Heronian triangle with consecutive integer sides that can be year dates. Heronian triangles are triangles that have all three sides and the area as integers. The three sides are 193, 194, 195, and the Area is 16,296 sq units. I have seen these called Super Heronian triangles, but I call them Sang-Heronian triangles after the earliest study I know about them by Edward Sang of Edinburgh, Scotland in1864 Because these bases are always equal, the altitude from that base must also be an integer. And one more biggie... If you construct the altitude to the even base, one side or the other of it will always form a primitive Pythagorean triangle. For each new bigger triangle, it switches sides. In the triangle for this date, the PPT is 95, 193, 195. I won't to write a little more about this than space here allows, so I will link it here then.

EVENTS
1389 King Richard II appoints Geoffrey Chaucer to the position of chief clerk of the king's works in Westminster. Although remembered today for his unfinished "Canterbury Tales" (he had intended 200 stories but only finished 22), he achieved fame during his lifetime as a philosopher, alchemist and astronomer, composing a scientific treatise on the astrolabe for his ten year-old son Lewis.

1831 Gauss to Schumacher: "I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound." *VFR

1844  Captain J.N. Taylor of the Royal Navy first demonstrated the fog horn. At the time, it was called a telephone - to mean far-signalling, thus an instrument like a fog-horn, used on ships, railway trains, etc., for signalling by loud sounds or notes. The 19 July 1844 Times (London) reported, "Yesterday week was a levee day at the Admiralty, and amongst the numerous models..was Captain J. N. Tayler's telephone instrument... The chief object of this powerful wind instrument is to convey signals during foggy weather. Also the Illustrated London News on 24 Aug. 1844 referred to "The Telephone; a Telegraphic Alarum. Amongst the many valuable inventions..that of the 'Telephone, or Marine Alarum and Signal Trumpet', by Captain J. N. Taylor."*TIS

1925 Heisenberg announced the basic principles of quantum mechanics. *VFR

1969 What is believed to be the first photo of a laser appeared on the cover of Electronics,on this date .

1979 The Gossamer Albatross completed the first wholly man-powered flight across the English Channel. See August 23, 1971. *VFR

2011 Google announces winners of Google Science Fair . The top three winners by age category are:

Lauren Hodge in the 13-14 age group. Lauren studied the effect of different marinades on the level of potentially harmful carcinogens in grilled chicken.

Naomi Shah in the 15-16 age group. Naomi endeavored to prove that making changes to indoor environments that improve indoor air quality can reduce people's reliance on asthma medications.

Shree Bose in the 17-18 age group. Shree discovered a way to improve ovarian cancer treatment for patients when they have built up a resistance to certain chemotherapy drugs.

BIRTHS
 1808 Reverend Robert Main (July 12, 1808 – May 9, 1878) English astronomer.
Born in Kent, the eldest son of Thomas Main, Robert Main attended school in Portsea before studying mathematics at Queens' College, Cambridge, where he graduated in 1834. He served for twenty-five years (1835-60) as First Assistant at the Royal Greenwich Observatory, and published numerous articles, particularly on stellar and planetary motion, stellar parallax, and the dimensions and shapes of the planets. From 1841 to 1861 he was successively an honorary secretary, a vice-president, and President of the Royal Astronomical Society, and in 1858 was awarded the Society's Gold Medal. In 1860 he became director of Radcliffe Observatory at Oxford University after the death of Manuel Johnson, and was elected as a Fellow of the Royal Society. *Today in Astronomy

1854 George Eastman's birthday (July 12, 1854 – March 14, 1932). Eastman was the American inventor of rolled photographic film. He formed the Eastman Kodak Company to bring photography to the average person. For \($25\), a person could buy a camera with 100 exposures. Eastman promised, "You push the button, we do the rest." Once all 100 pictures were taken, the camera and a \($10\) processing fee was returned to Kodak where they reloaded the camera with film and developed and printed the pictures. *This Day in Science History

1861 George Washington Carver African-American educator, scientist, chemist, inventor, botanist. After the Civil War, Southern farmers planted cotton year after year, and the soil lost its fertility. Yields dropped. Between 1890 and 1910, the cotton crop was devastated by the bolweevil. George Washington Carver was appointed head of the agriculture department at The Tuskegee Institute in Alabama by Booker T. Washington (1896). Carver discovered and taught how to maintain the fertility of the soil. Further, his discovered two new crops that would grow well there: peanuts and sweet potatoes. Further, Carver created a market by inventing hundreds of new uses for for these crops, from milk to printer's ink .*TIS

1875 Ernst Fischer (12 July 1875 – 14 November 1954) is best known for the Riesz-Fischer theorem in the theory of Lebesgue integration.*SAU His main area of research was mathematical analysis, specifically orthonormal sequences of functions which laid groundwork for the emergence of the concept of a Hilbert space. *Wik

1895 R(ichard) Buckminster Fuller (July 12, 1895 – July 1, 1983) was an American inventor, educator, author, philosopher, engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). He held over 2000 patents.*TIS

1913 Willis Eugene Lamb, Jr (July 12, 1913 – May 15, 2008) was an American physicist and joint winner, with Polykarp Kusch, of the Nobel Prize for Physics in 1955 "for his discoveries concerning the fine structure of the hydrogen spectrum." His experimental work spurred refinements in the quantum theories of electromagnetic phenomena.*TIS The Lamb shift was an energy difference between the 2S½ and 2P½ energy levels of the hydrogen atom. According to the current theory, these two levels should have the same amount of energy, but when the electrons were exposed to a magnetic field, the energy level of 2S½ was slightly different. This discovery led to the renormalization theory of quantum electrodynamics. *This Day in Science History

1922 Michael Ventris (12 July 1922 – 6 September 1956) English architect and cryptographer who in 1952 deciphered the Minoan Linear B script. These were the inscriptions on ancient clay tablets found in Crete and a few other locations; writings which had baffled archaeologists since their discovery in 1900. He showed the script to be Greek in its oldest known form, dating from about 1400 to 1200 BC, roughly the period of the events narrated in the Homeric epics. One of the most tantalizing riddles of classical archaeology was solved, but not without creating some puzzling situations. The reading of these tablets in the Greek language raised the question: How could a literate people in the fourteenth century BC become illiterate for almost five centuries, to regain literacy in the eighth century? Ventris died young, in an auto accident, soon after his triumph.*TIS

DEATHS
1682 Jean Picard (July 21, 1620 – July 12, 1682) French Jesuit, active astronomer, cartographer, hydraulics engineer, Jean Picard devised a movable-wire micrometer to measure the diameters of celestial objects such as the Sun, Moon and planets. For land surveying and leveling, he designed instruments that incorporated the astronomical telescope. He greatly increased the accuracy of measurements of the Earth, using Snell's method of triangulation (Mesure de la Terre, 1671). This data was used by Newton in his gravitational theory. Picard was one of the first to apply scientific methods to the making of maps. Among his other skills were hydraulics; he solved the problem of supplying the fountains at Versailles with water.*TIS

1834 David Douglas (25 June 1799 – 12 July 1834) Scottish botanist who was one of the most successful of the great 19th century plant collectors. He established about 240 species of plants in Britain. His first foreign plant-hunting expedition (1824) was made throughout the Pacific Northwest of the U.S. The Douglas fir, which he cultivated from 1827, is named after him. He introduced other conifers including the Sitka spruce, now commercially important to the timber industry, and numerous garden plants and shrubs, including the lupin, California poppy and the flowering currant. At age 35, he died in by accident in Hawaii, when he fell into a pit dug by the islanders to trap wild cattle where he was trapped with a bull that also fell into the pit. He was gored to death by the bull.*TIS (add to candidate for most unusual death. see also Eduord Lucas, and Francis Bacon, send your nominees)

1983 Ernst Gabor Straus (February 25, 1922 – July 12, 1983) was a German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions. His extensive list of co-authors includes Albert Einstein and Paul Erdős as well as other notable researchers including Richard Bellman, Béla Bollobás, Sarvadaman Chowla, Ronald Graham, László Lovász, Carl Pomerance, and George Szekeres. It is due to his collaboration with Straus that Einstein has Erdős number 2. *Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
Posted by Pat Ballew at 00:30 email@example.com:blogger.com,1999:blog-2433841880619171855.post-81014330937134986532020-07-11T00:00:00.000+01:002020-07-11T00:00:07.463+01:00On This Day in Math - July 11

 Ten decimal places of π are sufficient to give the circumference

 of the earth to a fraction of an inch,

and thirty decimal places would give the circumference of the visible universe

 to a quantity imperceptible to the most powerful microscope.
~Simon Newcomb

Today is the 193rd day of the year; 193 is one of a twin prime pair and is the sum of products of the first three twin primes pairs: 3*5 + 5*7 + 11*13 = 193. *Prime Curios

The square of 193 (37249) concatenated with its reverse (which is a prime) results in a palindrome that is the product of 2 palindromes, one non-prime (1001) and one prime (3721273).

193 is the smallest prime whose fifth power contains all digits from 1 to 9.

(I also like 193/71 is the closest ratio of two primes less than 2000 to the number e.)

EVENTS

1663 John Wallis, Savilian Professor of Geometry at Oxford, gave a specious proof of Euclid's parallel postulate. See W. W. Rouse Ball, Mathematical Recreations and Essays, 6th edition, pp. 314– 315.*VFR

1686 Leibniz published his first paper on the integral calculus in Acta eruditorum.*VFR This paper contains the first appearance in print of the elongated s integral notation used today. He had used the symbol earlier in a manuscript on Oct 29, 1675.

1699 Halley's final log entry for his first voyage of discovery commanding the Paramore, "The Gunns and Gunners Stores were delivered to the Tower Officers and that Same Evening we moord our Shipp at Deptford" *halleyslog.wordpress.com

1700 Royal Prussian Academy of Sciences at Berlin founded. Leibniz was primarily responsible for the founding and directed it for sixteen years. [HM 2, p. 310; American Journal of Physics, 34(1966), p. 22]*VFR

1731 Alexis-Claude Clairaut elected to the French academy. He was only eighteen. *VFR

1738 Isaac Greenwood, the first Hollis Professor at Harvard, was "ejected" from his chair for drunkenness. [I. B. Cohen, Some Early Tools of American Science, p. 36.] *VFR

1747 Benjamin Franklin writes to Peter Collinson, London Businessman and member of the Royal Society, to describe the, "wonderful effects of pointed bodies, both in drawing off and throwing off the electrical fire."* A history of physics in its elementary branches By Florian Cajori

1811 Italian scientist Amedeo Avogadro published his memoire about the molecular content of gases. *TIS

1814 Amp`ere submitted a paper on general solutions of differential equations. It contains thought-provoking remarks and interesting examples which had to wait several decades for proper understanding and recognition. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800– 1840, pp. 700ff, 1389]*VFR

1859 The Current Big Ben (the bell) is first heard ringing in the Westminster clock tower. Why Big Ben? After Benjamin Hall (1802-67). In Aug 1856 the bell, with Hall's name inscribed on it, was cast, but cracked after tests in October 1857. The substitute was also defective but worked sufficiently well to be hung in Oct 1858. Named Big Ben, it was first heard on 11 July 1859. Two months later it too cracked & fell silent for 4 years; it was repaired with help of Sir George Airy, astronomer royal, & rings to this day. *Oxford DNB@ODNB

1976 K&E produced its last slide rule, which it presented to the Smithsonian Institution. A common method of performing mathematical calculations for many years, the slide rule became obsolete with the invention of the computer and its smaller, hand-held sibling, the calculator. (*This Day in History-Computer History Museum)

1979 U.S. space station, Skylab, re-entered the Earth's atmosphere. It disintegrated, spreading fragments across the southeastern Indian Ocean and over a sparsely populated section of western Australia, where a cow died after being struck by a piece of falling debris. *TIS (Proving the potential effectiveness of weapons in space?)

In 1991, a solar eclipse cast a blanket of darkness stretching 9,000 miles from Hawaii to South America, lasting nearly seven minutes in some places. It was the so-called eclipse of the century. A total solar eclipse - the moon passing between the sun and the earth - is the moon's shadow cast on the casting its shadow on the earth's surface. Total eclipses occur almost once per year, but are often over an ocean or remote countries. The solar eclipse on July 11, 1991, was a thrill for scientists. It traveled over the several astronomical observatories on the top of Mauna Kea. Their 14,000 feet elevation was actually above the cloud level, which obstructed the view for those below. *TIS

On this day about "one year" ago German astronomer Johanne Galle discovered Neptune ... One Neptunian year that is! *rmathematicus, Thony Christie;
On July 11, 2011, Neptune completed its first full barycentric orbit since its discovery on September 23, 1846, *Wik

BIRTHS
1732 Joseph Jérôme Le Français de Lalande, (11 July 1732 – 4 April 1807) was a an astronomer, born in Bourg-en-Bresse, France. He determined the Moon's parallax from Berlin for the French Academy (1751). He was appointed professor of Astronomy, Collège de France (1762), and subsequently, director of the Paris Observatory. He published his Traité d'astronomie in 1764 - tables of the planetary positions that were considered the best available for the rest of the century. In 1801 he also published a comprehensive star catalogue. He died in 1807, apparently of tuberculosis. *TIS

1811 Sir William Robert Grove, (11 July 1811 – 1 August 1896) British physicist and a justice of Britain's high court (from 1880), who first offered proof of the thermal dissociation of atoms within a molecule. He showed that steam in contact with a strongly heated platinum wire is decomposed into hydrogen and oxygen in a reversible reaction. In 1839, Grove mixed hydrogen and oxygen in the presence of an electrolyte, and produced electricity and water. This Grove Cell was the invention of the fuel cell. The technology was not seriously revisited until the1960s. Through the electrochemical process, the energy stored in a fuel is converted - without combusting fuel - directly into DC electricity.*TIS

1857 Sir Joseph Larmor (11 July 1857 Magheragall, County Antrim, Ireland – 19 May 1942 Holywood, County Down, Northern Ireland), Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field. His theories were based on the belief that matter consists entirely of electric particles moving in the ether. His elaborate mathematical electrical theory of the late 1890s included the "electron" as a rotational strain (a sort of twist) in the ether. But Larmor's theory did not describe the electron as a part of the atom. Many physicists envisioned both material particles and electromagnetic forces as structures and strains in that hypothetical fluid. *TIS

1857 Alfred Binet (July 11, 1857 – October 18, 1911) who introduced his famous IQ test in 1905. *VFR French experimental psychologist, the director of the psychological laboratory of the Sorbonne, Paris (1894). He made fundamental contributions to the measurement of intelligence.With Theodore Simon, Binet produced a series of graded tasks typical of the intellectual development of children of different ages (1905). This scale was extended (1908-11), and the tasks were assigned to the age level at which average children could manage them. Thus children could be scored for the level, or mental age, they reached. This test formed the basis for the Stanford-Binet Tests.*TIS (today in Science also gives Binet's birthdate on July 11th, with a different description: French psychologist who was a pioneer in the field of intelligence testing of the normal mind. He took a different approach than most psychologists of his day: he was interested in the workings of the normal mind rather than the pathology of mental illness. He wanted to find a way to measure the ability to think and reason, apart from education in any particular field. In 1905 he developed a test in which he had children do tasks such as follow commands, copy patterns, name objects, and put things in order or arrange them properly. He gave the test to Paris schoolchildren and created a standard based on his data. From Binet's work, "IQ" (intelligence quotient), entered the vocabulary. The IQ is the ratio of "mental age" to chronological age, with 100 being average.)

1890 Giacomo Albanese (11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in São Paulo, Brazil, in 1936. *Wik

1902 Samuel Abraham Goudsmit (The Hague, July 11, 1902 — Reno, December 4, 1978) Dutch-born U.S. physicist who, with George E. Uhlenbeck, a fellow graduate student at the University of Leiden, Neth., formulated (1925) the concept of electron spin. It led to recognition that spin was a property of protons, neutrons, and most elementary particles and to a fundamental change in the mathematical structure of quantum mechanics. Goudsmit also made the first measurement of nuclear spin and its Zeeman effect with Ernst Back (1926-27), developed a theory of hyperfine structure of spectral lines, made the first spectroscopic determination of nuclear magnetic moments (1931-33), contributed to the theory of complex atoms and the theory of multiple scattering of electrons, and invented the magnetic time-of-flight mass spectrometer (1948).*TIS

1922 John William Scott Cassels (11 July 1922 in Durham - ) initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group, if it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods.
His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades. *Wik

DEATHS1382 Nicole Oresme (c. 1320–5 – July 11, 1382), was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series. *SAU
Oresme was Bishop of Liseux and died there, but I was recently (2011) at the Cathedral and cold find no mark of his life there.

"His most important contributions to mathematics are contained in "Tractatus de figuratione potentiarum et mensurarum difformitatum", still in manuscript. An abridgment of this work printed as "Tractatus de latitudinibus formarum" (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the intensio (the degree of heat at each point) and the extensio (e.g., the length of the heated rod): these two terms were often replaced by latitudo and longitudo, and from the time of St. Thomas until far on in the fourteenth century, there was lively debate on the latitudo formæ. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to the longitudo was the abscissa at a given point, and a perpendicular at that point, proportional to the latitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring the longitudo and latitudo vary. Hence he defines latitudo uniformis as that which is represented by a line parallel to the longitude, and any other latitudo is difformis; the latitudo uniformiter difformis is represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i.e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions.
Besides the longitude and latitude of a form, he considers the mensura, or quantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A form uniformiter difformis has the same quantity as a form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitude uniformiter difformis became the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles."
*Catholic Encyclopedia online

1733 Jakob Hermann (16 July 1678, Basel – 11 July 1733, Basel) was a Swiss mathematician who made contributions to dynamics. *SAU

1807 George Atwood was an English mathematician best known for his invention of a low-friction pulley system.*SAU He is the author of Phoronomia, an early treatise on Mechanics. In 1729, he proclaimed that it was as easy to graph a locus on the polar coordinate system as it was to graph it on the Cartesian coordinate system. However, no one listened. He was a distant relative of Euler. *Wik

1778 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
v Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page

1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.

He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.

In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.

He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik

1871 Germain Sommeiller (February 15, 1815 - July 11, 1871) French-Italian engineer who built the Mount Cenis (Fréjus) Tunnel (1857-70) through the Alps, the world's first important mountain tunnel. The two track railway tunnel unites Italian Savoy (north of the mountains) through Switzerland with the rest of Italy to the south. At 8 miles long and it was more than double the length of any previous tunnel. In 1861, after three years of tedious hand-boring a mere eight inches a day into the rock face, Sommeiller introduced the first industrial-scale pneumatics for tunnel digging. He built a special reservoir, high above the tunnel entrance, to produce a head of water that compressed air (to 6 atm.) for pneumatic drills, able to dig up to 20 times faster. Authorised on 15 Aug 1857, the tunnel opened on 17 Sep 1871, as a major triumph of engineering.*TIS Note his death was only a few months before the opening of his great project.

1909 Astronomer and mathematician Simon Newcomb  (March 12, 1835 – July 11, 1909) died in Washington D.C. He was such a revered scientist that President Taft attended his funeral.*VFR Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS

Newcomb is buried in Arlington National Cemetery
Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.

"The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention." He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy."

1995 Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach. *Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia email@example.com:blogger.com,1999:blog-2433841880619171855.post-79242360178653158052020-07-10T02:00:00.000+01:002020-07-10T02:00:14.942+01:00Memories of the UK, Signs of the Times (or of the Thames)

Repost of an old blog about British vernacular"

 In 1887 Oscar Wilde wrote: `We have really everything in common with America nowadays except, of course, language'. Some say he may have been paraphrasing something by George B. Shaw. Whichever said it first, they were wrong; the British are different. I've been over here for a while, and I don't giggle anymore when I hear a seven-year-old ask his mom to buy him some new rubbers (erasers). I even know I'm not looking for footweae when I go to a boot sale (flea-market). But sometimes the British road signs just take me back to square one.

The sign above is an example. It is located in Greenwich near the loaction where they are restoring the Cutty Sark. You have to figure out what it means. It is not just that they use the same words to mean different stuff. They just have a different mind set. North of my home here in Stoke Ferry as I drove towards Kings Lynn there was a sign that read, "Cats Eyes removed ahead" Yikes!!!

A common road sign that I have yet to figure out has the warning, "Beware of oncoming traffic in center of road"???? If there is a problem with oncoming traffic in the center of the road, shouldn't this sign be turned the other way and say something like, "Get your Butt back in your own lane!" You see? The British just think differently.

Ok, one more example. I was in London to see the "Tut" exhibit last weekend (a bit disappointing, actually) and in King's Cross station I noticed this sign.

The sign is located on an electronic schedule that tells you the track on which trains depart. When the station is busiest, they apparently turn them off so people won't crowd around them.... YES, READ IT AGAIN... In the peak periods they remove information. People blindly wandering from track to track apparently are less likely to congregate in one place and create congestion... Ok, I don't really know why they have such a sign, or why they would do it.... My only explanation... The British ARE firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-68838249010743438062020-07-10T00:00:00.000+01:002020-07-10T00:00:03.170+01:00On This Day in Math - July 10

That which is not good for the bee-hive cannot be good for the bees.

~ Marcus Aurelius

The 192nd day of the year; 192 is the smallest number that together with its double and triple contain every digit from 1-9 exactly once. There are three other values of n so that n, 2n, and 3n contain each non-zero digit exactly once. Can you find them?

192 is the sum of ten consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37)

192 is the number of edges on a 6th dimension hypercube, it is the last day of the year which is the number of edges of a hypercube.

Diophantus probably knew, and Lagrange proved, that every positive integer can be written as a sum of four perfect squares. Jacobi] proved the stronger result that the number of ways in which a positive integer can be so written equals 8 times the sum of its divisors that are not multiples of 4. Use this theorem to prove that there are 192 ways to express 14 as a sum of four squares.

See More Math Facts for every year date here

EVENTS

1600 Kepler's interest in optics arose as a direct result of his observations of the partial solar eclipse of 10 July 1600. Following instructions from Tycho Brahe, he constructed a pinhole camera; his measurements, made in the Graz marketplace, closely duplicated Brahe' and seemed to show that the moon's apparent diameter was considerably less than the sun's. Kepler soon realized that the phenomenon resulted from the finite aperture of the instrument (see Fig. 5); his analysis, assisted by actual threads, led to a clearly defined concept of the light ray, the foundation of modern geometrical optics.
Kepler's subsequent work applied the idea of the light ray to the optics of the eye, showing for the first time that the image is formed on the retina. He introduced the expression "pencil of light," with the connotation that the light rays draw the image upon the retina; he was unperturbed by the fact that the image is upside down. *Encyclopedia.com

1610 Galileo receives a letter from Cosimo II agreeing to his salary requests, and confirming him as "First Mathematician of our Stadium in Pisa" but with no requirements that he live or lecture in Pisa, "except when it may please you as an honor." *The Copernican Question: Prognostication, Skepticism, and Celestial Order By Robert S. Westman

1637 First meeting of the Acad´emie Fran¸caise. *VFR

1676 Flamsteed began living at the Observatory with his two servants. On 19 July, his long series of Greenwich observations began? *Rebekah Higgitt, Teleskopos

1794 Star in a crescent moon? Astronomer Royal Investigates. The results are read to the Royal Society..."An Account of an Appearance of Light, like a Star, Seen Lately in the Dark Part of the Moon, by Thomas Stretton, in St. John's Square, Clerkenwell, London; with Remarks upon This Observation, and Mr. Wilkins's. Drawn up, and Communicated by the Rev. Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal" *Phil. Trans. R. Soc. Lond. January 1, 1794 84:435-440;

1796 Date of the entry EγPHKA! num=Δ+Δ+Δ in Gauss's scientific diary, recording his discovery that every positive integer is the sum of three triangular numbers. [Thanks to Howard Eves] *VFR

1826 Cauchy presented a proof to the Acad´emie dealing with existence theorems for first-order dif-ferential equations. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, pp. 758 and 1401] *VFR

1843 Jacques Philippe Marie Binet, age 57, elected to the Acad´emie des Sciences to succeed Lacroix. He is an example of a mathematician who published much late in life. He worked in mechanics, elasticity, perturbation theory, determinants, and the calculus. [Ivor Grattan-Guiness, Convo¬lutions in French Mathematics, 1800–1840, pp. 191 and 1410] *VFR

1908 at 5:45 in the morning, Kammerlingh Onnes, of Leiden, wins the race to produce liquified helium. 75 liters of liquid air is used to condense 20 liters of liquid oxygen, from which 20 milli-liters of liquid helium under reduced pressure. *Quantum Generations: A History of Physics in the Twentieth Century By Helge Kragh

1925 The "Monkey Trial" of John T. Scopes began in Dayton, Tennessee. Clarence Darrow defended him. The prosecution, conducted by William Jennings Bryan, presented a strong case, and he was convicted of violating a state law prohibiting the teaching of evolution. Although the law was later overturned, this case provided a strong blow to science education. Scopes was not a biologist and never taught evolution. Rather he was a mathematics and physics teacher who volunteered to stand trial to furnish a test case. *VFR
The trial ran for 12 days. A local school teacher, John Scopes, was prosecuted under the state's Butler Act, but was supported by the American Civil Liberties Union. This law, passed a few months earlier (21 Mar 1925) prohibited the teaching of evolution in public schools. The trial was a platform to challenge the legality of the statute. Local town leaders,(wishing for the town to benefit from the publicity of the trial) had recruited Scope to stand trial. He was convicted (25 Jul) and fined $100. On appeal, the state supreme court upheld the constitutionality of the law but acquitted Scopes on the technicality that he had been fined excessively. The law was repealed on 17 May 1967. *TIS

1950 France honors Lazar Carnot (1753–1823) with a postage stamp. [Scott #B251]. *VFR

1950 The German Democratic Republic, to celebrate the 250th anniversary of the founding of the Academy of Sciences, Berlin, issued postage stamps picturing Leonhard Euler and Gottfried von Leibniz. [Scott #58, 66]. *VFR

Leibniz was also honored with stamp issues in 1980 and 1996 it seems.

1993 MASH fans will remember that there was always a sign telling how many miles to Toledo and frequently they talked of the hotdogs at Tony Pacos (they are good). On this date the Cake Walk and Jazz Band (I believe the band is called "The Cakewalken Jass Band") celebrated their twenty-fifth anniversary with a live broadcast at Tony Pacos that was broadcast on public radio in Toledo. So what does this have to do with mathematics? Well, Ray Heitger, their clarinetist, leader, and one of the founding members happens to be a math teacher. If you can't get to Toledo to hear them play, perhaps you can find one of their six LPs.*VFR
Tony Packo's Cafe is restaurant that started in the Hungarian neighborhood of Birmingham, on the east side of Toledo, Ohio at 1902 Front Street. The restaurant gained notoriety by its mention in several M*A*S*H episodes and is famous for its signature sandwich and large collection of hot dog buns signed by celebrities. In 2011 it listed five restaurants in the Toledo area. *Wik

BIRTHS

1682 Roger Cotes born (10 July 1682 — 5 June 1716). In January 1706 he was named the first Plumian professor of astronomy and natural philosophy at Cambridge. It was Cotes who first showed that e was the natural base to choose for the logarithm. *VFR He did not realize his full potential because he died at age 33, leaving anunfinished series of imposing researches on optics and a large number of other unpublished manuscripts. Newton, who seldom spoke well of anyone else, said of Cotes, "If Cotes had lived, we might have known something."
Thony Christie at the Renaissance Mathematicus has a nice post about Cotes.

1832 Alvan Graham Clark  (July 10, 1832 – June 9, 1897)  U.S. astronomer, one of an American family of telescope makers and astronomers who supplied unexcelled lenses to many observatories in the U.S. and Europe during the heyday of the refracting telescope. He began a deep interest in astronomy while still at school, then joined the family firm of Alvan Clark & Sons, makers of astronomical lenses. In 1861, testing a new lens, he looked through it at Sirius and observed faintly beside it, Sirius B, the twin star predicted by Friedrich Bessel in 1844. Carrying on the family business, after the deaths of his father and brother, Clark made the 40" lenses of the Yerkes telescope (still the largest refractor in the world). Their safe delivery was a source of anxiety. He died shortly after their first use. *TIS

1856 Nikola Tesla (10 July 1856 – 7 January 1943)Serbian-American inventor and researcher who designed and built the first alternating current induction motor in 1883. [This statement seems to be in error,according to Wikipedia which states," In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations, which, by manually turning switches on and off, Walter Baily demonstrated in 1879 as in effect the first primitive induction motor. Practical alternating current induction motors seem to have been independently invented by Galileo Ferraris(1885) and then Tesla (1887).]He emigrated to the United States in 1884. Having discovered the benefits of a rotating magnetic field, the basis of most alternating-current machinery, he expanded its use in dynamos, transformers, and motors. Because alternating current could be transmitted over much greater distances than direct current, George Westinghouse bought patents from Tesla the system when he built the power station at Niagara Falls to provide electricity power the city of Buffalo, NY. [Born in Croatia of Serbian parents. Some sources give birthdate as 9 Jul; he is said to have been born on the stroke of midnight.]

1878 Oliver Dimon Kellogg (10 July 1878 in Linwood, Pennsylvania, USA - 26 July 1932 in Greenville, Maine, USA) was appointed to the University of Missouri in 1905 where, despite a heavy teaching and administrative load he was able to publish impressive papers on potential theory. In 1908 he published three papers, namely Potential functions on the boundary of their regions of definition and Double distributions and the Dirichlet problem, both in the Transactions of the American Mathematical Society, and A necessary condition that all the roots of an algebraic equation be real in the Annals of Mathematics. In 1912 he published the important work Harmonic functions and Green's integral in the Transactions of the American Mathematical Society. This paper includes what today is called 'Kellogg's theorem' on harmonic and Green's functions. *SAU

1883 Frank Albert Benford, Jr., ((see note below about date of birth)1883 Johnstown, Pennsylvania – December 4, 1948) was an American electrical engineer and physicist best known for rediscovering and generalizing Benford's Law, a statistical statement about the occurrence of digits in lists of data.
Benford is also known for having devised, in 1937, an instrument for measuring the refractive index of glass. An expert in optical measurements, he published 109 papers in the fields of optics and mathematics and was granted 20 patents on optical devices.
His date of birth is given variously as May 29 or July 10, 1883. After graduating from the University of Michigan in 1910, Benford worked for General Electric, first in the Illuminating Engineering Laboratory for 18 years, then the Research Laboratory for 20 years until retiring in July 1948. He died suddenly at his home on December 4, 1948. *Wik

1928 Errett Albert Bishop (July 10, 1928 – April 14, 1983) (His) work is so wide ranging that it is difficult to give an overview in a biography such as this. Let us look at the book Selected papers which was published in 1986 and reprints some of Bishop's most significant contributions. The book divided Bishop's papers into five categories:
(1) Polynomial and rational approximation. Examples are extensions of Mergelyan's approximation theorem and the theorem of Frigyes Riesz and Marcel Riesz concerning measures on the unit circle orthogonal to polynomials. Bishop found new methods in dealing with these problems;
(2) The general theory of function algebras. Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures. In 1965 Bishop wrote an excellent survey Uniform algebras examining the interaction between the theory of uniform algebras and that of several complex variables.
(3) Banach spaces and operator theory. An examples of a paper by Bishop on this topic is Spectral theory for operators on a Banach space (1957). He introduced the condition now called the Bishop condition which turned out to be very useful in the theory of decomposable operators.
(4) Several complex variables. Examples of Bishop's papers in this area are Analyticity in certain Banach spaces (1962). He proved important results in this area such as the biholomorphic embedding theorem for a Stein manifold as a closed submanifold in Cn, and a new proof of Remmert's proper mapping theorem.
(5) Constructive mathematics. Bishop become interested in foundational issues around 1964, about the time he was at the Miller Institute. He wrote a famous text Foundations of constructive analysis (1967) which aimed to show that a constructive treatment of analysis is feasible.*SAU

DEATHS

1851 Louis-Jacques-Mandé Daguerre  (18 November 1787 – 10 July 1851) French painter and physicist who invented the daguerreotype, the first practical process of photography. Though the first permanent photograph from nature was made in 1826/27 by Joseph-Nicéphore Niepce of France, it was of poor quality and required about eight hours' exposure time. The process that Daguerre developed required only 20 to 30 minutes. The two became partners in the development of Niepce's heliographic process from 1829 until the death of Niepce in 1833. Daguerre continued his experiments, and he discovered that exposing an iodized silver plate in a camera would result in a lasting image after a chemical fixing process.*TIS

1910 Johann Gottfried Galle  (9 June 1812 – 10 July 1910) German astronomer who on 23 Sep 1846, was the first to observe the planet Neptune, whose existence had been predicted in the calculations of Leverrier. Leverrier had written to Galle asking him to search for the new planet at a predicted location. Galle was then a member of the staff of the Berlin Observatory and had discovered three comets. In 1838, while assistant to Johann Franz Encke, Galle discovered the dark, inner C ring of Saturn at the time of the maxium ring opening. In 1851, he became professor of astronomy at Breslau and director of the observatory there. In 1872, he proposed the use of asteroids rather than regular planets for determinations of the solar parallax, a suggestion which was successful in an international campaign (1888-89). *TIS

1916 John Emory McClintock (19 Sept 1840 in Carlisle, Pennsylvania , USA - 10 July 1916 in Bay Head, New Jersey, USA) was for many years the leading actuary in America. He published 30 papers between 1868 and 1877 on actuarial questions. His publications were not confined to questions relating to<nobr>life insurance policies</nobr> however. He published about 22 papers on mathematical topics. One paper treats difference equations as differential equations of infinite order and others look at quintic equations which are soluble algebraically. He published A simplified solution of the cubic in 1900 in the Annals of Mathematics. Another work, On the nature and use of the functions employed in the recognition of quadratic residues (1902), published in the Transactions of the American Mathematical Society, is on quadratic residues.*SAU

1936 Salvatore Pincherle (March 11, 1853 — July 10, 1936) worked on functional equations and functional analysis. Together with Volterra, he can claim to be one of the founders of functional analysis.*SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-31096253943258827702020-07-09T00:00:00.000+01:002020-07-09T00:00:01.647+01:00On This Day in Math - July 9

Epitaph (by Kepler, for himself)
Mensus eram coelos, nunc Terrae metior umbras.
Mens coelestis erat, corporis umbra jacet.
I used to measure the Heavens, now I measure the shadows of Earth.

The mind belonged to Heaven, the body's shadow lies here.

The 191st day of the year; 191 is a palindromic prime and when it is doubled and one is added to this result, the resulting number is yet another palindromic prime. (Students might consider why 11 is the only palindromic prime with an even number of digits.)

Derek Orr noticed that 199*n+(n-1) is a palindrome (not prime) for several other values of n, collect the whole set.

By adding up the values of the common US coins, one obtains 191 ¢ (silver dollar + half dollar + quarter + dime + nickel + penny) *From Number Gossip (This ignores the once minted 5 mil, or half-cent coin and the briefly lived 2 cent coins) Canadians would have a larger sum of coins since Canada has had a $1 coin (The Loonie) since 1987 and a $2 coin (The Toonie) for about 10 years. I think the Canadian total would be 341 (no half dollar) so maybe we can squeeze them in by the end of the year.

191 is the smallest palindromic prime p such that neither 6p - 1 nor 6p + 1 is prime. Also, The smallest multidigit palindromic prime that yields a palindrome when multiplied by the next prime: 191 * 193 = 36863. *Prime Curios
Find More Math Facts for every year date here

EVENTS

1595 Kepler gets the inspiration for his first model of the universe.. when the 23 year old Kepler, while teaching, made the first of a profound series of discoveries. Kepler fully elaborates this discovery in his Mysterium Cosmographicum, published less than a year later. It appeared to him that the respective radii of the orbits of the planets corresponded to the lengths determined by a specific sequence in which the five regular solids were placed within one another, with a sphere separating each solid from the other. The sphere (orbit) of Saturn enveloped a cube which in turn enveloped another sphere, the orbit of Jupiter. This circumscribed a tetrahedron, a sphere (the orbit of Mars), a dodecahedron, a sphere (the orbit of earth), an icosahedron, a sphere (the orbit of Venus), an octahedron, and the smallest sphere (the orbit of Mercury). The idea was the main theme of his Mysterium cosmographicum (1596). *Dave Richeson, Euler's Gem
On that day, while standing at the blackboard drawing a geometrical figure for his class, Kepler had an epiphany. He believed it was a divine inspiration. Kepler had drawn a triangle with a circle circumscribed around it, which meant that each of the triangle's corners touched the rim of the circle. Then he inscribed another circle inside the triangle, which meant that the center of each side of the triangle touched the inner circle.
When Kepler stepped back and looked at what he had drawn, he realized with a shock that the ratios of the two circles were the same as the ratios of the orbits of Saturn and Jupiter. And with that realization, inspiration struck. Jupiter and Saturn were the outermost planets of the solar system, and the triangle was the simplest polygon. Kepler wondered whether you could fit the orbits of the other planets around other geometric figures, and tried his best inscribing circles in squares and pentagons. But the planetary orbits refused to fit.
Then Kepler had a second epiphany. The solar system was three dimensional – so why would he think that its governing pattern would be found in two dimensional figures? Kepler turned to three dimensional objects, and found his answer in the five perfect solids. A perfect solid is a three dimensional figure, such as a cube, whose sides are all identical. Conveniently for Kepler, there are only five perfect solids: the tetrahedron (which has four triangular sides), cube (six square sides), octahedron (eight triangular sides), dodecahedron (twelve pentagonal sides), and icosahedron (twenty triangular sides). Each perfect solid can be inscribed in and circumscribed around a sphere. *Spark Notes

1714 Longitude Act receives royal assent. The Longitude Act offered rewards of up to £20,000 for a method of finding longitude at sea to within half a degree (equivalent to 2 minutes of time) after a six-week voyage to the West Indies. Smaller rewards were available for methods achieving lesser accuracy. The Act also nominated a number of Commissioners of Longitude, later known as the Board of Longitude, to assess submissions and decide on rewards. They included the Astronomer Royal at Greenwich and other scientific, maritime and political leaders. The Commissioners could also grant smaller sums of money to help bring promising ideas to sea-trial. *Richard Dunn @Lordoflongitude

 1743  Euler, in a letter to Goldbach, He had described to Goldbach a manor by which numbers of the form \(n^2 + 1\) might be divisible. On Oct 28, 1752 Euler Published a paper listing the 161 numbers less than 15,000 for which \( n^2+1 \) is a prime. He also listed eight numbers for which \( n^4 + 1 \) is a prime; {1, 2, 4, 6, 16, 20, 24, and 34}. *L. E. Dickson, History of the Theory of Numbers

1814 Gauss made the 146th and last entry in his scientific diary. He observed a connection between biquadradic residues and the lemniscate functions. This has become the most famous entry in the diary as it led to the Weil conjectures. See Gray, Expositions Mathematicae, 2(1984), 97–130. *VFR

1857 Weierstrass, in his inaugural speech at the Berlin Academy, stated that mathematics occupies an especially high place because only through its aid can a truly satisfying understanding of natural phenomena be obtained. *VFR

1912 A letter from U.S. Department of Agriculture, Central Office of the Weather Bureau, Washington, D.C. to Dr. Walker Abbe, in Cleveland, "Enclosing some papers which 'will seem childish' but 'present the one great need of our sciences -- a school & laboratory & class of enthusiastic physics-mathematics students specially devoted to the earth's atmosphere'. He adds 'May the time soon come when you may be called home to be the leader of such men'." *Imperial College & Science Museum Libraries

1917 This image of a solar flare taken from Mt Wilson observatory shows a solar flare 140,000 miles high. The white dot is image of the Earth drawn to scale. I came across this at a site called thegildedcentury .

1941 British cryptologists break the secret code used by the German army to direct ground-to-air operations on the Eastern front.
British experts had already broken many of the Enigma codes for the Western front. Enigma was the Germans' most sophisticated coding machine, necessary to secretly transmitting information. The Enigma machine, invented in 1919 by Hugo Koch, a Dutchman, looked like a typewriter and was originally employed for business purposes. The Germany army adapted the machine for wartime use and considered its encoding system unbreakable. They were wrong. The Brits had broken their first Enigma code as early as the German invasion of Poland and had intercepted virtually every message sent through the occupation of Holland and France. Britain nicknamed the intercepted messages Ultra.
Now, with the German invasion of Russia, the Allies needed to be able to intercept coded messages transmitted on this second, Eastern, front. The first breakthrough occurred on July 9, regarding German ground-air operations, but various keys would continue to be broken by the Brits over the next year, each conveying information of higher secrecy and priority than the next. (For example, a series of decoded messages nicknamed "Weasel" proved extremely important in anticipating German anti-aircraft and antitank strategies against the Allies.) These decoded messages were regularly passed to the Soviet High Command regarding German troop movements and planned offensives, and back to London regarding the mass murder of Russian prisoners and Jewish concentration camp victims. *History.com

1953 France issued a stamp picturing Gaspard Monge. [Scott #279].
(Does anyone else think he looks like Marlon Brando??)

1981 Nintendo releases the arcade game Donkey Kong featuring the debut of Mario. *Wik

1996 With the satellite SOHO, they discover that solar flares causes sun quakes. *NSEC Scientists have shown for the first time that solar flares produce seismic waves in the Sun's interior that closely resemble those created by earthquakes on our planet. Dr. Alexander G. Kosovichev, a senior research scientist from Stanford University, and Dr. Valentina V. Zharkova from Glasgow (United Kingdom) University found the tell-tale seismic signature in data on the Sun's surface collected by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO) spacecraft immediately following a moderate-sized flare on July 9, 1996. "Although the flare was a moderate one, it still released an immense amount of energy," said Dr. Craig Deforest, a researcher with the SOHO project. "The energy released is equal to completely covering the Earth's continents with a yard of dynamite and detonating it all at once."

2004 The day after a transit of Venus occurred as predicted by Horrocks using William Crabtree's measures of the size of Venus and the Earth-Sun distance, a commemorative street nameplate in memory of William Crabtree was unveiled at the junction of Lower Broughton Road and Priory Grove which marks the northern boundary of Crabtree Croft where he observed the transit. *Wik

2006 Tesla Memorial at Canadian side of Niagara Falls unveiled. The bronze statue by Les Drysdale depicts Tesla atop an AC motor, in commemoration of Tesla's engineering achievements at Niagara Falls. The marker at the site credits Tesla with the " "world's first hydroelectic power system". Since this power plant suppossedly "the first power reached Buffalo at midnight, November 16, 1896" this will surprise folks who are aware that Thomas Edison's electrical power plant in New York was in 1882. (What Tesla did was momentus, whether it was first or not).

BIRTHS

1845 Birthdate of George Howard Darwin (9 July 1845 – Cambridge, 7 December 1912), fifth child of the evolutionist Charles Darwin. After graduating second wrangler and Smith's prizeman at Cambridge in 1866 he studied law before settling down to his life work in mathematical astronomy. He addressed the Fifth International Congress of Mathematicians at Cambridge in 1912 on his work on the three body problem. *VFR He championed a theory (no longer accepted) that the Moon was once part of the Earth, in what is now the Pacific Ocean. His was the first mathematical analysis of the evolution of Earth's Moon. He suggested that since the effect of the tides has been to slow the Earth's rotation and to cause the Moon to recede from the Earth, then by extrapolating back 4.5 billion years ago the Moon and the Earth would have been very close, with a day being less than five hours. Before this time the two bodies would actually have been one, until the Moon was torn away from the Earth by powerful solar tides that would have deformed the Earth every 2.5 hours. *TIS

1855 Spiridon Gopcevic (July 9, 1855 – ? 1928) was a Serbian astronomer and historian. He is also known by his pen name of Leo Brenner. In 1893 he founded Manora Observatory on Mali Lošinj. This observatory was named for his wife, a wealthy Austrian noblewoman. At this observatory, Spiridon used the 17.5cm refractor telescope at the observatory to make observations of Mars, the rings of Saturn, and other planets. However he would eventually close the observatory in 1909 due to financial problems.
From 1899 until 1908 he was the founder and editor of the Astronomische Rundschau, a popular scientific journal. He spent several years in America before returning to Europe and editing an army journal in Berlin during the war. The circumstances of his death are somewhat uncertain, but he appears to have been impoverished.
The crater Brenner on the Moon was named after him (based on his nom de plume) by his friend Phillip Fauth. A new observatory was built on Mali Lošinj in 1993, and was named "Leo Brenner". *Today in Astronomy

1911 John Archibald Wheeler (July 9, 1911 – April 13, 2008) was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission. One of the later collaborators of Albert Einstein, he tried to achieve Einstein's vision of a unified field theory. He is also known for having coined the terms black hole, quantum foam and wormhole and the phrase "it from bit". For most of his career, Wheeler was a professor at Princeton University and was influential in mentoring a generation of physicists who made notable contributions to quantum mechanics and gravitation.*Wik I love this Wheeler quote, "In any field, find the strangest thing and then explore it." Thanks to Arjen Dijksman <s>@</s>materion

1931 Valentina Mikhailovna Borok (9 July 1931, Kharkiv, Ukraine, USSR–4 February 2004, Haifa, Israel) was a Soviet Ukrainian mathematician. She is mainly known for her work on partial differential equations.*Wik

DEATHS
1856 Count Amedeo Avogadro (9 August 1776, Turin, Piedmont – 9 July 1856) Italian chemist and physicist who found that at the same temperature and pressure equal volumes of all perfect gases contain the same number of particles, known as Avogadro's Law (1811) leading to the Avogadro's constant being 6.022 x 1023 units per mole of a substance. He realized the particules could be either atoms, or more often, combinations of atoms, for which he coined the word "molecule." This explained Gay-Lussac's law of combining volumes (1809). Further, Avogadro determined from the electrolysis of water that it contained molecules formed from two hydrogen atoms for each atom of oxygen, by which the individual oxygen atom was 16 times heavier than one hydrogen atom (not 8 times as suggested earlier by Dalton.) The Italian, Romano Amadeo Carlo Avogadro, had suggested [in 1811] that all gases have the same number of molecules in a given volume. Loschmidt figured out [in 1865] how many molecules that would be which is the number now known as Avogadro's constant. John D. Cook suggested that maybe it should be called Loschmidt's constant, and pointed out three interesting coincidences involving Avogadro's Constant:
NA is approximately 24! (i.e., 24 factorial.)
The mass of the earth is approximately 10 NA kilograms.
The number of stars in the observable universe is 0.5 NA.
*John D. Cook, The Endeavour Blog

1953 Henri Padé (December 17, 1863 – July 9, 1953) made important contributions to the theory of continued fractions *SAU A Padé approximant is the "best" approximation of a function by a rational function of given order – under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed by Henri Padé, but goes back to Georg Frobenius who introduced the idea and investigated the features of rational approximations of power series.
The Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. For these reasons Padé approximants are used extensively in computer calculations. *Wik

1980 Arend Heyting (May 9, 1898 – July 9, 1980) is important in the development of intuitionistic logic and algebra. (try saying that three times really fast)*SAU Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics. The inclusion of Brouwer's name in the Brouwer–Heyting–Kolmogorov interpretation is largely honorific, as Brouwer was opposed in principle to the formalisation of certain intuitionistic principles (and went as far as calling Heyting's work a "sterile exercise").*Wik

1984 Edna Ernestine Kramer Lassar (May 11, 1902 - July 9, 1984) died of pneumonia at her home in Manhattan. She graduated magna cum laude from Hunter College and earned a Ph.D. at Columbia in 1930. She is best known for her book The Nature and Growth of Modern Mathematics, which is an excellent exposition of much of modern mathematics. It is very accessible to undergraduates. For more about her, see Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell. *VFR

1996 Douglas George Chapman (March 20, 1920 - July 9, 1996)was a Canadian-born U.S. mathematical statistician and an expert on wildlife statistics. He was one of the scientific advisors to the International Whaling Commission that warned in the 1960s that the number of whales being taken by the whaling industry was far in excess of what the population could stand, and proposed annual fin whale catch quotas that would permit the depleted populations of this species to recover. His later research on fish farming expanded to include mollusk aquaculture and he directed a program to develop quantitative methods to aid in the management of fisheries resources.*TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-47013156943009650952020-07-08T00:00:00.000+01:002020-07-08T00:00:01.202+01:00On This Day in Math - July 8

I never came across one of Laplace's "Thus it plainly appears"

 without feeling sure that I have hours of hard work before me to fill up the chasm

 and find out and show how it plainly appears.
Nathanial Bowditch, Quoted in F Cajori, The Teaching and History of Mathematics in the United States
(LaPlace's classic, "Mecanique Celeste", is a very difficult book, and Biot, who helped him prepare it for printing said that Laplace himself would frequently get lost in following his own line of reasoning and insert, "il est aise a voir".
 Bowditch translated the work and Legendre wrote of the translation, "Your work is not merely a translation with a commentary; I regard it as a new edition, augmented and improved, and such a one as might have come from the hands of the author himself, ... if he had been solicitously studious of being clear." )

The 190th day of the year; 190 is the largest number with only distinct prime Roman numeral palindrome factors that is a Roman numeral palindrome (190 = CXC = II * V * XIX). *Prime Curios

190 is a Harshad or Niven number divisible by the sum of its digits. In recreational mathematics, a Harshad number (or Niven number) in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known as n-Harshad (or n-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver.

190 is the 19th triangular number, the sum of the first 19 integers. A nice problem relating triangular numbers to magic squares was asked in 1941 in the American Mathematical Monthly, posed by Royal Vale Heath, widely known for creating ingenious mathematical puzzles: "What is the smallest value of n for which the n2 triangular numbers 0, 1, 3, 6, 10, . . . n2(n2 – 1)/2 can be arranged to form a magic square?" An explanation, and answer is in this blog by Ivars Peterson

Find More Math Facts for every year date here

EVENTS

1672 Newton's first publication is in a letter to the Philosophical Transactions: "A Serie's of Quere's Propounded by Mr. Isaac Newton, to be Determin'd by Experiments, Positively and Directly Concluding His New Theory of Light and Colours; and Here Recommended to the Industry of the Lovers of Experimental Philosophy, as they Were Generously Imparted to the Publisher in a Letter of the Said Mr. Newtons of July 8.1672" (Thanks to Thony Christie) *Philosophical Transactions

1680 Hooke demonstrates sound vibration. This was done by putting flour on a glass plate, and bowing on the edge of glass. Hooke had observed that the motion of the glass was vibrate perpendicular to the surface of the glass, and that the circular figure of the flour changed into an oval one way, and the reciprocation of it changed it into an oval the other way. This phenomenon was rediscovered by Chladni in the eighteenth century, and given his name "Chladni figures". *Daniel P McVeigh, "An Early History of the Telephone 1664-1865"

1706 de Moivre wrote to Johann Bernoulli on 8 July 1706 telling him about Machin's series for π he suggested that Johann Bernoulli might tell Jakob Hermann about Machin's unproved result. He did so and Hermann quickly discovered a proof that Machin's series converges to π. He produced techniques that show other similar series also converge rapidly to π and he wrote on 21 August 1706 to Leibniz giving details. Two years later, on 6 July 1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π.
In 1706 William Jones published a work Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners. (This is the book in which Jones first uses Pi in the mathematical sens it is now used) This contains on page 243 the following passage:-
There are various other ways of finding the lengths or areas of particular curve lines, or planes, which may very much facilitate the practice; as for instance, in the circle, the diameter is to the circumference as 1 to (16/5- 4/239) - 1/3(16/53- 4/2393) &c. = 3.14159 &c. = π. This series (among others for the same purpose, and drawn from the same principle) I received from the excellent analyst, and my much esteemed friend Mr John Machin; and by means thereof, van Ceulen's number, or that in Art. 64.38 may be examined with all desirable ease and dispatch.
Jones also reports that this formula allows π be calculated:-
... to above 100 places; as computed by the accurate and ready pen of the truly ingenious Mr John Machin. No indication is given in Jones's work, however, as to how Machin discovered his series expansion for π.

1831 Quetelet officially uses the term, "l'homme moyen" in an article about the different ages at which men commit crimes. *Statistics on the Table: The History of Statistical Concepts and Methods By Stephen M. Stigler

1835 Liberty bell cracked. *VFR Or maybe not In the 1830s, the bell was adopted as a symbol by abolitionist societies, who dubbed it the "Liberty Bell". It acquired its distinctive large crack sometime in the early 19th century—a widespread story claims it cracked while ringing after the death of Chief Justice John Marshall in 1835.*Wik

1842 Francis Baily (1774-1844) UK, at an eclipse in Italy, focuses attention on the corona and prominences and identifies them as part of the Sun's atmosphere. *NSEC

1842 Dominique Francois Jean Arago (1786-1853), French astronomer. Studied solar eclipse of July 08, 1842 and concluded the sun exist of gas.*NSEC

1881, a patron came into Edward Berner's drug store in Two Rivers, Wisconsin, and sat down at the soda-fountain counter. Since it was the Sabbath, the customer couldn't have the desirable, but scandalous, flavored soda water. Berner compromised by putting ice cream in a dish and poured over it the chocolate syrup that was previously only served as flavoring in ice-cream sodas. That was an ice cream Sunday! The name became "sundae", after the day on which Berner served it. TIS

1933 Jansky announced detection of radio radiation from galactic center.*VFR Before Jansky observed the Milky Way in the 1930s, physicists speculated that radio waves could be observed from astronomical sources. In the 1860s, James Clerk Maxwell's equations had shown that electromagnetic radiation is associated with electricity and magnetism, and could exist at any wavelength. Several attempts were made to detect radio emission from the Sun by experimenters such as Nikola Tesla and Oliver Lodge, but those attempts were unable to detect any emission due to technical limitations of their instruments.
Karl Jansky made the discovery of the first astronomical radio source serendipitously in the early 1930s. As an engineer with Bell Telephone Laboratories, he was investigating static that interfered with short wave transatlantic voice transmissions. Using a large directional antenna, Jansky noticed that his analog pen-and-paper recording system kept recording a repeating signal of unknown origin. Since the signal peaked about every 24 hours. *Wik

2002 Well into his mid-nineties, Donald Coxeter gives the keynote address at the Janos Bolyai Conference on Hyperbolic Geometry with a new paper on the Descartes circle theorem as extended by Phillip Beecroft. His Opening remarks:

The Absolute property of four mutally tangent circles that I am describing seems to have been discovered by Mr. Phillip Beecroft, of Hyde Academy, Cheshire, England, and published in The Lady and Gentleman's Dairy... In Beecroft's own words, "If any four circles be described to touch each other mutually, another set of four circles of mutual contact may be described whose points of contach shall coincide with those of the first four." He then proceeded to give a new and elegant proof of the 1842 theorem, which extended the four circle theorem of Descartes to be, in essence, an eight circle theorem.
*Siobhan Roberts, King of Infinite Space

BIRTHS

1760 Christian Kramp (July 8, 1760 – May 13, 1826) was a French mathematician, who worked primarily with factorials.
As Bessel, Legendre and Gauss did, Kramp worked on the generalised factorial function which applied to non-integers. His work on factorials is independent of that of James Stirling and Vandermonde. He was the first to use the notation n! (Elements d'arithmétique universelle, 1808). In fact, the more general concept of factorial was found at the same time by Arbogast.*TIS For more on the symbols and history of the factorial see here.

1777 Daniel Friedrich Hecht (8 July 1777 in Sosa – 13 March 1833 in Saxony) was a German mathematician. He was a mine manager, then a teacher and finally a professor of mathematics. He is most notable for writing high school textbooks on maths and geometry. *Wik

1838 Count Ferdinand von Zeppelin Germany aviation pioneer who built the first rigid dirigible airships, named Zeppelins. He patented his idea on 31 Aug 1895 and formed a company to build airships in 1898. Many thought his invention incredible, and called him "Foolish Count". His first airship took off in 2 Jul 1900 at Lake Constance, where it had been assembled in a floating assembly shed. He continued to improve the design and built a fleet of airships for commercial passenger service. During WW I, Zeppelins were used to bomb Britain beginning 19 Jan 1915 with attacks on Great Yarmouth and King's Lynn. After the war, passenger service included transatlantic flights. Zeppelin use ended after the 6 May 1937 Hindenburg fire disaster at Lakehurst, N.J., U.S.A.*TIS

1895 Igor Yevgenyevich Tamm (8 July 1895 – 12 April 1971) Soviet physicist who shared the 1958 Nobel Prize for Physics with Pavel A. Cherenkov and Ilya M. Frank for his efforts in explaining Cherenkov radiation. Tamm was an outstanding theoretical physicist, after early researches in crystallo-optics, he evolved a method for interpreting the interaction of nuclear particles. Together with I. M. Frank, he developed the theoretical interpretation of the radiation of electrons moving through matter faster than the speed of light (the Cerenkov effect), and the theory of showers in cosmic rays. He has also contributed towards methods for the control of thermonuclear reactions. *TIS
one of my favorite math stories is from George Gamow's autobiography and is about Tamm.

"Here is a story told to me by one of my friends who was at that time
a young professor of physics in Odessa. His name was Igor Tamm (Nobel
Prize laureate in Physics, 1958). Once when he arrived in a neighboring
village, at that period when Odessa was occupied by the Reds, and was
negotiating with a villager as to how many chickens he could get for
half a dozen silver spoons, the village was captured by one of the
Makhno bands, who were roaming the country, harassing the Reds. Seeing
his city clothes (or what was left of them), the capturers [sic]
brought him to the Ataman, a bearded fellow in a tall black fur
hat with machine-gun cartridge ribbons crossed on his broad chest and
a couple of hand grenades hanging on the belt.

'You son-of-a-bitch, you Communist agitator, undermining our Mother
Ukraine! The punishment is death.'

'But no,' answered Tamm, 'I am a professor at the University of Odessa
and have come here only to get some food.'

'Rubbish!' retorted the leader. 'What kind of professor are you ?'

'I teach mathematics.'

'Mathematics?' said the Ataman. 'All right! Then give me an estimate of
the error one makes by cutting off Maclaurin's series at the nth term.
Do this, and you will go free. Fail, and you will be shot!'

Tamm could not believe his ears, since this problem belongs to a rather
special branch of higher mathematics. With a shaking hand, and under
the muzzle of the gun, he managed to work out the solution and handed
it to the Ataman.

'Correct!' said the Ataman. 'Now I see that you really are a professor.
Go home!'

Who was this man? No one will ever know. If he was not killed later, he
may well be lecturing now on higher mathematics in some Ukrainian
university."

I tell this story every other year or so to my physics students when
they cannot be bothered to remember the form of the remainder in Taylor
expansions....

1904 Henri (-Paul) Cartan, (July 8, 1904 – August 13, 2008) mathematician born in Nancy, France. His father, Elie Cartan, was also a mathematician. Henri made fundamental advances in the theory of analytic functions, worked on the theory of sheaves, homological theory, algebraic topology and potential theory. Along with others, such as Weil and Dieudonné, Henri Cartan wrote under the name Bourbaki. Bourbaki's Eléments de mathématique contains more than 30 volumes and aims to present mathematics so as to illustrate the axiomatic structure of modern mathematics. *TIS

1915 Kenneth O. May (July 8, 1915, Portland, Or. – December 1,1977) was an American mathematician and historian of mathematics, who developed May's theorem. The Kenneth O. May Prize is awarded for outstanding contributions to the history of mathematics. Ken May established Historia Mathematica, and preserved it by separating it from its creator, "The distinguished predecessors of HM were associated with their founders and died with them. If HM is to avoid this fate, we must prepare and carry through a prompt transfer of editorial responsibility to younger hands." His list of publications numbers above 300. *Henry S. Tropp, E'loge, Isis 70, Sept 1979, Pgs 419-422

DEATHS

1390 Albert of Saxony died. He wrote an excellent logic text and published two works on squaring the circle. *VFR ert was born at Rickensdorf near Helmstedt, the son of a farmer in a small village; but because of his talent, he was sent to study at the University of Prague and the University of Paris.
At Paris, he became a master of arts (a professor), and held this post from 1351 until 1362. In 1353, he was rector of the University of Paris. After 1362, Albert went to the court of Pope Urban V in Avignon as an envoy of Rudolf IV, Duke of Austria, in order to negotiate the founding of the University of Vienna. The negotiations were successful, and Albert became the first rector of this University in 1365.
In 1366, Albert was elected bishop of Halberstadt (counted as Albert III), Halberstadt being the diocese in which he was born. As Bishop of Halberstadt, he allied himself with Magnus with the Necklace, Duke of Brunswick-Lüneburg, against Gebhard of Berg, Bishop of Hildesheim, and was taken prisoner by Gebhard in the battle of Dinckler in 1367.
He died at Halberstadt in 1390.*Wik

1695 Christiaan Huygens (14 April 1629 – 8 July 1695) Dutch mathematician, astronomer, and physicist, who founded the wave theory of light, discovered the true shape of the rings of Saturn, and contributed to the science of dynamics - the study of the action of forces on bodies. Using a lens he ground for himself, on 25 Mar 1655, he discovered the first moon of Saturn, later named Titan. In 1656, he patented the first pendulum clock, which he developed to enable exact time measurement while observing the heavens. Huygens studied the relation of the length of a pendulum to its period of oscillation (1673) and stated theories on centrifugal force in circular motion which influenced Sir Isaac Newton in formulating his Law of Gravity. Huygens also studied and drew the first maps of Mars. On 14 Jan 2005, a NASA space probe, named after Huygens, landed on Titan. *TIS

1902 John Daniel Runkle (October 11, 1822 – July 8, 1902) was a U.S. educator and mathematician. B.S. in mathematics, 1851, Harvard College, second president of the Massachusetts Institute of Technology, was associated with the Nautical Almanac computation project from 1849 to 1884. In 1858 he founded the journal Mathematical Monthly and edited it for three years, when publication ceased. In 1860 he was a member of the committee that prepared the "Objects and Plan of an Institute of Technology" which led to the establishment of MIT. In 1862 he became MIT's first secretary, and in 1865 he joined the new faculty as professor of mathematics, where he remained until 1902. He served as president pro-tem, 1868-1870, and was MIT's second president, 1870-1878. He was married to Catherine Robbins Bird Runkle. *MIT History

1971 Kurt Werner Friedrich Reidemeister (October 13, 1893 – July 8, 1971) was a mathematician born in Braunschweig (Brunswick), Germany.
He received his doctorate in 1921 with a thesis in algebraic number theory at the University of Hamburg under the supervision of Erich Hecke. In 1923 he was appointed assistant professor at the University of Vienna. While there he became familiar with the work of Hans Hahn and Wilhelm Wirtinger. In 1925 he became full professor at University of Königsberg, where he stayed until 1933, when he was forced to leave because of his opposition of the Nazis.
Reidemeister's interests were mainly in combinatorial group theory, combinatorial topology, geometric group theory, and the foundations of geometry. His books include Knoten und Gruppen (1926), Einführung in die kombinatorische Topologie (1932), and Knotentheorie (1932). He was the brother of Marie Neurath.*Wik

1979 Shin'ichiro Tomonaga (March 31, 1906 – July 8, 1979) Japanese physicist who shared the Nobel Prize for Physics in 1965 (with Richard P. Feynman and Julian S. Schwinger of the U.S.) for independently developing basic principles of quantum electrodynamics. He was one of the first to apply quantum theory to subatomic particles with very high energies. Tomonaga began with an analysis of intermediate coupling - the idea that interactions between two particles take place through the exchange of a third (virtual particle), like one ship affecting another by firing a cannonball. He used this concept to develop a quantum field theory (1941-43) that was consistent with the theory of special relativity. WW II delayed news of his work. Meanwhile, Feynman and Schwinger published their own independent solutions.

2008 Sixto Ríos García (January 4, 1913; Pelahustán, Toledo - July 8, 2008; Madrid,) was a Spanish mathematician, known as the father of Spanish statistics.
He has held the positions of Director of the School of Statistics at the University of Madrid, Director of the Institute for Operations Research and Statistics CSIC, Director, Department of Statistics, Faculty of Mathematical Sciences at the Complutense University and President of the Spanish Society Operational Research, Statistics and Information. It was academic correspondent of the National Academy of Sciences of Buenos Aires, and organizer and founder, commissioned by Unesco, School of Statistics, University of Caracas. He was a member of the drafting committee of Statistical Abstracts and fellow of the International Statistical Institute and the Institute of Mathematical Statistics. Wik-ES

2010 David Harold Blackwell (April 24, 1919 – July 8, 2010) was Professor Emeritus of Statistics at the University of California, Berkeley, and is one of the eponyms of the Rao–Blackwell theorem. Born in Centralia, Illinois, he was the first African American inducted into the National Academy of Sciences, and the first black tenured faculty member at UC Berkeley.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-48778129520197837932020-07-07T00:00:00.000+01:002020-07-07T00:00:12.487+01:00On This Day in Math - July 7

Probability is a mathematical discipline whose aims are akin to those,

for example, of geometry of analytical mechanics.

In each field we must carefully distinguish three aspects of the theory:
(a) the formal logical content,
(b) the intuitive background,
(c) the applications.
The character, and the charm, of the whole structure cannot be appreciated without

considering all three aspects in their proper relation.
William Feller, An Introduction to Probability Theory and its Applications

The 189th day of the year; the product of the primes in a prime quadruplet always end in 189, except for the very first quadruplet 3x5x7x11.(A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form {p, p+2, p+6, p+8} you can see some of the smaller ones listed here

There are 14 prime years in the 21st Century (2017 will be the third), but the 189th century would be the first to contain as few as five prime years (18803, 18839, 18859, 18869 and 18899).

Narayana, an Indian mathematician in the 14th century, came up with an interesting Fibonacci-like series: A cow produces one calf every year. Beginning in its fourth year, each calf produces one calf at the beginning of each year. How many cows and calves are there altogether after n years? For the 15th year, the total is 189. (How many mature and immature?)

2357 is a prime number. 23357 is also prime. 233357 is also prime but 2333357 is not, and then 23333357 is; and yes, this is somehow related to the number 189. I came across a sequence on OEIS which gave "Numbers k such that (7*10^k + 71)/3 is prime." Like you may have, I wondered, "Why would someone search for primes of so unusual a sequence?" Well, if you take those exponents, and subtract 2 from them, you get the number of threes that when placed between the digit 2 and the digits 57, will produce a prime. So I can inform you today that not only is (7*10189 +71 )/3 a prime number, but that prime number is a 2 followed by 187 threes followed by 57. And you thought 189 was just some hum-drum number!!!!!

See More Math Facts for every year date here

EVENTS

1339 There was an annular-total eclipse, with the total part of the track finding its way between the Orkney and Shetland Islands without touching either. At this location the track of totality was only 1 km wide, with a duration of 1 second! Presuming that you could position a boat to an accuracy of 1 km, totality must have been a ring of Baily's Beads. *NSEC

1637  In 1625 (Christen Sørensen) Longomontanus suggested to the King, Christian IV, that he should build an observatory to replace Tycho's Stjerneborg, which had been demolished in 1601. The observatory, the Rundetaarn (Round Tower), was conceived as part of the Trinitatis Complex: a university church, a library and the observatory. The foundation stone was laid on 7 July 1637 and the tower was finished in 1642. Longomontanus was appointed the first director of the observatory, after Leiden 1632 only the second national observatory in Europe. The church and Library were finished in 1657. *RMAT, Tycho's last bastion

1668, Sir Isaac Newton received his M.A. from Trinity College in Cambridge.*TIS

1742 Goldbach's conjecture was sent in a letter to Leonhard Euler on 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. *TIS

1747 Johann Sebastian Bach dedicated his Musikalisches Opfer (Musical Offering) to Frederick the Great. For a discussion of the mathematical significance of this cerebral music, see Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. *VFR

1777 Johan Bernoulli, then astronomer Royal, Berlin, is paid a sum of 84 pounds for the Sexcentenary tables. "To Mr. John Hyacinth Magellan....for the use of Mr. Bournoulli .. as a reward for his care and trouble in constructing a manuscript Book of Tables for facilita."
Two years later they would pay 28.35 pounds to Dr. Charles Hutton for translating the preface of the tables.

1788 Caroline Herschel's nebula discovery,* History of Astronomy @HistAstro

1823 William Rowan Hamilton passed into Trinity College, Dublin. He was easily first out of the 100 candidates. *VFR

1847 Lassel discovered a satellite of Neptune. *VFR (this date does not concur with other dates on these discoveries) In 1846 Lassell discovered Triton, the largest moon of Neptune, just 17 days after the discovery of Neptune itself by German astronomer Johann Gottfried Galle. In 1848 he independently co-discovered Hyperion, a moon of Saturn. In 1851 he discovered Ariel and Umbriel, two new moons of Uranus.*Wik

1855, a letter from Michael Faraday in The Times newspaper, London, described the polluted state of the River Thames he had observed on a boat trip: "The whole of the river was an opaque pale brown fluid. In order to test the degree of opacity, I ... dropped [pieces of card] into the water at every pier the boat came to; before they had sunk an inch below the surface they were indistinguishable, though the sun shone brightly at the time." His words, he said, were no exaggeration, they were "the simple truth." He asserted, "If there be sufficient authority to remove a putrescent pond from the neighborhood of a few simple dwellings, surely the river which flows for so many miles through London ought not to be allowed to become a fermenting sewer." *TIS I wrote a few years ago about the return of the seahorse to the muddy waters of the Thames.

1960 Press conference announces discovery of laser to the world. "VoilÁ. that Was It! The Laser was Born!" *Hughes Research Lab Web page.

BIRTHS

1638 Francois or Francois Bertrand Barrême Barrême,(7 July 1638, Tarascon, France - 1703, Paris France) is considered one of the founders of accounting . After having engaged in trading in Italy , he moved to Paris where he gave lessons in bookkeeping and became a protégé of Colbert . Expert for the accounts of the Accounting Chamber of Paris and King's ordinary arithmetician, he is the author of books of mathematical conversions. His books were so common that today his name is used for what was once in English called a "ready reckoner", a table of numbers used to facilitate simple calculations, esp one for applying rates of discount, interest, charging, etc, to different sums . *Wik

1746 Giuseppe Piazzi (July 7, 1746 - July 22, 1826) an Italian mathematician and astronomer. He discovered the asteroid Ceres and established an observatory at Palermo, now the Osservatorio Astronomico di Palermo – Giuseppe S. Vaiana. (for more detail see the source article) *Today in Astronomy

*Wik

1752 Joseph-Marie Jacquard born (7 July 1752 – 7 August 1834). *VFR French silk weaver, (born Lyons), inventor of the Jacquard programmable power loom for brocaded fabric. His loom would mechanically produce any pattern, controlled by perforated control cards (1805). This served as the impetus for the technological revolution of the textile industry and is the basis of the modern automatic loom. The concept of using punched cards was later applied by Hollerith to keeping track of the 1890 US census data. The idea futher evolved to computer input punched cards. *TIS

1816 Rudolf Wolf Swiss (7 July 1816 – 6 December 1893) astronomer and astronomical historian. Wolf's main contribution was the discovery of the 11 year sunspot cycle and he was the codiscoverer of its connection with geomagnetic activity on Earth. In 1849 he devised a system now known as Wolf's sunspot numbers. This system is still in use for studying solar activity by counting sunspots and sunspot groups. In mathematics, Wolf wrote on prime number theory and geometry, then later on probability and statistics - a long paper discussed Buffon's needle experiment. He estimated by Monte Carlo methods.*TIS

1888 Archibald Goldie (7 July 1888 in Glenisla, Angus, Scotland - 24 Jan 1964 in London, England) studied at the universities of St Andrews and Cambridge. He served in the Meteorological Service of the British Army in World War I and continued to work in various branches of the Meteorological Office.*SAU

1906 William Feller (July 7, 1906 – January 14, 1970). He once said that multiplication, especially before breakfast, is seldom commutative. He died in 1970. *VFR
Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators".*Wik

DEATHS

1900 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *VFR

1927 Magnus Gustaf Mittag-Leffler died (16 March 1846 – 7 July 1927) . Swedish mathematician who founded the international mathematical journal Acta Mathematica and whose contributions to mathematical research helped advance the Scandinavian school of mathematics. Mittag-Leffler made numerous contributions to mathematical analysis (concerned with limits and including calculus, analytic geometry and probability theory). He worked on the general theory of functions, concerning relationships between independent and dependent variables. His best known work concerned the analytic representation of a one-valued function, this work culminated in the Mittag-Leffler theorem.*TIS

1930 Sir Arthur Conan Doyle (22 May 1859 – 7 July 1930) Scottish novelist, physician, spiritualist. His fictional detective, Sherlock Holmes, emulates the scientist, diligently searching through data and to make sense of it. "It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." *TIS

1942 William Henry Young (London, 20 October 1863 - Lausanne, 7 July 1942) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.*SAU

1975 William Hodge (17 June 1903 – 7 July 1975) studied at Edinburgh and Cambridge Universities. After some time at Bristol and in the USA he returned to Cambridge and became Lowndean Professor of Astronomy and Geometry. His main interests were in Algebraic Geometry and Differential Geometry. He became an honorary member of the EMS in 1954. He was knighted in 1959. *SAU His discovery of far-reaching topological relations between algebraic geometry and differential geometry—an area now called Hodge theory and pertaining more generally to Kähler manifolds—has been a major influence on subsequent work in geometry. *Wik

2014 Klaus Peters,( --, July 7, 2014) mathematician and STEM Publisher for over 50 years, passed away on July 7, 2014. Klaus, who received his doctorate from University of Erlangen in 1962, became well-known in the mathematical community largely through A.K. Peters Ltd, publisher of scientific and technical books, specializing in mathematics and computer science, as well as journals Experimental Mathematics, Internet Mathematics, and the Journal of Graphics Tools. Klaus was a familiar face at mathematics meetings around the world, and recently consulted with the AMS publishing division on a number of different projects, including Really Big Numbers. He was a strong and eloquent advocate for scholarly publishing. *AMS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-4383143347608514012020-07-06T00:00:00.000+01:002020-07-06T00:00:03.334+01:00On This Day in Math - July 6

You, who wish to study great and wonderful things,

who wonder about the movement of the stars,

must read these theorems about triangles.

Knowing these ideas will open the door to all of astronomy

and to certain geometric problems.
Johann Regiomontanus De Tringulis Omnimodis

The 188th day of the year; 188 is the largest known even number that can be expressed as the sum of two (distinct) primes in exactly five ways. *Prime Curios Students might seek smaller numbers that can be so expressed..

Neither 1882 nor 1883 contain a one or an eight. *@Derektionary

There are 188 11 bead necklaces using two colors, if the necklace can not be turned over.

188 is a Happy number: trajectory under iteration of sum of squares of digits map to 1.

188 is a product of 4 times a number (47). Any such number is the difference of two squares, one of which is the square of one more than the number n/4, and one of which is the square of one less. 48^2-46^2 = 188

 See More Math Facts for every year date here

EVENTS

1656 Huygen, in a letter to Carcavi, gives the solution, without proof, to a dice throwing probability problem posed by Fermat. (If A wins for Throwing a six, and B wins by throwing a seven, and after A throws once, B and A each roll twice in turns. What are the odds of A winning?) *A History of Probability and Statistics and Their Applications Before 1750 By Anders Hald

1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π. In 1706 William Jones had published a work Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners. (This is the book in which Jones first uses Pi in the mathematical sense it is now used) This contains on page 243 the following passage:-
There are various other ways of finding the lengths or areas of particular curve lines, or planes, which may very much facilitate the practice; as for instance, in the circle, the diameter is to the circumference as 1 to (16/5- 4/239) - 1/3(16/53- 4/2393) &c. = 3.14159 &c. = π. This series (among others for the same purpose, and drawn from the same principle) I received from the excellent analyst, and my much esteemed friend Mr John Machin; and by means thereof, van Ceulen's number, or that in Art. 64.38 may be examined with all desirable ease and dispatch.
Jones also reports that this formula allows π be calculated:-
... to above 100 places; as computed by the accurate and ready pen of the truly ingenious Mr John Machin.
No indication is given in Jones's work, however, as to how Machin discovered his series expansion for π so when de Moivre wrote to Johann Bernoulli on 8 July 1706 telling him about Machin's series for π he suggested that Johann Bernoulli might tell Jakob Hermann about Machin's unproved result. He did so and Hermann quickly discovered a proof that Machin's series converges to π. He produced techniques that show other similar series also converge rapidly to π and he wrote on 21 August 1706 to Leibniz giving details. Two years later, on 6 July 1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π.

1785 The Continental Congress of the United States adopted the decimal system of money with the dollar as unit.

1815 Total solar eclipse on the North Pole. (Ok, I admit, I wouldn't have thought that could happen!)

1819 When Marie Madeleine Sopie Blanchard ascended in her hydrogen balloon to watch a firework, she would become the first woman to lose her life while flying. Her craft crashed on the roof of a house and she fell to her death. *yovisto.

1909 Einstein resigns his position at the Bern Patent Office to move to Zurich to take up his first full-time academic position in the newly established chair of theoretical physics at the University of Zurich. His lectures were extremely popular due to his humor, unusual presentations, patience and accommodation to his students to make sure they understood. *Brody & Brody, The Science Class You Wish You Had

In 1920, a radio compass was used for first time for aircraft navigation. In a test of the radio compass as an aid to navigation, an F5L left Hampton Roads and flew directly to the battleship Ohio (BB 12), 94 miles at sea in a position unknown to the pilot. Without landing, the plane made the return trip to Hampton Roads, this time navigating by signals from Norfolk. *TIS

2016 Astronomy Magazine announces that China has completed the world's largest radio telescope.

E.T. may be easier to find now that China has just finished installation of the 4,450 triangular panels on the world's largest radio telescope, the Five Hundred Meter Aperture Spherical Telescope (FAST). The telescope was finished nearly three months ahead of schedule, with the original ETA in September. With its enormous size of 30 soccer fields, FAST has taken nearly five years and $180 million to build.
So how big is it? One of the scientists that worked on building FAST told Xinhua that if the dish were to be completely filled with wine, there would be enough to give five bottles to all seven billion people on Earth.
The next largest radio telescope is the 305-meter-wide Arecibo Telescope in Puerto Rico, which was completed in 1963. The Arecibo Telescope has held the crown of largest radio telescope for 53 years. FAST is 64 percent larger.

*Astronomy Magazine

BIRTHS

1849 Alfred Bray Kempe (6 July 1849, Kensington, London – 21 April 1922, London) published a false "proof" of the four color theorem in 1879 which stood until Heawood showed the mistake 11 years later. The 'proof' is however still the basis for the computer aided proof discovered 100 years later.*SAU

1883 Ernst Arnold Kohlschütter (July 6, 1883 – May 28, 1969) a German astronomer and astrophysicist from Halle.
In 1908 he was awarded his Ph.D. from the University of Göttingen.
In 1911 he began working at the Mount Wilson Observatory, studying the spectra of the Sun and stars. In collaboration with Walter Sidney Adams, and in 1914 they discovered that the absolute luminosity of a star was proportional to the relative intensity of the lines in the spectrum. This allowed astronomers to determine the distance of stars, including main sequence and giants, using the spectroscope.
He became the director of the Bonn observatory in 1925. Therein he was dedicated to astrometric studies.
The crater Kohlschütter on the Moon is named in his honor. *Today in Astronomy

1910 Lothar Collatz  (July 6, 1910, Arnsberg, Westphalia – September 26, 1990, Varna, Bulgaria) was a German mathematician. In 1937 he posed the famous Collatz conjecture, which remains unsolved.
The Collatz conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers, or as wondrous numbers.
Take any natural number n. If n is even, divide it by 2 to get n / 2, if n is odd multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called "Half Or Triple Plus One", or HOTPO indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.

Paul Erdős said about the Collatz conjecture: "Mathematics is not yet ready for such problems." and also offered $500 for its solution.
In 2006, researchers Kurtz and Simon, building on earlier work by J.H. Conway in the 1970s, proved that a natural generalization of the Collatz problem is undecidable. However, as this proof depends upon the generalization, it cannot be applied to the original Collatz problem. *Wik

DEATHS

 1476 Regiomontanus, aka Johann Mueller, (6 Jun 1436, 6 Jul 1476 at age 40)the father of trigonometry as a science independent of astronomy. According to a rumor repeated by Gassendi in his Regiomontanus biography he was assassinated by relatives of George of Trebizond whom he had criticized in his writings. More likely he died in an epidemic raging in Rome at the time.The ideas behind the law of sines, like those of the law of cosines, predate the word sine by over a thousand years. Theorems in Euclid on lengths of chords are essentially the same ideas we now call the law of sines. The law of sines for plane triangles was known to Ptolemy and by the tenth century Abu'l Wefa had clearly expounded the spherical law of sines. It seems that the term "law of sines" was applied sometime near 1850, but I am unsure of the origin of the phrase.
The spherical law of sines was first presented by Johann Muller in his De Triangulis Omnimodis in 1464. This was the first book devoted wholly to trigonometry (a word not then invented). David E. Smith suggests that the theorem was Muller's invention.
The German astronomer and mathematician who was chiefly responsible for the revival and advancement of trigonometry in Europe. His book De triangulis omnimodis (1464) is a systematic account of methods for solving triangles. Much of the material on spherical trigonometry in Regiomontanus' On Triangles was taken directly and without credit from the twelfth-century work of Jabir ibn Aflah otherwise known as Geber, as noted in the sixteenth century by Gerolamo Cardano.
In Jan 1472 Muller made observations of a comet which were accurate enough to allow it to be identified with Halley's comet 210 years later (being three returns of the 70 year period comet). He also observed several eclipses of the Moon. His interest in the motion of the Moon led him to make the important observation that the method of lunar distances could be used to determine longitude at sea. However, instruments of the time lacked the necessary accuracy to use the method at sea. *TIS
Thony C who writes the excellent history blog, The Renaissance Mathematicus, noted, "However at least in the case of Regiomontanus appearances are deceptive; what we have here is a date of death that is anything but certain.". See his explanation of the remark here.
The title page of "On Triangles" by Regiomontanus is here. Although the work was written in 1464, it was not published until 1533.

1854 Georg Simon Ohm (17 March 1789 – 6 July 1854) was a German physicist. As a high school teacher, Ohm began his research with the recently invented electrochemical cell, invented by Italian Count Alessandro Volta. Using equipment of his own creation, Ohm determined that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current. This relationship is now known as Ohm's law.*Wik

1915 Lawrence Hargrave(29 Jan 1850, 6 Jul 1915 at age 65) Australian aeronaut and inventor best known for his invention of the box kite. Hargrave "flew" on 12 Nov 1894, by attaching himself to a huge four kite construction attached to the ground by piano wire. Due to their abilities to carry heavy payloads, steady flight, and capacity for high altitude flight, these kites have had many industrial and military uses in the past. Box kites were used until the 1930's to carry meteorological equipment for high altitude weather studies and by the Royal Air Force as sea rescue equipment to deliver radio aerials. Hargrave also made important studies of wing surfaces and worked with rotary engines and gliders. *TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-38899410579158123432020-07-05T00:00:00.000+01:002020-07-05T00:00:01.966+01:00On This Day in Math - July 5

There is no smallest among the small and no largest among the large,

But always something still smaller and something still larger.

Quoted in E Maor, To Infinity and Beyond: a Cultural History of the Infinite

The 187th day of the year; 187^(1*8*7)+1+8+7 is prime. There are only two such (non-zero) numbers. Students might search for the other.

The 187th prime is 1117. 11*17 = 187

 187² and 187³ don't have 1, 7, or 8.
*Math Year-Round @MathYearRound

With 187 people in a room, there's a 50% chance that 4 share the same birthday *Derek Orr

 187 = 94^2 - 93^2

More Math Facts for every year date here

EVENTS
In 1643, an exceptionally strong wind occurred in Essex County, Mass. The description by Governor John Winthrop is the first record suggestive of a tornado in the U.S.: "There arose a sudden gust so violent for one-half hour as it blew down multitudes of trees. It lifted up their meeting house at Newbury, the people being in it. It darkened the air with dust, yet through God's great mercy it did no hurt, but only killed one Indian with the fall of a tree." However, no tornado-like funnel shape - so likely to be noted, if seen - was not included in his log. So, it was likely not a tornado, in fact, but a severe straight-line squall with strong downburst winds. Reverend Increase Mather cited a likely tornado in Jul 1680 storm at Cambridge, Mass*TIS

1687 Halley wrote to Newton that his Principia was finally published. [Westfall, p. 468] *VFR 1687 – ushering in a tidal wave of changes in thought that would significantly accelerate the already ongoing scientific revolution by giving it tools that produced technologically valuable results, which had theretofore been otherwise unobtainable. (Thony Christie has pointed out that the use of "published" may give a false impression to the modern reader, even though this is the date printed on the title page of the document. The actual words, used by Halley were, "I have at length brought your Book to an end, and hope it will please you. the last errata came just in time to be inserted. I will present from you the books you desire to...." )

1698 Johann Bernoulli, in a letter to Leibniz, defined the notion of a function. The term "function" is due to Leibniz. [Cajori, Historical Introduction to the Mathematical Literature, p. 96]*VFR

1766 Ben Franklin writes from England to Rev Ezra Stiles, "I have lately propos'd our ingenious and learned Contriman Mr: Winthorp, as a Member of the Royal Society." On Feb 20, 1766. John Winthrop Esqr. Hollisian Professor of Mathematics and Natural Philosophy was unanimously elected Fellow of the Royal Society in London. *Franklin Papers, Natl Archives

1951 – William Shockley invents the junction transistor. *Wik

2012 Gresham College announces the appointment of Raymond Flood, Fellow of Kellogg College, Oxford, as Professor of Geometry and Other Mathematical Sciences. The Geometry chair at Gresham College is the oldest in England, dating back to the College's founding in 1597. Gresham College was the first higher education institution in England besides the Universities of Oxford and Cambridge, and it was created with the guiding principle of providing free education to the traders and people of London so that England could maintain a position at the forefront of a global economy. Gresham College's central position in science and mathematics has seen the Royal Society formed within the College, and past luminaries including Henry Briggs, Sir Christopher Wren, Robert Hooke, Sir Christopher Zeeman and Sir Roger Penrose. *Gresham Press Release

BIRTHS
1820 William John Macquorn Rankine, (5 July 1820 – 24 December 1872) Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. As the chair (1855) of civil engineering and mechanics at Glasgow, he developed methods to solve the force distribution in frame structures. Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853. Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. *TIS While many students never encounter it, there is a temperature scale named after Rankine. It is the Fahrenheit scale equivalent of the Kelvin scale for Celsius.

1867 Andrew Ellicott Douglass (July 5, 1867, Windsor, Vermont – March 20, 1962, Tucson, Arizona) American astronomer and archaeologist who coined the name dendrochronology for tree-ring dating, a field he originated while working at the Lowell Observatory, Flagstaff, Ariz. (1894-1901). He showed how tree rings could be used to date and interpret past events. Douglass also sought a connection between sunspot activity and the terrestrial climate and vegetation. The width of tree rings is a record of the rainfall, with implications on the local food supply in dry years. Archaeologist Clark Wissler collaborated in this work by furnishing sections of wooden beams from Aztec Ruin and Pueblo Bonito so Douglass could cross-date the famous sites. Thus the study of tree rings enables archaeologists to date prehistoric remains. *TIS

1888 Louise Freeland Jenkins (July 5, 1888 – May 9, 1970) was an American astronomer.
She was born in Fitchburg, Massachusetts. In 1911 she graduated from Mount Holyoke College, then she received a Master's degree in astronomy in 1917 from the same institution. From 1913 to 1915 she worked at the Allegheny Observatory in Pittsburgh.
About 1921 she moved to Japan, becoming a teacher at the Women's Christian College, a missionary school. She returned to the United States in 1925 after her father died. A year later she returned to teach at a school in Himeji. (Hinomoto Gakuen girl's high school.)
In 1932 she returned to the US and became a staff member at Yale University Observatory. She was co-editor of the Astronomical Journal starting in 1942, and continued in this post until 1958. She would return to visit Japan later in her life.
She was noted for her research into the trigonometric parallax of nearby stars. She also studied variable stars.
The crater Jenkins on the Moon is named in her honor. *Today in Astronomy

1946 Gerardus (Gerard) 't Hooft (July 5, 1946 - ) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions".
His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization, and the holographic principle. *Wik

DEATHS
1865 Oskar Bolza died (12 May 1857–5 July 1942). Bolza was a German mathematician, and student of Felix Klein. He was born in Bad Bergzabern, Bolza published The elliptic s-functions considered as a special case of the hyperelliptic s-functions in 1900 which related to work he had been studying for his doctorate under Klein. However, he worked on the calculus of variations from 1901. Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907). His text Lectures on the Calculus of Variations published by the University of Chicago Press in 1904,[3] became a classic in its field and was republished in 1961 and 2005.[4] After the death of his friend Maschke in 1908, Bolza became unhappy in the United States and, in 1910, he and his wife returned to Freiburg in Germany where he was appointed as an honorary professor. Chicago gave him the title of 'non-resident professor of mathematics' which he retained for the rest of his life.*Wik He returned to Germany in 1910, where he researched function theory, integral equations and the calculus of variations. In 1913, he published a paper presenting a new type of variational problem now called "the problem of Bolza." The next year, he wrote about variations for an integral problem involving inequalities, which later become important in control theory. Bolza ceased his mathematical research work at the outbreak of WW I in 1914.*TIS

1911 George Johnstone Stoney (15 February 1826 – 5 July 1911) Irish physicist who introduced the term electron for the fundamental unit of electricity. At the Belfast meeting of the British Association in Aug 1874, in a paper: On the Physical Units of Nature, Stoney called attention to a minimum quantity of electricity. He wrote, "I shall express 'Faraday's Law' in the following terms ... For each chemical bond which is ruptured within an electrolyte a certain quantity of electricity traverses the electrolyte which is the same in all cases." Stoney offered the name electron for this minimum electric charge. When J.J. Thomson identified cathode rays as streams of negative particles, each carrying probably Stoney's minimum quantity of charge, the name was applied to the particle rather than the quantity of charge.*TIS

1926 Peter Scott Lang graduated from Edinburgh University and after a period as assistant in Edinburgh he became Regius Professor of Mathematics at St Andrews. He held this position for 42 years. *SAU

1932 Rene Louis Baire died (21 January 1874 – 5 July 1932) a French mathematician most famous for his Baire category theorem, which helped to generalize and prove future theorems. His theory was published originally in his dissertation Sur les fonctions de variable réelles ("On the Functions of Real Variables") in 1899.*Wik French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

1977 Henry Scheffé (New York City, USA, 11 April 1907 – Berkeley, California, USA, 5 July 1977) worked in several different areas of Statistics, including linear models, analysis of variance and nonparametrics.*SAU He is known for the Lehmann–Scheffé theorem and Scheffé's method.

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia email@example.com:blogger.com,1999:blog-2433841880619171855.post-399770351612703202020-07-04T00:00:00.000+01:002020-07-04T00:00:07.173+01:00On This Day in Math - July 4

Things that people learn purely out of curiosity

 can have a revolutionary effect on human affairs
~Frederick Seitz - born 100+ years ago today

The 186th day of the year; 186 is the product of the first four primes less; the product of the first four positive integers (7 x 5 x 3 x 2 - 4 x 3 x 2 x 1 = 186) . *Prime Curios

186 is the sum of consecutive primes, 186 = = 89 + 97,

186 is a sphenic (wedge) number, product of 3 distinct primes: 186 = 2*3*31

and from Jim Wilder @wilderlab An equation for July 4th: 7⁴ = 2401 = (2 + 4 + 0 + 1)⁴ And a followup from World Observer@WKryst2011 points out that there are only two other such year dates. (student's should find both)

More Math Facts for every year date here.

EVENTS
1054 The Crab Nebula supernova is recorded in China and Japan. *VFR The Crab Nebula (catalogue designations M1, NGC 1952, Taurus A) is a supernova remnant and pulsar wind nebula in the constellation of Taurus. Corresponding to a bright supernova recorded by Chinese astronomers in 1054, the nebula was observed later by John Bevis in 1731. *Wik

1826 Thomas Jefferson , principal author of the Declaration of Independence dies on U.S. Independence day. (See Date under Deaths) He was buried at his home, Monticello. He wrote his own epitaph: "Here was buried Thomas Jefferson, author of the Declaration of Independence, of the statute of Virginia for religious freedom, and father of the University of Virginia." *VFR I find it striking that when he lists his accomplishments, being President of the US did not make his top three.

1662 "By and by comes Mr. Cooper ... of whom I entend to learn Mathematiques; and so begin with him today ... . After an hour's being with him at Arithmetique, my first attempt being to learn the Multiplication table, then we parted till tomorrow." Samuel Pepys, in his diary....At the time he was something like a modern Secretary of the Navy. *VFR

1744 Euler wrote Christian Goldbach that he has finished his book Introductio in analysin infinitorum (Lausanne 1748). In this work the trigonometric and logarithmic functions were first treated in their modern form. *VFR

1802 The United States Military Academy at West Point established by act of congress earlier in the year opened on July 4. This school was the first engineering school in the U.S. Charles Davies, a noted textbook writer, taught there.*VFR Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.

1819 William Herschel writes to his sister, Caroline, "Lina, there is a great comet. I want you to come and assist me. Come to dine and spend the day here.... we shall have time to prepare maps and telescopes. I saw it's situation last night, it has a long tail." He was eighty years old at the time, and he was still at work when he died, two years later. *Timothy Ferris, Coming of Age in the Milky Way

1843 Liouville began an address to the Academy of Sciences with the words: "I hope to interest the Academy in announcing [that in] the papers of Evariste Galois I have found a solution, as precise as it is profound, of this beautiful problem: whether or not it [the general equation of fifth degree] is solvable by radicals." This work of Galois was published in 1846. *VFR

1862 Charles Lutwidge Dodgson, mathematics teacher at Oxford, went boating on the Isis, a tributary of the Thames, with the three daughters of Henry George Liddell, dean of Christ Church, Oxford. He was especially fond of Alice Liddell, then ten, and it was mainly for her that he began the story of another Alice's tumble down a rabbit hole. The work was published exactly three years later as Alice's Adventures under Ground under the pseudonym Lewis Carroll, with the famous illustrations by John Tenniel (see note). This work is a favorite of mathematicians, so if you haven't read it recently, you should. See 26 November 1864. [Note: "When Charles Dodgson – more widely known as Lewis Carroll – made drawings in the early 1960s for his book Alice's Adventures in Wonderland, he was disappointed with the results. He employed cartoonist John Tenniel to create the now-famous illustrations, while his original ideas were consigned to the archive of Christ Church College, Oxford, where he worked as a lecturer in mathematics until his death in 1898. TATE ETC. sent a cultural historian to view Dodgson's rarely seen drawings which feature in Tate Liverpool's 'Alice in Wonderland' exhibition. " *Tate ETC] From Nov 2011 to Jan 2012 the Tate Liverpool was showing these original works as part of the "Alice in Wonderland" exhibit. You can see some of them at the web page where I found the notes above.)

1934 Leo Szilard patented the chain-reaction design for the atomic bomb.

1963 The San Francisco Chronicle carried a report entitled, "A Milestone in Math—Professor's New Concept," by David Perlman. This popular account of Paul J. Cohen's proof of the independence of the axiom of choice was probably the first published. *VFR

1971  Michael S. Hart posts the first e-book, a copy of the United States Declaration of Independence, on the University of Illinois at Urbana–Champaign's mainframe computer, the origin of Project Gutenberg. *wik

1994 Replica of Hubble space telescope is dedicated in his hometown, on the west side of the Webster County Courthouse in Marshfield, Mo.

1997 Mars Pathfinder lands on the surface of Mars. Launched on December 4, 1996 by NASA aboard a Delta II booster a month after the Mars Global Surveyor was launched, it landed on July 4, 1997 on Mars's Ares Vallis, in a region called Chryse Planitia in the Oxia Palus quadrangle. The lander then opened, exposing the rover which conducted many experiments on the Martian surface. *Wik

2014 U S Independence day occurs on Friday. In what year will it next appear on a Friday? And the time after that?

BIRTHS
1790 Sir George Everest, (4 July 1790 – 1 December 1866) British military engineer and geodesist, born in Gwernvale, Powys, Wales, UK. He worked on the trigonometrical survey of India (1818-43), providing the accurate mapping of the subcontinent. For more than twenty-five years and despite numerous hardships, he surveyed the longest arc of the meridian ever accomplished at the time. Everest was relentless in his pursuit of accuracy. He made countless adaptations to the surveying equipment, methods, and mathematics in order to minimize problems specific to the Great Survey: immense size and scope, the terrain, weather conditions, and the desired accuracy. Mount Everest, formerly called Peak XV, was renamed in his honour in 1865. *TIS Mathematically, he was the uncle of Mary Everest Boole, the wife of George Boole, and a mathematician in her own right who is remembered for
encouraging children to explore mathematics through playful activities such as 'curve stitching'. (string-art) *Wik The Preparation of the Child for Science

1868 Henrietta Swan Leavitt (July 4, 1868 – December 12, 1921) American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies.*TIS

1906 Dan Rutherford (4 July 1906 in Stirling, Scotland - 9 Nov 1966 in St Andrews, Fife, Scotland)studied at St Andrews and Amsterdam. He spent most of his career in St Andrews becoming Gregory Professor of Applied Mathematics. In spite of this title most of his research was in pure mathematics and in particular in algebra. He became President of the EMS in 1940 and 1963. *SAU

1911 Frederick Seitz (July 4, 1911 – March 2, 2008) American physicist who made fundamental contributions to the theory of solids, nuclear physics, fluorescence, and crystals. As Eugene Wigner's first doctoral student, late in 1932, Seitz developed the cellular method of deriving solid-state wave functions. The widespread application of this Wigner-Seitz method to the understanding of metals is regarded as the catalyst for the formation of the field of solid-state physics in the U.S. His subsequent research focused on the theory and properties of crystals. He studied dislocations and imperfections in crystal structures, the effect of irradiation on crystals, and the process of diffusion (the movement of atoms or particles caused by random collision) in crystalline materials.*TIS

1936 Birthday of Guy Otttewel, writer of the eclipse book Understanding Eclipses and many other astronomical publications. *NSEC

1945 John Allen Paulos (July 4, 1945 - )born in Denver, Colorado. Currently a professor at Temple University, he is the author of the popular book Innumeracy. *VFR American mathematician and author of books encouraging people to make sense of the statistics and figures that inform their lives. He represents that mathematics as a subject that is easy to learn and understand. Paulos argues that ignorance of basic mathematical concepts discourages critical thinking and results in costly mistakes and misguided decisions by both political leaders and ordinary people in their everyday lives.*TIS

DEATHS
1742 Guido Grandi died. He corresponded with Leibniz on the sum of the series 1−1+1−1+1−•••. *VFR Luigi Guido Grandi (October 1, 1671 – July 4, 1742) was an Italian priest, philosopher, mathematician, and engineer born in Cremona. He was Jesuit-educated and became a member of the Camaldolese order. He became a professor of philosophy at the Camaldolese monastery in Florence in 1700 and a professor of mathematics in 1714.
In mathematics Grandi is best known for studying the rose curve, a curve which has the shape of a petalled flower, and for Grandi's series. He named the rose curve rhodonea. He also contributed to Note on the Treatise of Galileo Concerning Natural Motion in the first Florentine edition of Galileo Galilei's works and helped introduce Gottfried Leibniz's ideas on calculus to Italy. He also worked as an engineer, being superintendent of water at Tuscany, and in that capacity he was involved in the drainage of the Chiana Valley. In 1709 he visited England where he was elected a Fellow of the Royal Society.*Wik

1826 Thomas Jefferson (13 Apr 1743, 4 Jul 1826 at age 83) U.S. president who was throughout his lifetime an extraordinarily learned man, including interests in mathematics and natural sciences. He corresponded with such men as Joseph Priestley, and sometimes contributed time and money to progress in these fields. He collected and classified fossils. He was interested in the experiments being made in ballons and submarines. While visiting Europe, he sent home various mechanical and scientific gadgets produced including a polygraph and phosphorus matches. At his Monticello estate, he practiced scientific farming, and was always on the lookout for a significant new plant or seed. Jefferson died shortly before 1pm. His old friend, John Adams, died a few hours later.*TIS

1901 Peter Guthrie Tait (28 April 1831 – 4 July 1901) Scottish physicist and mathematician who helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics.*TIS Tait was a fellow-pupil of Maxwell at Edinburgh Academy and both of them went on to study at Edinburgh University and Cambridge. Tait became Professor of Mathematics at Queen's College Belfast and then moved to the Chair of Natural Philosophy at Edinburgh which he occupied for more than 40 years. With his collaborations with Maxwell, Thomson (Lord Kelvin) and Hamilton he made important contributions in both mathematics and physics. He became one of the first honorary members of the EMS in 1883. *SAU

1910 Giovanni Virginio Schiaparelli, (14 March 1835 - 4 July 1910) Italian astronomer who is remembered for his observations of Mars over seven oppositions and named the "seas" and "continents". In 1877, he saw on the surface of the planet Mars the markings that he called canali (channels), later misinterpreted as "canals." He made extensive studies, both observational and theoretical, of comets, determining from the shapes of their tails that there was a repulsive force from the sun. He showed that meteor swarms travel through space in cometary orbits. He explained the regular meteor showers as the result of the dissolution of comets and proved it for the Perseids. He suggested that Mercury and Venus rotate on their axes, discovered the asteroid Hesperia (1861) and was a major observer of double stars.*TIS

1934 Marie Marja Sklodowska Curie (7 November 1867 – 4 July 1934) was a Polish-born French chemist and physicist. In 1898, her celebrated experiments on uranium minerals led to discovery of two new elements. First she separated polonium, and then radium a few months later. The quantity of radon in radioactive equilibrium with a gram of radium was named a curie (subsequently redefined as the emission of 3.7 x 1010 alpha particles per sec.) With Henri Becquerel and her husband, Pierre Curie, she was awarded the 1903 Nobel Prize for Physics. She was then sole winner of a second Nobel Prize in 1911, this time in Chemistry. Her family won five Nobel awards in two generations. She died of radiation poisoning from her pioneering work before the need for protection was known.*TIS

1962 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

1986 Oscar Zariski's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties.*SAU

1987 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

2002 Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work (developing the theory of distributions, a new notion of generalized functions motivated by the Dirac delta-function of theoretical physics). He was the first French mathematician to receive the Fields medal. For a long time he taught at the École polytechnique. *Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-61745806612770065172020-07-03T00:00:00.000+01:002020-07-03T00:00:00.476+01:00On This Day in Math - July 3

Music is the pleasure the human mind experiences from counting

 without being aware that it is counting.
 ~Gottfried Leibniz

The 185th day of the year; the decimal expansion of the first 185 digits of Euler's constant is prime. *Prime Curios

185 is the sum of two square numbers in two different ways: \( 13^2+ 4^2 \) and \(11^2 + 8^2 \) I'm not sure it is commonly known that this implies that these pairs can be used as the opposite sides of a quadrilateral forcing the diagonals to be perpendicular(if the sides of a quadrilateral are 13, 11, 4, 8; then the quadrilateral has perpendicular diagonals.)

Like all odd numbers, 185 is the difference of the squares of consecutive integers, 93^2 - 92^2 = 185, because it ends in five, it is the difference of two squares of integers that are five apart; 21^2 - 16^2 = 185

See more Math Facts for every year date here.

EVENTS
1822 Charles Babbage described his ideas for a "difference engine" to the Royal Society. *VFR

1841, John Couch Adams decided to determine the position of an unknown planet by the irregularities it causes in the motion of Uranus. He entered in his journal; "Formed a design in the beginning of this week in investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus... in orderto find out whether they may be attributed to the action of an undiscovered planet beyond it..." In Sep 1845 he gave James Challis, director of the Cambridge Observatory, accurate information on where the new planet, as yet unobserved, could be found; but unfortunately the planet was not recognized at Cambridge until much later, after its discovery at the Berlin Observatory on 23 Sep 1846. *TIS

2011 Astronomers using the Hubble Space Telescope discovered a fourth moon orbiting the icy dwarf planet Pluto. The tiny, new satellite – temporarily designated P4 -- was uncovered in a Hubble survey searching for rings around the dwarf planet.

  Two labeled images of the Pluto system taken by the Hubble Space Telescope's Wide Field Camera 3 ultraviolet visible instrument with newly discovered fourth moon P4 circled. The image on the left was taken on June 28, 2011. The image of the right was taken on July 3, 2011. Credit: NASA, ESA, and M. Showalter (SETI institute)

BIRTHS
1820 Ernest de Jonquières (3 July 1820 Carpentras, France – 12 Aug 1901 Mousans-Sartoux, France) was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU

1849 Prosper-René Blondlot (3 July 1849 – 24 November 1930) was a French physicist, best remembered for his mistaken "discovery" of N rays, a phenomenon that subsequently proved to be illusory.
In order to demonstrate that a Kerr cell responds to an applied electric field in a few tens of microseconds, Blondlot, in collaboration with Ernest Bichat, adapted the rotating-mirror method that Léon Foucault had applied to measure the speed of light. He further developed the rotating mirror to measure the speed of electricity in a conductor, photographing the sparks emitted from two conductors, one 1.8 km longer than the other and measuring the relative displacement of their images. He thus established that the speed of electricity in a conductor is very close to that of light.
In 1891, he made the first measurement of the speed of radio waves, by measuring the wavelength using Lecher lines. He used 13 different frequencies between 10 and 30 MHz and obtained an average value of 297,600 km/s, which is within 1% of the current value for the speed of light. This was an important confirmation of James Clerk Maxwell's theory that light was an electromagnetic wave like radio waves.
In 1903, Blondlot announced that he had discovered N rays, a new species of radiation. The "discovery" attracted much attention over the following year until Robert W. Wood showed that the phenomena were purely subjective with no physical origin. The French Academy of Sciences awarded the Prix Leconte (₣50,000) for 1904 to Blondot, although they hedged on the reason, citing the totality of his work rather than the discovery of N-rays.
Little is known about Blondlot's later years. William Seabrook stated in his Wood biography Doctor Wood, that Blondlot went insane and died, supposedly as a result of the exposure of the N ray debacle: "This tragic exposure eventually led to Blondlot's madness and death." Using an almost identical wording this statement was repeated later by Martin Gardner, possibly without having investigated into the subject: "Wood's exposure led to Blondlot's madness and death." However, Blondlot continued to work as a university professor in Nancy until his early retirement in 1910. He died at the age of 81; at the time of the N-ray affair he was nearly 60 years old. *Wik

1866 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1930s before the war Baker's graduate students would meet at what they called Professor Baker's "Tea Party", who met once a week to discuss the areas of research in which we were all interested. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole to co-present on the subject of Polytopes in higher dimensions.

1897 Jesse Douglas (3 July 1897 – 7 September 1965) born in New York City. He did important work on Plateau's problem, which asks for the minimal surface connecting a given boundary. For this work he received a Fields medal in 1936, the first time that they were given. *VFR ..the Plateau problem... had first been posed by the Italian-French mathematician Joseph-Louis Lagrange in 1760. The Plateau problem is one of finding the surface with minimal area determined by a fixed boundary. Experiments (1849) by the Belgian physicist Joseph Plateau demonstrated that the minimal surface can be obtained by immersing a wire frame, representing the boundaries, into soapy water. Douglas developed what is now called the Douglas functional, so that by minimizing this functional he could prove the existence of the solution to the Plateau problem. Douglas later developed an interest in group theory.*TIS

1933 Frederick Justin Almgren,(July 3, 1933, Birmingham, Alabama–February 5, 1997, Princeton, New Jersey) Almost certainly Almgren's most impressive and important result was only published in 2000, three years after his death. Why was this? The paper was just too long to be accepted by any journal. Brian Cabell White explains the background in a review of the book published in 2000 containing the result:-
By the early 1970s, geometric analysts had made spectacular discoveries about the regularity of mass-minimizing hypersurfaces. (Mass is area counting multiplicity, so that if k sheets of a surface overlap, the overlap region is counted k times.) In particular, the singular set of an m-dimensional mass-minimizing hypersurface was known to have dimension at most m - 7. By contrast, for an m-dimensional mass-minimizing surface of codimension greater than one, the singular set was not even known to have m-measure 0. Around 1974, Almgren started on what would become his most massive project, culminating ten years later in a three-volume, 1700-page preprint containing a proof that the singular set not only has m-dimensional measure 0, but in fact has dimension at most (m - 2). This dimension is optimal, since by an earlier result of H Federer there are examples for which the dimension of the singular set is exactly (m - 2). ... Now, thanks to the efforts of editors Jean Taylor and Vladimir Scheffer, Almgren's three-volume, 1700-page typed preprint has been published as a single, attractively typeset volume of less than 1000 pages.*SAU

1933 William (Bill) Parry FRS (3 July 1934–20 August 2006) was an English mathematician. During his research career, he was highly active in the study of dynamical systems, and, in particular, ergodic theory, and made significant contributions to these fields. He is considered to have been at the forefront of the introduction of ergodic theory to the United Kingdom. He played a founding role in the study of subshifts of finite type, and his work on nilflows was highly regarded.*Wik

1945 Saharon Shelah (July 3, 1945 - ) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Shelah is one of the most prolific contemporary mathematicians. As of 2009, he has published nearly 900 mathematical papers (together with over 200 co-authors). His main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.*Wik

DEATHS
1749 William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November, 1711 he became a Fellow of the Royal Society, and was later its Vice-President.*Wik

1789 Jakob Bernoulli II died. *VFR Born in Basel in 1759 (17 October), the son of Johann (II).  assistant to Daniel in experimental physics

 He graduated in Jurisprudence in 1778 but also studied Maths and Physics. In 1782, he applied for Daniel's former chair but was unsuccessful.

He became secretary to an imperial representative in Venice

In 1786 he went to Petersburg, to the Academy of Science (Fuss recommended him to Dashkoff) and in 1788 became ordentlich academy member for mathematics.

He married one of Euler's granddaughters, Charlotte.

At thirty years of age, he drowned in the Neva. *Brian Daugherty

1991 Ernst Witt (June 26, 1911-July 3, 1991) was a German mathematician born on the island of Als (German: Alsen). Shortly after his birth, he and his parents moved to China, and he did not return to Europe until he was nine.
Witt's work was mainly concerned with the theory of quadratic forms and related subjects such as algebraic function fields.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-67029990117329932502020-07-02T00:00:00.000+01:002020-07-02T00:00:03.234+01:00On This Day in Math - July 2

OOPS...

Heavier-than-air flying machines are impossible.
I have not the smallest molecule of faith in aerial navigation other than ballooning,
or of the expectation of good results from any of the trials we hear of. 1895
And in a Letter to Baden-Powell (1896) Radio has no future.

William Thomson, Lord Kelvin

The 184th day of the year; 184 = 23 * 23 (concatenation of the first two primes).

The smallest number that can be written as q * pq + r * p r, where p, q and r are distinct primes (184 = 3 * 23 + 5 * 25). *Prime Curios

184 =8 x 21 + 16, so 25^2-21^2 = 184

EVENTS

1133 First trade security agreement between Pisans and Alibibn Yusof of Morocco.Under such an agreement, Guilielmo, father of Leonardo brought his young son (who would much later be called Fibonacci) to Bugia, where he would learn of the Arabic calculation system that he would introduce to his homeland in his Liber Abbaci in 1202. *Devlin, The Man of Numbers

In 1698 Thomas Savery was issued British Letters Patent No.356 for what he called "The Miner's Friend; or an engine to raise water by fire" which was the first application of steam power for pumping water. The steam powered pump had no piston. Two years earlier Savery was issued British Letters Patent No.347 for his invention for "Navigation improved; or the art of rowing ships of all rates in calms with a more easy, swift, and steady motion than oars can." ( which involved paddle-wheels driven by a capstan and which was dismissed by the Admiralty following a negative report by the Surveyor of the Navy,Edmund Dummer.)*TIS*Wik

1779 One of the earliest mentions of blackboards in Colonial America was in a letter from John Taylor, a tutor at Queens College (to become Rutgers University)to a graduate student, John Bogart, that he was asking to take over his classes while Taylor was away on military duties. "I have spoken to Mr. Briton to make a blackboard.." *Kidwell, Hastings, & Roberts; Tools of American Mathematics Teaching.

1832 Legendre writes to Nathanial Bowditch regarding his translation of LaPlace's "Mecanique Celeste" ,"Your work is not merely a translation with a commentary; I regard it as a new edition, augmented and improved, and such a one as might have come from the hands of the author himself, ... if he had been solicitously studious of being clear." LaPlace's classic is a very difficult book, and Biot, who helped him prepare it for printing said that Laplace himself would frequently get lost in following his own line of reasoning and insert, "il est aise a voir" (It is easy to see). *The Teaching and History of Mathematics in the United States, F. Cajori

1850 Stokes's theorem made its first appearance as a postscript to a letter from Sir William Thompson (Lord Kelvin) to Stokes. It first appeared publicly as question 8 on the Smith's Prize exam for 1854. Stokes drew up this competitive exam, which was taken by the best mathematics students at Cambridge University. By the time Stokes died the theorem was universally known as "Stokes's theorem." [Spivak, Calculus on Manifolds, p. viii].

1865 Sylvia Ann Howland died in 1865, leaving roughly half her fortune of some 2 million dollars (equivalent to $31,291,000 in 2016) to various legatees, with the residue to be held in trust for the benefit of Hetty Robinson, Howland's niece. The remaining principal was to be distributed to various beneficiaries on Robinson's death.

Robinson produced an earlier will, leaving her the whole estate outright. To the will was attached a second and separate page, putatively seeking to invalidate any subsequent wills. Howland's executor, Thomas Mandell, rejected Robinson's claim, insisting that the second page was a forgery, and Robinson sued.

In the ensuing case of Robinson v. Mandell, Charles Sanders Peirce testified that he had made pairwise comparisons of 42 examples of Howland's signature, overlaying them and counting the number of downstrokes that overlapped. Each signature featured 30 downstrokes and he concluded that, on average, 6 of the 30 overlapped, 1 in 5. Benjamin Peirce showed that the number of overlapping downstrokes between two signatures also closely followed the binomial distribution, the expected distribution if each downstroke was an independent event. When the admittedly genuine signature on the first page of the contested will was compared with that on the second, all 30 downstrokes coincided, suggesting that the second signature was a tracing of the first.

Benjamin Peirce, Charles' father, then took the stand and asserted that, given the independence of each downstroke, the probability that all 30 downstrokes should coincide in two genuine signatures was \frac {1}{2.666* 10^{21}} *wik

1866 Alfred Russell Wallace writes to Darwin with to suggest a name change for his basic principal of Evolution:

I wish.. to suggest ... adopting Spencer's term, (which he generally uses in preference to Natural Selection, viz, "Survival of the Fittest"
*Mario Livio, Brilliant Blunders, pg 29

1883 Helmholtz writes to Heinrich Hertz to congratulate him on his investigations. "I have read with the greatest interest your investigation on the cathode ray discharge, and cannot refrain from writing to say Bravo!" Hemholtz was not given to token praise, and was the opinion that was most valued by Hertz. *Hertz Miscellaneous Papers

1897 – Italian scientist Guglielmo Marconi obtains a patent for radio in London.*Wik

1982 Science (p. 39) reported that Steven Smale had proved that the average-case behavior of the simplex algorithm for linear programming is far better than the worse-case behavior, which is exponential. [Mathematics Magazine 56 (1983), p. 55]. *VFR

1944 Grace Hopper meets Howard Aiken for the first time. Here is her description of the meeting:

Until 1944, I had been a thoroughly respectable mathematician. I had never met a digit, and I wanted nothing to do with digits. I came into the computer business in a unique fashion. I was ordered to the Navy Liaison Officer at Harvard. I left Midshipmen School on Friday, and on Monday morning, 2nd July 1944, I reported to the Navy Liaison Officer, Harvard. He took me by the hand, and led me over to an underground laboratory. I had just acquired one-and-a-half stripes. There stood a large object, with three stripes, who took one look at me and said: "Where the hell have you been?" I spluttered, and said that I had had two days' travel time. He said: "For the last three months." I said: "Midshipmen's School", and he said he had told them it was not necessary. By this time I was practically cowering, of course, but with one-and-a-half stripes, I would stand up straight and listen to three stripes. He waved his hand and said: "That's a computing machine." I said, "Yes, Sir." What else could I say? He said he would like to have me compute the coefficients of the arc tangent series, for Thursday. Again, what could I say? "Yes, Sir." I did not know what on earth was happening, but that was my meeting with Howard Hathaway Aiken. In the long run, he taught me one very important thing. One can always make a mistake once, but it must not be made a second time. That was a very good thing to learn. He also flatly informed me that he had told the Bureau of Naval Personnel not to send him a female. At this point, and over the next few months, I learned another lesson. I could have taken the attitude of showing him, and making him take that back. Instead, I decided it would be far better to learn to work with him. This is a lesson we all need to learn: of not showing people, but learning to work with people. It certainly made a difference in getting things done in the computer field.
*SAU

1992 On July 2, fearing for the impact that a park service removal of homeowners around Elkmont, Tennessee in the Great Smokey Mountain Natl Park would have on a variety of local fireflys, Lynn Faust wrote a letter to Professor Steven Stogratz, who had recently written a paper in Science Magazine about synchronized flashing of the firelies (lightning bugs) known to exist in Southeast Asia. Ms. Faust's letter would, in Strogatz's words, "shatter a (scientific) myth that had lasted for decades."
The letter, in Ms. Faust's own hand, can be read  here. (My thanks to both Professor Strogatz and Ms. Faust for their cooperation in sharing this letter.)

2011 Simon Chua, 58, received Australia's B. H. Neumann Award for pioneering efforts in training and honing the talent of young Filipino mathematicians for the past 15 years.
The Australian Mathematics Trust (AMT) bestowed the award to Chua on July 2, 2011. The B. H. Neumann Awards are presented annually for "important contributions over many years to the enrichment of mathematics learning in Australia and its region," according to the AMT.
The award is named in honor of Bernhard H. Neumann, the so-called father of Australian mathematics, who "provided outstanding leadership, support and encouragement for mathematics and the teaching of mathematics at all levels."
Chua, who is president and co-founder of the Mathematics Trainers Guild-Philippines (MTG), is the first Asian to receive the award.
Through the MTG, Filipino students have won numerous medals in math competitions abroad including in China, United States, Singapore, Thailand, Hong Kong and Indonesia.
In 2006, Chua became the first Filipino to win the Paul Erdos Award from the World Federation of National Mathematics Competitions. *MathDL

 BIRTHS
1622 Rene-Francoise de Sluse (2 July 1622 – 19 March 1685) born. 1830 "It is true that Fourier is of the opinion that the principle object of mathematics is the public utility and the explanation of natural phenomena; but a scientist like him ought to know that the unique object of science is the honor of the human spirit and on this basis a question of [the theory of] numbers is worth as much as a question about the planetary system." Jacobi to Legendre. Big Kline, p. 1037. VFR

1842 George Thom (2 July 1842 in Forgue near Huntly, Scotland - 20 Dec 1916 in Aberdeen, Scotland) graduated from Aberdeen and then became Principal of Doveton College in Madras, India. He returned to Scotland as Vice-Principal of Chanonry School Aberdeen and then became Rector of Dollar Institution (later to become Dollar Academy). He held this post for 24 years. He was a founder member of the EMS and became the fifth President in 1886. *SAU

 1847 Andrew Gray graduated from Glasgow University and was appointed assistant and secretary to Lord Kelvin. He became Professor of Physics at University College Bangor and then returned to Glasgow as Kelvin's successor. He produced many books and papers in both mathematics and physics.*SAU

1852 Birthdate of William Burnside, whose Theory of Groups (1897, 1911) is now a classic. His suspicion that every group of odd order is solvable was proved in 1962 by Walter Feit and John G. Thompson. *VFR He is known mostly as an early contributor to the theory of finite groups. In 1897 Burnside's classic work Theory of Groups of Finite Order was published. The second edition (published in 1911) was for many decades the standard work in the field. A major difference between the editions was the inclusion of character theory in the second.
Burnside is also remembered for the formulation of Burnside's problem (which concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it) and for Burnside's lemma (a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Cauchy.

1862 Sir William Henry Bragg (2 July 1862 – 10 March 1942) was a pioneer British scientist in solid-state physics who was a joint winner (with his son Sir Lawrence Bragg) of the Nobel Prize for Physics in 1915 for research on the determination of crystal structures. During the WW I, Bragg was put in charge of research on the detection and measurement of underwater sounds in connection with the location of submarines. He also constructed an X-ray spectrometer for measuring the wavelengths of X-rays. In the 1920s, while director of the Royal Institution in London, he initiated X-ray diffraction studies of organic molecules. Bragg was knighted in 1920. *TIS

1885 Émile Henriot (2 July 1885 - 1 February 1961) was a French chemist notable for being the first to show definitely that potassium and rubidium are naturally radioactive.
He investigated methods to generate extremely high angular velocities, and found that suitably placed air-jets can be used to spin tops at very high speeds - this technique was later used to construct ultracentrifuges.
He was a pioneer in the study of the electron microscope. He also studied birefringence and molecular vibrations.
He obtained his DSc in physics in 1912 the Sorbonne, Paris, under Marie Curie. *Wik

1906 Hans Bethe, (July 2, 1906 – March 6, 2005) German-born American theoretical physicist who helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. Bethe did work relating to armour penetration and the theory of shock waves of a projectile moving through air. He studied nuclear reactions and reaction cross sections (1935-38). In 1943, Oppenheimer asked Bethe to be the head of the Theoretical Division at Los Alamos on the Manhattan Project. After returning to Cornell University in 1946, Bethe became a leader promoting the social responsibility of science. He received the Nobel Prize for Physics (1967) for his work on the production of energy in stars. *TIS

DEATHS
1566 Nostradamus, French astrologer died on this day (b. 1503). I wonder if he predicted THIS in his prophacies.

1591 Vincenzo Galilei ( c. 1520 – 2 July 1591) Italian, music theorist, lutenist and composer, who as the father of Galileo Galilei, adopted experimentation to prove aspects of acoustics, and may thus have influenced his son, Galileo, away from pure, abstract mathematics and towards making experiments and investigation. Vincenzo's discoveries in acoustics included some of the physics of vibrating strings and columns of air. In particular he was the first to show that the ratio of an interval was proportional to string lengths but varied as the square of the tension applied to the strings and as the cubes of volumes of air. He recognized the superiority of equal tempered tuning and compiled a codex of pieces illustrating the use of all 24 major and minor keys as early as 1584.*TIS

1613 Bartholomeo Pitiscus (August 24, 1561 – July 2, 1613) was a Polish theologian who first coined the word Trigonometry. *SAU Pitiscus achieved fame with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introduced the word "trigonometry" to the English and French languages, translations of which had appeared in 1614 and 1619, respectively. It consists of five books on plane and spherical trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619).*Wik

 1621 Thomas Harriot (Oxford, c. 1560 – London, 2 July 1621) died of a cancerous ulcer on his left nostril. While in America in 1586 he learned to "drink" tobacco smoke from the Indians. This probably makes him the earliest recorded tobacco fatality. He is best known for his contributions to algebra, including the invention of the symbol for less than, \( \lt \) and greater than, \( \gt \) . He might have adopted this symbol from a decoration on an Indian's back. See C. L. Smith, "On the origin of '<' and '>'," The Mathematics Teacher, 57(1964), 479–481 for a picture of this Indian.*VFR
He also is credited with the mathematical symbol for "therefore" \(\therefore \) His executors posthumously published his Artis Analyticae Praxis on algebra in 1631; Nathaniel Torporley was the intended executor of Harriot's wishes, but Walter Warner in the end pulled the book into shape. It may be a compendium of some of his works but does not represent all that he left unpublished (more than 400 sheets of annotated writing). It isn't directed in a way that follows the manuscripts and it fails to give the full significance of Harriot's writings.*Wik He introduced a simplified notation for algebra and his fundamental research on the theory of equations was far ahead of its time. He was able to solve equations, even with negative or complex roots. However, he published no mathematical work in his lifetime. (Artes analyticae praxis, posthumous, 1631). Especially early in his career, he worked on navigation for his patron Walter Raleigh. Harriot carried out extensive telescopic observations of the satellites of Jupiter and of sunspots. When investigating optics, he discovered the sine law and measured the refractive indices of 13 different substances. He investigated free motion and motion resisted in air, and ballistic curves.*TIS Thomas Harriot was an English mathematician who did outstanding work on the solution of equations, recognising negative roots and complex roots in a way that makes his solutions look almost like a present day solution.*SAU
The solution of quadratic equations by the method of factoring was often referred to as Harriot's method because of his introduction of the method in his writing.
It is not possible today to find Harriot's grave. Although he was buried near the altar of St Christopher le Stocks in London,the church was destroyed in the great fire of 1666. There is a plaque in the entrance hall of the Bank of England, which is close to the site of Harriot's grave. It reproduces the original Latin wording of his epitaph.(p474) An English translation would read:

Stay, traveler, lightly tread;
Near this spot lies all that was mortal
Of that most celebrated man Thomas Harriot.
He was that most learned Harriot . . .
Who cultivated all the sciences and excelled in all . . .
A most studious searcher after truth . . .

1644 William Gascoigne (1612 – 2 July 1644) was an English astronomer, mathematician and maker of scientific instruments from Middleton, Leeds who invented the micrometer. He was one of "nos Keplari" a group of astronomers in the north of England who followed the astronomy of Johannes Kepler which included, Jeremiah Horrocks and William Crabtree. Gascoigne's micrometer is shown at right from a drawing by Hooke. Gascoigne, was working on a Keplerian optical arrangement when a thread from a spider's web happened to become caught at exactly the combined optical focal points of the two lenses. When he looked through the arrangement Gascoigne saw the web bright and sharp within the field of view. He realized that he could more accurately point the telescope using the line as a guide, and went on to invent the telescopic sight by placing crossed wires at the focal point to define the centre of the field of view. Gascoigne died at the Battle of Marston Moor, Yorkshire, *Wik

1874 Gouverneur Emerson American physician, statistician and agriculturalist who prepared a series of tables of deaths and causes in Philadelphia, during thirty years from 1807. These showed, for example, the excessive mortality of males during childhood. He began practice in Philadelphia on 4 Aug 1820, where yellow fever broke out a few weeks later, with 73 deaths by that fall. Emerson recorded cases, dates, locations, and outcomes. He concluded no current medical treatments was especially effective. When smallpox reappeared there, with 325 deaths in 1824, Emerson drafted a bill for control measures. There were only 6 cases of smallpox in the city in 1825, and 3 in 1826. In retirement, he turned to peach culture, and studied phosphate and guano fertilizers. *TIS

1947 Nikolai Grigorievich Chebotaryov (15 June [O.S. 3 June] 1894 – 2 July 1947) proved his density theorem generalising Dirichlet's theorem on primes in an arithmetical progression*SAU

1963 Seth Barnes Nicholson (November 12, 1891 – July 2, 1963) was an American astronomer best known for discovering four satellites of Jupiter. As a graduate student at the University of California, while photographing the recently- discovered 8th moon of Jupiter with the 36-inch Crossley reflector, he discovered a 9th (1914). During his life career at Mt.Wilson Observatory, he discovered two more Jovian satellites (1938) and the 12th (1951), as well as a Trojan asteroid, and computed orbits of several comets and of Pluto. His main assignment at Mt. Wilson was observing the sun with the 150-foot solar tower telescope, and he produced annual reports on sunspot activity and magnetism for decades. With Edison Pettit, he measured the temperatures of the moon, planets, sunspots, and stars in the early 1920s. *TIS

2002 Daniel Chonghan Hong (3 Mar 1956; 2 Jul 2002 at age 46) Korean theoretical physicist specializing in statistical physics and nonlinear dynamic physics, who with colleague Hugo Caram, originated the void diffusing-void model of granular flow, which is recognized as an effective theoretical treatment for a broad range of dynamical phenomena in granular media. In general, his work ranged from percolation network, viscous fingering, granular flows to traffic equations. He studied and taught in America from 1981, and wrote articles for popular magazines on various topics. He died at the young age of 46 of cardiac arrest. *TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-89725102549076180822020-07-01T00:00:00.000+01:002020-07-01T00:00:02.222+01:00On This Day in Math - July 1

Mathematics, rightly viewed, possesses not only truth, but supreme beauty

a beauty cold and austere, like that of sculpture,

without appeal to any part of our weaker nature,

without the gorgeous trappings of painting or music,

yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

 The true spirit of delight, the exaltation,
the sense of being more than Man,

which is the touchstone of the highest excellence,

is to be found in mathematics as surely as in poetry.
--BERTRAND RUSSELL,

The 183rd day of the year; the concatenation of 183 and 184, 183184 is a perfect square. There are no smaller numbers for which the concatenation of two consecutive numbers is square. (Students might seek the next such pair of numbers. They are small enough to be year dates)

The sum of the first 183 primes minus 183 is prime.

183 is the eighth of the 12 year-days which are perfect totient numbers. (There are only 57 such numbers under 103). A list of the perfect totient numbers seems to suggest that all of them are multiples of three, but then you get to 4375, the smallest perfect totient number that is not divisible by 3.[a perfect totient number is a number that is the sum of it's iterated totients, that is, the number of integers smaller than, and relatively prime to 183 + the number smaller than and less than that result, + ... down to one, "For example, start with 327. Then φ(327) = 216, φ(216) = 72, φ(72) = 24, φ(24) = 8, φ(8) = 4, φ(4) = 2, φ(2) = 1, and 216 + 72 + 24 + 8 + 4 + 2 + 1 = 327 " *Wik
Get more Math Facts for every year date here

EVENTS

1349 Sometimes, a little astronomical knowledge can be a dangerous thing, even to those who possess it. A tale from medieval England is passed down from the chronicles of the scholar Thomas Bradwardine of a witch who attempted to force her will on the people through knowledge of an impending eclipse. Bradwardine, who had studied astronomical predictions of Arabian astronomers, saw through the ruse, and matched the prediction of the July 01, 1349 A.D. lunar eclipse with a more precise one of his own. No word survives as to the fate of the accused, but one can only suspect banishment or worse.*listosaur.com

1694 Opening of the University of Halle in Germany. Georg Cantor later taught there. *VFR

1770 – Lexell's Comet passed closer to the Earth than any other comet in recorded history, approaching to a distance of 0.0146 a.u. *OnThisDay & Facts @NotableHistory discovered by astronomer Charles Messier

1798 Napoleon's fleet reached Alexandria, bearing Monge and Fourier.*VFR

1819 William George Horner's (1786–1837) method of solving equations is presented to the Royal Society.*VFR In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form. Horner's method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini's rule. Student's often learn this process as synthetic division. *Wik

1847 The United States issued its first two postage stamps. They pictured Benjamin Franklin and George Washington respectively [Scott #1-2]. *VFR

1852 Dirichlet delivers a memorial lecture at the Berlin Academy in honor of his close friend Jacobi, calling him the greatest member of the Academy since Lagrange. *VFR

1856 Weierstrass appointed Professor of Mathematics at the Royal Polytechnic School in Berlin. *VFR

In 1858, the Wallace-Darwin theory of evolution was first published at the Linnaean Society in London*. The previous month Charles Darwin received a letter from Alfred Wallace, who was collecting specimens in the East Indies. Wallace had independently developed a theory of natural selection - which was almost identical to Darwin's. The letter asked Darwin to evaluate the theory, and if worthy of publication, to forward the manuscript to Charles Lyell. Darwin did so, almost giving up his clear priority for he had not yet published his masterwork The Origin of Species. Neither Darwin nor Wallace were present for the oral presentation at the Linnaean Society, where geologist Charles Lyell and botanist Joseph Hooker presented both Wallace's paper and excerpts from Darwin's unpublished 1844 essay.*TIS
In his annual report the following May, society president Thomas Bell wrote, "The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear." *Futility Closet

1873 From a letter dated July 1, 1873, in the Coast Survey files in the National Archives in Washington. Peirce writes, "Newcomb, in a paper .... says he finds that pendulums hung by springs twist and untwist as they oscillate and says this will affect the time of oscillation."The Charles S. Peirce-Simon Newcomb Correspondence by Carolyn Eisele.

1894 The New York Mathematical Society changed its name to the American Mathematical Society to reflect its national charter. [AMS Semicentennial Publications, vol. 1, p. 74]. *VFR

1908 International agreement to use SOS for distress signal signed. An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

1918 Florian Cajori (1859–1930) appointed professor of the history of mathematics at the University of California, Berkeley, one of the few such chairs in the the world. During the next twelve years he published 159 papers on the history of mathematics. *VFR

1948 The Bell System Technical Journal publishes the first part of Claude Shannon's "A Mathematical Theory of Communication", regarded as a foundation of information theory, introducing the concept of Shannon entropy and adopting the term Bit. *Wik

1964 The New York Times, in a full page ad, announced that Paul Newman and Joanne Woodward would play a game on an elliptical pool table. It had a pocket at one focus so that if the ball passed over the other focus it would bank off the rail into the pocket. [UMAP Journal, 4(1983), p. 176; Recreational Mathematics Magazine, no. 14, January-February 1964] *VFR

1980 A method of trisecting any given acute angle Origami is demonstrated. Hisashi Abe invented this idea and published in July, 1980 edition of the Japanese journal "Suugaku Seminar"(Mathematics Seminar). For this method, and more ways to trisect the angle, see this post.

*Takaya Iwamoto

2001 The last occurrence that there were 3 eclipses in one month, and of which two solar eclipses. For July 2000 being on 1st a partial solar eclipse, 16th a total lunar eclipse, and 31st a partial solar eclipse. The next occurrence with a month with 3 eclipses will be December 2206 with a partial solar eclipse on 1st and 30th and a total lunar eclipse on 16th. Ref. Fred Espenak 06/00 SEML. *NSEC

2010 Grigori Yakovlevich Perelman turned down the Clay Millineum prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. On March 18 It had been announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. *Wik

2015 Michael Elmhirst Cates, becomes the 19th Lucasian Professor of Mathematic at the University of Cambridge. Professor Cates is a physicist and Professor of Natural Philosophy and Royal Society Research Professor at the University of Edinburgh. Previous recognitions for Prof. Cates include Maxwell Medal and Prize (1991), the Paul Dirac Medal and Prize (2009), and the Weissenberg Award (2013). He will assume the chair from another Physicist, Michael Green. He follows a line that began with Isaac Barrow and Isaac Newton and includes Charles Babbage, Paul Dirac, and Stephen Hawking

BIRTHS
1646 Gottfried Wilhelm Leibniz (July 1, 1646 – November 14, 1716) born in Leipzig, Germany. Leibniz occupies a prominent place in the history of mathematics and the history of philosophy. He developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685[4] and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers. In philosophy, Leibniz is mostly noted for his optimism, e.g. his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or a priori definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He wrote works on politics, law, ethics, theology, history, philosophy, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. As of 2010, there is no complete gathering of the writings of Leibniz.*Wik

1779 John Farrar (July 1, 1779 – May 8, 1853) born at Lincoln, Massachusetts. As Hollis professor of mathematics and natural philosophy at Harvard, he was responsible for a sweeping modernization of the science and mathematics curriculum, including the change from Newton's to Leibniz's notation for the calculus. *VFR

1788 Jean Victor Poncelet (July 1, 1788 – December 22, 1867) born in Metz, France. He taught engineering and mechanics, but had a hobby of much greater interest—projective geometry. *VFR French mathematician and engineer whose study of the pole and polar lines associated with conic led to the principle of duality. While serving as an engineer in Napoleon's 1812 Russian campaign as an engineer, he was left for dead at Krasnoy, but then captured. During his imprisonment he studied projective geometry and wrote a treatise on analytic geometry. Released in 1814, he returned to France, and in 1822 published Traité des propriétés projectives des figures in which he presented his fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity. As a professor of mechanics (1825-35), he applied mechanics to improve waterwheels and was able to double their efficiency.*TIS

1848 Emil Weyr (1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1906 Jean Dieudonn´e (1 July 1906 – 29 November 1992) born. *VFR French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS

DEATHS

1957 Donald McIntosh (Banffshire, 13 January 1868 – Invernesshire, 1 July 1957) graduated from the University of Aberdeen and taught at George Watson's Ladies College in Edinburgh. He was appointed a Director of Education. He became Secretary of the EMS in 1899 and President in 1905. *SAU

1963 Bevan Braithwaite Baker (1890 in Edinburgh, Scotland - 1 July 1963 in Edinburgh, Scotland) graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London. *SAU

1971 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

1983 Richard Buckminster Fuller (July 12, 1895 – July 1, 1983) was a U.S. engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). Fuller also invented a wide range of other paradigm-shifting machines and structural systems. He was especially interested in high-strength-to-weight designs, with a maximum of utility for minimum of material. His designs and engineering philosophy are part of the foundation of contemporary high-tech design aesthetics. He held over 2000 patents.*TIS
This is another one who died within two weeks of his date of birth. I must organize data on this...

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-52466954440960161562020-06-30T00:00:00.000+01:002020-06-30T00:00:01.260+01:00On This Day in Math - June 30

You know we all became mathematicians for the same reason:

we were lazy.
Max Rosenlicht

The 182nd day of the year; there are 182 connected bipartite graphs with 8 vertices. *What's So Special About This Number

The 182nd prime (1091) is the smaller of a pair of twin primes (the 40th pair, actually) *Math Year-Round @MathYearRound(Students might convince themselves that it was not necessary to say it was the smaller of the pair.)

Language time:

182 is called a pronic, promic, or heteromecic and even an oblong number. Pronic Numbers are numbers that are the product of two consecutive integers; 2, 6, 12, 20, ..(doubles of triangular numbers). Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history.

Oblong is from the Latin ob (excessive) + longus (long). The word oblong is also commonly used as an alternate name for a rectangle. In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word eteromhkes[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. . "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral...". (note that with this definition, a square is not a subset of rectangles.)

More Math Facts for every year date here.

EVENTS
1601. Johannes Kepler uses a camera obscura of his own design set up in a tent to view solar eclipses in Graz on 30 June 1601 . Infamously whilst he was busy observing the solar eclipse on the market place in Graz a thief stole his purse with thirty silver florins. It was Kepler that coined the name camera obscura. The earliest use of the term "camera obscura" is found in his 1604 book, Ad Vitellionem Paralipomena.*RMAT Art Historian J V Field has suggested that in the same book he invented two other math/science ideas: "The two inventions in question are the point at infinity' and the retinal image. The first is apparently merely mathematical whereas the second is certainly conceived as having physical existence, but the two processes of invention are both closely bound up with Kepler's conception of the role of mathematical reasoning in natural philosophy, and they consequently have much in common. "

1686 The Royal Society made the decision to publish De Historia Piscium, a lavishly-illustrated history of fishes by John Ray and Francis Willughby. The books was beautiful, but turned out to be such a poor seller that the Society almost went bankrupt. At one point Edmond Halley's salary could not be paid during the same period when he was trying to get Newton to complete his epic masterpiece, The Principia. Fortunately for science, Halley accepted a deal for something like one-hundred copies of the fish book, and then mostly funded the publication of Newton's classic himself over the next year. I don't know if Halley ever managed to sell any of the De Historia Piscium that he took in lieu of salary. *PB old notes.

1737 John Harrison, after positive results on the test of his first sea-clock, receives the first money awarded by the Board of Longitude (23 years after the Act to create the Board). Harrison received 500 Pounds, 250 Pounds to be paid immediately, and another 250 Pounds after completing a second clock that passes testing at sea. *Derek Howse, Britain's Board of Longitude: The Finances 1714-1828

1742 Euler replied (see June 7 post) in a letter dated 30 June 1742, and reminded Goldbach of an earlier conversation they had ("...so Ew vormals mit mir communicirt haben.."), in which Goldbach remarked his original (and not marginal) conjecture followed from the following statement, "Every even integer greater than 2 can be written as the sum of two primes," which is thus also a conjecture of Goldbach. In the letter dated 30 June 1742, Euler stated:"Dass ... ein jeder numerus par eine summa duorum primorum sey, halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe necht demonstriren kann." ("every even integer is a sum of two primes. I regard this as a completely certain theorem, although I cannot prove it.")*Wik
As of this date, no one else has proved it either. It is one of the oldest open questions in mathematics.
Euler also claimed that prime numbers of the form 4n+ 1 are represented uniquely as a sum of two squares. He also mentions that 641 divides 232 + 1, thereby disproving Fermat's claim that all numbers Fermat numbers F(n)= \( 2^{2^n}+1\) are prime. Years later we have not found another which is prime.

1812 Congress authorized the President of the US to issue interest bearing Treasury Notes for the first time in history. The interest was fixed at "five and two-fifths per centum a year." *Kane, Famous First Facts (students might calculate the present value of a $100 investment on that date compounded to the present)

1808 Sir Humphrey Davy announced the discovery of magnesium (Mg), calcium (Ca), strontium (Sr) and barium (Ba) on this day in 1808
Throughout his career Davy isolated several metal elements from their compounds through the process of electrolysis, using a primitive electrical battery called a voltaic pile.
Davy also announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days ealier, on 21 Jun 1808. *TIS

1860 Oxford evolution debate took place at the Oxford University Museum on 30 June 1860, seven months after the publication of Charles Darwin's On the Origin of Species. Several prominent British scientists and philosophers participated, including Thomas Henry Huxley, Bishop Samuel Wilberforce, Benjamin Brodie, Joseph Dalton Hooker and Robert FitzRoy.
The debate is best remembered today for a heated exchange in which Wilberforce supposedly asked Huxley whether it was through his grandfather or his grandmother that he claimed his descent from a monkey. Huxley is said to have replied that he would not be ashamed to have a monkey for his ancestor, but he would be ashamed to be connected with a man who used his great gifts to obscure the truth *Wik

1894 Tower Bridge opens, In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS

1905 Albert Einstein's paper, "On the electrodynamics of moving bodies" (special relativity) is received at the Journal Annalen der Physik.
"Einstein develops the special theory of relativity in this paper. His concern, as he makes clear in the introduction, is that then current electrodynamics harbors a state of rest, the ether state of rest, and the theory gives very different accounts of electrodynamic processes at rest or moving in the ether. But experiments in electrodynamics and optic have provided no way to determine which is the ether state of rest of all inertial state of motion. Einstein shows that Maxwell-Lorentz electrodynamics has in fact always obeyed a principle of relativity of inertial motion. We just failed to notice it since we tacitly thought that space and time had Newtonian properties, not those of special relativity. " *John D Norton, Einstein, 1905, Pitt.edu

1908 A Comet(?) explodes above Tunguska, Siberia. *VFR In 1908, at around 7:15 am, northwest of Lake Baikal, Russia, a huge fireball nearly as bright as the Sun was seen crossing the sky. Minutes later, there was a huge flash and a shock wave felt up to 650 km (400 mi) away. Over Tunguska, a meteorite over 50-m diameter, travelling at over 25 km per second (60,000 mph) penetrated Earth's atmosphere, heated to about 10,000 ºC and detonated 6 to10 km above the ground. The blast released the energy of 10-50 Megatons of TNT, destroying 2,200 sq km of forest leaving no trace of life. The Tunguska rock came out of the Taurid Meteor storm that crosses Earth's orbit twice a year. The first scientific expedition for which records survive was made by Russian mineralogist Leonid Kulik in 1927. *TIS

1945 The first distribution of John von Neumann's First Draft of a Report on the EDVAC, containing the first published description of the logical design of a computer with stored-program and instruction data stored in the same address space within the memory (von Neumann architecture)*Wik

1946 ENIAC formally accepted by the government. See 2 October 1955*VFR

In 1948, the transistor was demonstrated by its inventors, John Bardeen and Walter Brattain, scientists at the Bell Telephone Laboratory in Murray Hill, NJ.* It was a simple, tiny device utilizing the electronic semiconducting properties of a germanium wafer. The transistor represented a significant advance in technology. As it was developed over the next few years, it was incorporated into electronic equipment as a functional replacment for the vacuum tube. Such use of transistors provided great savings in space and electrical power consumption. This made possible the small portable, battery-powered transistor radios which were sold to the public by late 1954.*TIS

1954 Solar eclipse in Britain. The about 3 minutes totality was visible in the Faroes and the southern line was crossing the northernmost Shetland. Many people in England do remember this eclipse and is often mistaken as total for those who saw a large partial eclipse. The eclipse track traveled across Norway, Sweden, Lithuania, Byelorussia, and Russia. *NSEC

1955 Sperry Rand formed. In 1955 Sperry acquired Remington Rand and renamed itself Sperry Rand. Acquiring then Eckert-Mauchly Computer Corporation and Engineering Research Associates along with Remington Rand, the company developed the successful UNIVAC computer series and signed a valuable cross-licensing deal with IBM. *Wik

1972 The International Time Bureau adds the first leap second to Coordinated Universal Time (UTC). *Wik

1973
A group of scientist boarded a prototype French Concorde airplane to chase a solar eclipse. The eclipse promised a luxurious view if you stood at the right place on the planet: a maximum of 7 minutes and 4 seconds as the moon passed over the Sahara Desert. It would be just 28 seconds short of the longest possible eclipse viewable from Earth; in the preceding several hundred years, there had only been one eclipse longer than this one, and there would not be a longer total solar eclipse until June 2150. Not satisfied with one of the longest eclpises in recent history, the group managed to negotiate a viewing flight on the still in testing Concorde. Closing in at maximum velocity, Concorde would swoop down from the north and intercept the shadow of the moon over northwest Africa. Traveling together at almost the same speed, Concorde would essentially race the solar eclipse across the surface of the planet, giving astronomers an unprecedented opportunity to study the various phenomena made possible by an eclipse. In one flight, Concorde had given astronomers more eclipse observing time than all the previous expeditions last century—generating three articles in Nature and a wealth of new data. *Motherboard

2011 Mr Ballew finally hung up his spurs and rode off into the sunset with his sweetheart, Jeannie.

2015 A Leap second is added to the clock in the last second before 8pm, so there will be a minute with 61 seconds. Between 1972 and 2012, a leap second has been inserted about every 18 months, on average. However, the spacing is quite irregular and apparently increasing: there were no leap seconds in the seven-year interval between January 1, 1999 and December 31, 2005, but there were nine leap seconds in the eight years 1972–1979. *Wik

BIRTHS

1748 Dominique Cassini (30 June 1748 – 18 October 1845) was a French mathematician and surveyor who worked on his father's map of France. He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later.
He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy's watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father's map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments.
Cassini's Mémoires pour servir à l'histoire de l'observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik

1791 Félix Savart (June 30, 1791, Charleville-Mézières, Ardennes – March 16, 1841, Paris) became a professor at Collège de France in 1836 and was the co-originator of the Biot-Savart Law, along with Jean-Baptiste Biot. Together, they worked on the theory of magnetism and electrical currents. Their law was developed about 1820. The Biot-Savart Law relates magnetic fields to the currents which are their sources. Félix Savart also studied acoustics. He developed the Savart wheel which produces sound at specific graduated frequencies using rotating disks.
Félix Savart is the namesake of the unit of measurement for musical intervals, the savart, though it was actually invented by Joseph Sauveur.*Wik

1856 Cargill Knott (June 30, 1856 – October 26, 1922) born. He graduated from Edinburgh University and was then an assistant in the Physics department. With Barclay and Fraser he was one of the writers who originally proposed the founding of the EMS. He went to the Imperial University in Tokyo as Professor. He returned to a lectureship in Edinburgh and eventually became a Reader in Applied Mathematics. He became Secretary and Treasurer of the EMS in 1883 and President in 1893 and 1918.*SAU

1880 Birthdate of Rudolf Fueter  (30 June 1880 in Basel; 9 August 1950 in Brunnen) who worked with functions with non-commutative variables and also in number theory. *SAU

DEATHS

1660 William Oughtred, (5 March 1575 – 30 June 1660) inventor of the slide rule (1621) and a staunch royalist, died in a transport of joy on hearing the news of the restoration of Charles II. Augustus De Morgan later remarked, "It should be added, by way of excuse, that he was eighty-six years old." *VFR an Episcopal minister who invented the earliest form of the slide rule, two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner rule with tongue-in-groove linear construction came later. He introduced the familiar multiplication sign x in a 1631 textbook, along with the first use of the abbreviations sin, cos and tan.*TIS

1919 John William Strutt 3rd Baron of Rayleigh (of Terling Place)(12 November 1842 – 30 June 1919) was an English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his investigations into the densities of the most important gases and his successful isolation of argon, an inert atmospheric gas.*TIS

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = email@example.com:blogger.com,1999:blog-2433841880619171855.post-39614476455683614982020-06-29T00:00:00.000+01:002020-06-29T00:00:01.867+01:00On This Day in Math - June 29

Jeannie, Happy birthday.
The 181st day of the year; 181 is the 9th palindromic prime number.

1f you square 181 and add 7, you get 32768. So what? Well 32768 is 215. STILL not impressed? The only other numbers for which n2 + 7 is a power of 2 are 1, 3, 5, and 11.... full stop. And to take this beyond the coincidental, if you replace the 7 with any other integer, there will never be more than two solutions.

and the 181-digit palindromic number made up of all 7's except for the center being 181 (7777...7718177...77777) is a palindromic prime with a palindromic prime decimal length.

181 is the both the difference and the sum of consecutive squares:
\( 181 = 91^2 – 90^2 = 9^2 + 10^2 \)

 Every natural number greater than 181 can be written as sum of cubes of the first two primes. (students might be asked to find all examples of numbers less than 181 that can be written in this fashion, such as 35= 23 + 33)

More Math Facts for every year day here.

EVENTS

In 3123 BC, a Sumerian astronomer saw a devastating asteroid, perhaps a half-mile wide, according to an interpretation of a clay tablet, made by researchers from Bristol University, reported in The Times on 31 Mar 2008. The ancient date was indicated by a computer recreation of the night sky using symbols on the tablet recording the positions of constellations The Planiform tablet found by Henry Layard at Nineveh, likely a 700 BC copy of the astronomer's notes, described in cuneiform a "white stone bowl approaching" that "vigorously swept along." The asteroid probably crashed into the Austrian Alps, leaving a swath of cataclysmic damage such as, for example, the Genesis destruction of Sodom and Gomorrah.*TIS

1456 According to one story that first appeared in a 1475 posthumous biography and was subsequently embellished and popularized by Pierre-Simon Laplace, Callixtus III excommunicated the 1456 apparition of Halley's Comet, believing it to be an ill omen for the Christian defenders of Belgrade from the besieging armies of the Ottoman Empire. No known primary source supports the authenticity of this account. The 29 June 1456 papal bull of Callixtus III calling for a public prayer for the success of the crusade, makes no mention of the comet. By 6 August, when the Turkish siege was broken the comet had not been visible in either Europe or Turkey for several weeks. *Wik

(John Francis Rigaud, 1785)*Wik

1785 Letitia Ann Sage became the first British woman to fly. From St George's Fields on the south side of the Thames, Vincenzo Lunardi and his partner Biggin, with two invitees, Mrs. Sage and a Colonel Hastings were supposed to make the flight, but the Hydrogen balloon wouldn't take off because of the weight. (Mrs Sage, a actress and model was also a somewhat large woman, rumored to weigh appx 200 pounds.) Lunardi and Hastings stepped down, and the balloon took off with Biggin and Mrs. Sage. It landed 90 minutes later, near Harrow, where the two aeronauts had to be rescued by a group of boys from Harrow School from the angry farmer whose crops were damaged. *Wik (There were even suggestions that rather more amorous events had occurred in the flight.)

1799 The Royal Charter for the Royal Institute is promised. Ever since its founding year the Royal Institution has maintained close links with the Royal Family. On 29 June 1799, George Finch, Earl of Winchilsea (1752-1826), the President of what had until then had been called simply the "Institution" reported to a meeting of its committee of Managers 'that he had had the Honour of mentioning this Institution to his Majesty [George III], and that his Majesty was graciously pleased to honour it with His Patronage and to allow it to be called the Royal Institution'. The actual charter was presented on January 13 in 1800. *Royal Institute web page

1803 An open letter to the public, and the Congress of the United States on the topic "Of The Construction of Iron Bridges" is posted by Thomas Paine. Paine had discussed this work with President Jefferson in a letter while he was in England. *The National Intelligencer and Washington Advertiser, (Washington, DC) Wednesday, June 29, 1803; Issue CCCCXIX;

1877 After proving that the points in a square can be put in one-to-one correspondence with the points on a line segment Cantor wrote his friend Dedekind "Je le vois, mais je ne le crois pas." (I see it, but I don't believe it.) [Dauben, Georg Cantor, p. 55]*VFR

1927 Gellivara 1073: Minor planet discovered September 14, 1923 by Johann Palisa at Vienna. Named for the small town Gällivare in Swedish Lapland where in the year 1927 astronomers from several countries observed the Total Solar Eclipse of 1927 Named by the astronomer J. Rheden and endorsed by Anna Palisa.*NSEC
A Poster advertising viewing of Solar Eclipse from London, Midland, and Scotland Railway *GreatAmericanEclipse @AmericanEclipse

In 1954, the Atomic Energy Commission, by a vote of 4 to1 decided against reinstating Dr. J. Robert Oppenheimer's access to classified information. The Atomic Energy Act of 1946 required consideration of "the character, associations, and loyalty" of the individuals engaged in the work of the Commission. Substantial defects of character and imprudent and dangerous associations, particularly with known subversives who place the interests of foreign powers above those of the United States, were considered reasons for disqualification. The Commission regarded his associations with persons known to him to be Communists exceeded tolerable limits of prudence and self-restraint, and lasted too long to be justified as merely the intermittent and accidental revival of earlier friendships.*TIS

1956 The interstate highway system was signed into law by President Eisenhower. Even (odd) numbered roads run East–West (North–South) with the numbers increasing from South to North (West to East). Roads with three digit numbers are loops around cities (when the first digit is even) or spurs (first digit odd); In either case the last two digits are the main road number. *VFR
Eisenhower had seen the speed and efficiency in moving troops and equipment on the four-lane autobahns in Germany during WW II. The idea of federal support of interstate limited-access routes in the U.S. had begun with a study under the Federal-Aid Highway Act of 1938. Little progress was made on building these roads while federal funding was low. When the Federal-Aid Highway Act of 1956 committed federal funds to the States for 90% of the cost, construction began in earnest for the System of Interstate and Defense Highways having at least four lanes with no at-grade railroad crossings. *TIS

2016 - My Jeannie is celebrating her birthday today, and I'm celebrating having her in my life... all the good I ever do is a reflection of a single sun.

BIRTHS

1716 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page

1818 Pietro Angelo Secchi (29 June 1818 – 26 February 1878) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall. *TIS

1868 George Ellery Hale  (June 29, 1868 – February 21, 1938) born. American astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200" reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him - the Hale telescope.*TIS

1893 Prasanta Chandra Mahalanobis FRS[1] (29 June 1893 – 28 June 1972) was an Indian scientist and applied statistician. He is best remembered for the Mahalanobis distance, (a statistical measure of the distance between a point P and a distribution D, - a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. ) and for being one of the members of the first Planning commission of free india. He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute, and contributed to the design of large-scale sample surveys *Wik

1893 Eduard Cech, (June 29, 1893 – March 15, 1960) Czech topologist born in Stračov, Bohemia (then Austria-Hungary, now Czech Republic). His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1904 Topologist Witold Hurewicz (June 29, 1904 - September 6, 1956) born. Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative...". *Wik He died in 1956 when he fell off a pyramid while attending a conference in Mexico.

1942 K. Jon Barwise (June 29, 1942 – March 5, 2000) an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.*Wik

DEATHS
1895 T(homas) H(enry) Huxley (4 May 1825 – 29 June 1895) was an English biologist , known as "Darwin's Bulldog" for his promotion of Darwinism which led him to an advocacy of agnosticism (a word he coined). At the age of 12 he was reading advanced works on geology, and by early adolescence he recorded the results of simple self-conducted experiments. As a ship's assistant surgeon on HMS Rattlesnake he studied marine specimens by microscope. During the 1850's he published papers on animal individuality, the cephalous mollusks (ex. squids), the methods of paleontology, and the methods and principles of science and science education. *TIS

1924 Robert Simpson Woodward (July 21, 1849–June 29, 1924) was an American physicist and mathematician, born at Rochester, Michigan. He graduated C.E. at the University of Michigan in 1872 and was appointed assistant engineer on the United States Lake Survey. In 1882 he became assistant astronomer for the United States Transit of Venus Commission. In 1884 he became astronomer to the United States Geological Survey, serving until 1890, when he became assistant in the United States Coast and Geodetic Survey. In 1893 he was called to Columbia as professor of mechanics and subsequently became professor of mathematical physics as well. He was dean of the faculty of pure science at Columbia from 1895 to 1905, when he became president of the Carnegie Institution of Washington, whose reputation and usefulness as a means of furthering scientific research was widely extended under his direction. He was elected to the National Academy of Sciences in 1896. In 1898-1900 he was president of the American Mathematical Society, and in 1900 president of the American Association for the Advancement of Science. In 1915 he was appointed to the Naval Consulting Board. He died in 1924 in Washington, D.C.*Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-49731839329242494702020-06-28T00:00:00.000+01:002020-06-28T00:00:15.980+01:00On This Day in Math - June 28

In my opinion, a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy -- an opinion, moreover, which has been expressed by many philosophers.
Henri Lebesgue

The 180th day of the year; 180 can be formed with the only the first two primes... 180 = 22 x 32 x (2+3) *Prime Curios

180 is the sum of two square numbers: \( 12^2 + 6^2 \). It can also be expressed as either the sum of six consecutive primes: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive primes: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37.

Beautiful trigonometry, arctan1 + arctan2 + arctan3 = pi/2 =180o

More Math Facts for every year day here.

EVENTS
1451 Sort of the American version of the Medes and Lydians. The Seneca and Mohawk tribes were preparing for war when a total solar eclipse swept over both their camps late in the afternoon of this early summer day. Both immediately sued for peace. (ref. DB 6/97: "A star Called the Sun" by George Gamow). *NSEC

1489 Last total solar eclipse on Easter Island before the one on 11 July 2012. The next will be on 25 February 2324. Ref. More Mathematical Astronomical Morsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

1751 The first volume of Diderot's and d'Alembert's Encyclopedie appeared. See Hawkins, Jean d'Alembert p. 69.*VFR

1774 A Bill passed by Parliament included a clause to pay John Harrison for inventing a Timekeeper for finding Longitude at Sea. H5 was put on trial by the King himself in 1772, and performed superbly. The Board of Longitude, however, had refused to recognize the results of this trial, so John and William petitioned Parliament. They were finally awarded £8750 by this Act of Parliament. Perhaps more importantly, John Harrison was finally recognized as having solved the longitude problem. *Nat. Maritime Museum @NMMGreenwich, *ticktocktony.com

1832, the first American case of a cholera epidemic was reported in New York City. Previously, Europe and the Americas were unaffected by the First Cholera pandemic of 1817 when cholera, long endemic to the Indian subcontinent, spread to Arabia, Syria, and southern Russia. This abated in the early 1820's, but a new cholera cycle began in 1826. It invaded the British Isles in Oct 1831. Canada was struck shortly before cholera reached New York. Cholera was a horrible disease, spread through fouled water. Its victims died after hours of cramps, diarrhea, and vomiting. Crowded into unsanitary slums, the poor suffered most. Many of the city's elite fled to the countryside. In America, the disease's hold broke by Dec 1832.*TIS

1884 Sonya Kovalevskaya officially appointed extraordinary professor at Stockholm University. [The Mathematical Intelligencer, vol. 6, no. 1, p. 29; *VFR ]

1949 Wolfgang Pauli writes to Carl Jung to with theories of the "Pauli effect", which Jung described as synchronicity. Pauli was famous among his colleagues for the numerous instances in which demonstrations involving equipment suffered technical problems only when he was present. He was actually banned from the laboratory of Otto Sturn a frequent dinner companion. Pauli and Jung both believed there was an effect, and tried to explain it. In this letter Pauli uses an example from the I-ching, the Chinese book of changes, to describe his thoughts on the effect. *Charles P. Enz, No Time to be Brief: A Scientific Biography of Wolfgang Pauli,

In 1958, the Mackinac Bridge, the world longest suspension bridge, was dedicated. Ceremonies began on 24 Jun with the first "Governor's Walk" across the bridge. (It had opened to traffic on 1 Nov 1957.) This bridge joins the upper and lower peninsulas of the state of Michigan, reducing the crossing time, from a couple of hours, to just 10 minutes. Ceremonial groundbreaking took place at the St. Ignace end of the bridge on 7 May 1954, and on the opposite shore at Mackinaw City the next day. Meanwhile caissons and superstructures were assembled as far away as Indiana, Pennsylvania and Ohio. Including approaches, the total length is 26,444-ft, needing 34 bridge support foundations. The main span is 3,800-ft long. *TIS

2009 Stephen Hawking gave a party for time travelers at 12:00 UT on this day. He did not announce the event until after it was over, and it appears that no one else cared to attend. Below is the invitation, so if you missed it up until now, it's not to late to choose not to attend. (So much for free will)

*daily Mail online

2011 "6.28" has become popular as Tau day with many people who think 2 pi (or 6.28...) is more appropriate, or just a nice addition to Pi-day, on March 14 (or 3.14... )

Births
1875 Henri Lebesgue (June 28, 1875 – July 26, 1941) He introduced the concept of Lebesgue Measure, a device for measuring the 'length' of complicated sets of points on the line, and so is known as the father of modern integration theory. *VFR French mathematician whose generalization of the Riemann integral revolutionized the field of integration. He was maître de conférences (lecture master) at the University of Rennes until 1906, when he went to Poitiers, first as chargé de cours (assistant lecturer) of the faculty of sciences and later as...*TIS

1894 Einar Hille (28 June 1894 – 12 February 1980) born. In the preface of his Analytic Function Theory (1959) he wrote "It is my hope that students of this book may come to respect the historical continuity of the subject." More authors should include historical footnotes as good as those in this book.*VFR Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. His name persists among others in the Hille–Yosida theorem. *Wik

1920 Nicolaas Hendrik "Nico" Kuiper (28 June 1920, Rotterdam - 12 December 1994, Utrecht) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.
Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.
He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985.*Wik

1948 Kenneth Alan "Ken" Ribet (June 28, 1948 -) is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include algebraic number theory and algebraic geometry.
He earned his bachelor's degree and master's degree from Brown University in 1969, and his Ph.D. from Harvard University in 1973.
Ribet is credited with paving the way towards Andrew Wiles's proof of Fermat's last theorem. Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre was indeed true, and thereby proved that Fermat's Last Theorem would follow from the Taniyama–Shimura conjecture. Crucially it also followed that the full conjecture was not needed, but a special case, that of semistable elliptic curves, sufficed. An earlier theorem of Ribet's, the Herbrand–Ribet theorem, the converse to Herbrand's theorem on the divisibility properties of Bernoulli numbers, is also related to Fermat's Last Theorem. *Wik

1972 Ngô Bảo Châu (June 28, 1972 - ) is a Vietnamese and French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands and Diana Shelstad. In 2004, Chau and Laumon were awarded the Clay Research Award for their achievement in solving the fundamental lemma proposed by Robert Langlands for the case of unitary groups. Chau also became the youngest professor in Vietnam in 2005. His proof of the general case was selected by Time as one of the Top Ten Scientific Discoveries of 2009. In 2010, he received the Fields Medal and in 2012, the Legion of Honour He is the first Vietnamese to receive the Fields Medal *Wik

DEATHS
1768 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church.

1889 Maria Mitchell (August 1, 1818 – June 28, 1889) First American professional woman astronomer, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Sciences. She died at age 70 in Lynn, Mass.

1930 William J Greenstreet graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette.

1956 Friedrich Riesz (Jan. 22, 1880, in Győr; Feb. 28, 1956, in Budapest)
One of the most significant personalities among Hungarian mathematicians.
At the beginning he studied engineering at the Technical University of Zurich, but he soon realized that he was much more interested in mathematics than in technical subjects. So he continued to study at the Royal Hungarian University of Sciences in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he studied for a year in Göttingen and attended the lectures of David Hilbert and Hermann Minkowski. He obtained his PhD degree and diploma of secondary school teacher of mathematics and physics in Budapest.

1952 William Watson (15 June 1884, Musselburgh, East Lothian, Scotland
- 28 June 1952 , Edinburgh, Scotland) graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh.*SAU

1972 Prasanta Chandra Mahalanobis FRS (29 June 1893 – 28 June 1972) was an Indian scientist and applied statistician. He is best remembered for the Mahalanobis distance, (a statistical measure of the distance between a point P and a distribution D, - a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. ) and for being one of the members of the first Planning commission of free india. He made pioneering studies in anthropometry in India. He founded the Indian Statistical Institute, and contributed to the design of large-scale sample surveys *Wik

1893 Eduard Cech, (June 29, 1893 – March 15, 1960) Czech topologist born in Stračov, Bohemia (then Austria-Hungary, now Czech Republic). His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1984 Claude Chevalley  (11 February 1909, Johannesburg – 28 June 1984, Paris) had a major influence on the development of several areas of mathematics including Ring Theory and Group Theory *SAU

1974 Vannever Bush (March 11, 1890 – June 28, 1974) American electrical engineer and administrator who and oversaw government mobilization of scientific research during World War II. At the age of 35, in 1925, he developed the differential analyzer, the world's first analog computer. It was capable of solving differential equations. He put into concrete form that which began 50 years earlier with the incomplete efforts of Babbage, and the theoretical details developed by Kelvin. This machine filled a 20 x 30 foot room. He innovated one of the largest growing media in our time, namely hypermedia as fulfilled in the Internet with hypertext links *TIS

 1989 Charles Wilderman Trigg,(Feb 7, 1898 Baltimore, Md; June 28, 1989 San Diego, Ca.) American engineer, mathematician and educator. Educated in engineering, mathematics and education at University of Pittsburgh, University of Southern California and University of California at Los Angeles. Worked as an industrial chemist and engineer, 1917-1943, and as an educator and administrator, 1946-1963. Served in the United States Navy during World War II. Book review editor of the Journal of Recreational Mathematics. Considered one of the foremost recreational mathematicians of the twentieth century. *U of Calgary Archives

2015 Louis Norberg Howard, (12 March, 1929; Chicago, Il - June 28,2015) emeritus professor of mathematics at MIT, and McKenzie emeritus professor at Florida State University, died on Sunday, at the age of 86.
Howard joined the MIT mathematics faculty in 1955 as an assistant professor, and was promoted to full professor in 1964. He retired from MIT in 1984.
Howard was an applied mathematician who worked primarily in the field of fluid dynamics. He made fundamental contributions to a broad range of subjects, including hydrodynamic stability and geophysical flows. He made a number of key advances in our understanding of turbulent convection, flows in Hele-Shaw cells, salt-finger zones, rotating flows, and reaction-diffusion equations. The power of his mathematical modeling was evident when he transformed qualitative ideas about the bounds on turbulent transport into rigorous mathematical arguments that initiated the field of upper-bound theory.
He received his BA in physics from Swarthmore College in 1950, and his MA and PhD in mathematical physics from Princeton, in 1952 and 1953, respectively, under the supervision of Donald Spencer. He took an appointment as a Higgins lecturer in mathematics at Princeton in 1953, after which he became a research associate in mathematics and aeronautics at Caltech in 1955.
Howard was named a fellow of the American Academy of Arts and Sciences in 1965 and the American Physical Society in 1984, and was elected to the National Academy of Sciences in 1977. In 1997, he was honored with the prestigious Fluid Dynamics Prize of the American Physical Society. *MIT News

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-13376233029451349882020-06-27T00:00:00.000+01:002020-06-27T00:00:07.166+01:00On This Day in Math - June 27

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.
Augustus de Morgan

The 179th day of the year; 179 is a prime whose square has one each of the digits from 0 to 4.

179 is a "Knockout Prime" of the form K(3,2) since 17, 19, and 79 are all prime.

179 is an emirp, a prime whose reversal, 971 is also prime, and the combination sum and product 179 * 971 + 179 + 971=174959 is also an emirp.

1793 has all odd digits, 5735339. *Derek Orr

More Math Facts for every year date here

EVENTS
 432 B.C. Meton observed the summer solstice and began his cycle. Meton was one of the first Greek astronomers to make accurate astronomical observations. It is widely believed that, working with Euctemon, he observed the summer solstice, which marked the Athenian New Year, in 432 BC.
The Metonic cycle appears in the oldest known astronomical device, the Antikythera Mechanism (2nd century BC) together with its multiple the Callippus cycle of 76 years.
The foundations of Meton's observatory in Athens are still visible just behind the podium of the Pnyx, the ancient parliament. Meton found the dates of equinoxes and solstices by observing sunrise from his observatory. The bisectrice of the observatory lies in an easterly direction, between the Acropolis and the Lycabetus hill.*Wik

1739 "Heavens!, Maupertuis is a flea. Is he ever in one place?" So wrote Francoise de Graffigny to a friend about the French mathematician/man of letters, Pierre-Louis Moreau de Maupertuis. Graffigny affectionately gave the nickname to describe his "frenetic ubiquity." *Mary Terrall, The Man Who Flattened the Earth.

In 1847, New York and Boston were linked by telegraph wires. This enabled the New York newspapers to receive foreign news brought by Cunard's steamers to the Boston port about 190 miles away. When the Cambria next arrived in Boston, three New York Newspapers on 18 Jul 1846 carried identical brief first-day telegraphic summaries of the Cambia's news*. This telegraph link opened three years after the first U.S. telegraph line was opened on 24 May 1844 with a message sent by Samuel Morse 80 miles from Washington D.C. and Baltimore, Md.*TIS

1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat's great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth $50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik

1966 An almost 300 year old conjecture of Leonhard Euler is proven wrong. Euler had conjectured that, in the fashion that \(x^2 + y^2 = z^2 \) it always takes n terms to sum to an n-th power: two squares, three cubes, four fourth powers,etc. In 1966, L. J. Lander and T. R. Parkin found the first counterexample: four fifth powers that sum to a fifth power. They showed that \( 27^5 + 84^5 + 110^5 + 133^5 = 144^5.\) In 1988 Noam Elkies of Harvard University found a counterexample for fourth powers: \(2,682,440^4 + 15,365,639^4 + 187,960^4 = 20,615,673^4. Subsequently, Roger Frye of Thinking Machines Corporation did a computer search to find the smallest example: 95,800^4 + 217,519^4 + 414,560^4 = 422,481^4.*David Darling

1967 The first ATM in England that was put into use was by Barclays Bank in Enfield Town in North London, United Kingdom, on 27 June 1967. This machine was the first in the UK and was used by English comedy actor Reg Varney, at the time so as to ensure maximum publicity for the machines that were to become mainstream in the UK. This instance of the invention has been credited to John Shepherd-Barron of printing firm De La Rue, who was awarded an OBE in the 2005 New Year's Honours List. His design used special cheques that were matched with a personal identification number, as plastic bank cards had not yet been invented. *Wik (The plaque posted at the sight makes the claim to be the first cash machine in the world, but cash dispensing machines had been installed in Tokyo and another shortly after in Upsalla.)

1977 Italy issued a postage stamp honoring Filippo Brunelleschi (1377–1446). [Scott #1266]. *VFR

1980 Creighton Carvello recited 20,013 digits of π from memory in nine hours and one minute. *VFR

BIRTHS1767 Alexis Bouvard (27 June 1767 – 7 June 1843) French astronomer and director of the Paris Observatory, who is noted for discovering eight comets and writing Tables astronomiques of Jupiter and Saturn (1808) and of Uranus (1821). Bouvard's tables accurately predicted orbital locations of Jupiter and Saturn, but his tables for Uranus failed, leading him to hypothesize that irregularities were caused by an unknown perturbing body. This spurred observations leading to the discovery of Neptune by Adams and Leverrier.*TIS

1806 Augustus de Morgan (27 June 1806 – 18 March 1871) born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. "De Morgan's Laws", are contained in his first book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR

The rules can be expressed in English as:

"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
*Wik
When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.

1850 Jorgen Pedersen Gram.(June 27, 1850 – April 29, 1916) Danish mathematician. Today he is best known for his criterion of linear independence of functions. The Gram-Schmidt Orthonormal Basis Theorem in Linear Algebra was first published by him in 1883.
1940 Daniel G. Quillen bon in Orange, New Jersey. In 1978 he won a Fields Medal as the "prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particu¬larly ring theory and module theory." *VFR French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc, she corresponded with Lagrange who recognised her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer. TIS

1931 Martinus Justinus Godefriedus Veltman (born June 27, 1931 in Waalwijk) is a Dutch theoretical physicist. He shared the 1999 Nobel Prize in physics with his former student Gerardus 't Hooft for their work on particle theory. In 1963/64, during an extended stay at SLAC he designed the computer program Schoonschip for symbolic manipulation of mathematical equations, which is now considered the very first Computer algebra system. He was awarded the Nobel Prize for Physics in 1999 together with 't Hooft, "for elucidating the quantum structure of electroweak interactions in physics". Veltman is now retired and holds a position of Emeritus Professor at the University of Michigan. Asteroid 9492 Veltman is named in his honor. *Wik

DEATHS 1829 James Smithson (ca. 1765 – 27 June 1829) English scientist who provided funds in his will for the founding of the Smithsonian Institution, Washington, D.C. "for the increase and diffusion of knowledge." He had inherited his fortune chiefly through his mother's family. He was a chemist and minerologist who published 27 scientific papers. The mineral smithsonite (carbonate of zinc) was named for him.*TIS

1831 Sophie Germain (April 1, 1776 – June 27, 1831)died before she could receive the honorary doctorate Gauss had persuaded the University of Gottingen to give her. *VFR

1880 Carl Borchardt (22 February 1817 – 27 June 1880) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1952 Max Dehn died (November 13, 1878 – June 27, 1952). He solved Hilbert's third problem in 1900 (shortly after receiving his Ph.D. un¬der Hilbert on another topic in the foundations of geometry): a tetrahedron cannot be cut up into finitely many pieces and reassembled into a cube of equal volume. Thus Dehn became the first mathematician to join "the honors class" of mathematicians who had solved one of the twenty-three problems Hilbert posed in Paris in 1900.

1975 Sir Geoffrey Ingram Taylor OM (7 March 1886 – 27 June 1975) was a British physicist, mathematician and expert on fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century". His final research paper was published in 1969, when he was 83. In it he resumed his interest in electrical activity in thunderstorms, as jets of conducting liquid motivated by electrical fields. The cone from which such jets are observed is called the Taylor cone for his namesake. In the same year Taylor was appointed to the Order of Merit. He suffered a stroke in 1972 which effectively put an end to his work; he died in Cambridge in 1975.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-56471182652496198602020-06-26T00:00:00.000+01:002020-06-26T00:00:03.414+01:00On This Day in Math - June 26

When you measure what you are speaking about and express it in numbers,
you know something about it,
but when you cannot express it in numbers
your knowledge about is of a meagre and unsatisfactory kind.
William Thompson, Lord Kelvin

The 178th day of the year; 178 = 2 x 89. Note that 2 and 89 are the smallest and the largest Mersenne prime exponents under 100. *Prime Curios

178 is a palindrome in base 6,\( [454]_6 \) and in base 8 \([262]_8\)

Strangely enough, 178 and 196 are related... In fact, 178 has a square with the same digits as 196:
1782 = 31,684
1962 = 38,416
178 has also a cube with the same digits as 196:
1783 = 5,639,752
1963 = 7,529,536
*Zoo of Numbers
More Math Facts for each year day here.

EVENTS
1424 Of the 20 total eclipses to visit the Orkneys and Shetland Islands in the period 1 - 3000AD it was the 13th longest in the whole of the UK at 3 minutes 56 seconds it was surpassed in Orkney by those of 364, 885, 1185, 1433, 2681. The eclipse track traveled across Denmark, Germany, Poland, Ukraine, Moldavia, and the Black Sea. (ref. SW-UK eclipses) *NSEC

 1614 The first lottery of significance in the new world was held on this date by the Virginia Company. The first Great Prize was 4,500 Crowns. *JN Kane, Famous First Facts (I have seen the date of this lottery also given as 1612)

1765 Benjamin Franklin writes to Peter Collinson about numerous topics including Accounts of Spouts and Whirlwinds, and a comment on his earlier kite experiments; but includes, "I am endeavouring to answer Dr. Parsons's Request relating to the Indian Names of the Cardinal Numbers." *franklinpapers

In 1819, The first US patent for a velocipede, a predecessor of the bicycle, was issued to William K. Clarkson Jr. of New York. Little information remains available, however, because a fire at the Patent Office in 1836 destroyed the patent record, and it was not restored. The photo shows the Draisine design of the period (Europe, 1816). Bicycles were introduced to the US also in 1819 and were manufactured by David and Rogers in Troy, NY*TIS

1881 The great comet of 1881. Observed on the night of June 25-26 at 1h. 30m. A.M. from a print by Étienne Léopold Trouvelot, a French artist, astronomer and amateur entomologist. He is noted for the unfortunate introduction of the Gypsy Moth into North America. *The New York Public Library Digital Collections

 1896 An early x-ray photograph of Sir William Crookes's hand, taken with a cathode tube that bears his name, the Crookes Tube. The man taking these pioneering radiographs was the engineer Alan Archibald Campbell Swinton, later a Fellow of the Royal Society. He took the first x-ray images in Britain in January 1896 and by a year later the medical professions were bringing him surgical cases for analysis. *Keith Moore, Royal Society Blog

In 1974, at 8:01 a.m., a package of Wrigley's chewing gum with a bar code printed on it passed over a scanner at the Marsh Supermarket, Troy, Ohio, and became the first product ever logged under the new Universal Product Code (UPC) computerized recognition system. Invented by IBM, and approved for use in 1973, the UPC is a 12-number bar code representing the manufacturer's identity and an assigned product number. Within nanoseconds, this information is read with a laser beam moving at around 10,000 inches per second and transfers it to the store's database computer for price lookup and inventory management*TIS

In 1984, the National Maritime Museum, of which the Royal Observatory, Greenwich is a part, encouraged people up and down the Line to organise events in order to mark the so-called 'centenary' of the Prime Meridian. Although the International Meridian conference took place in October 1884, the Museum designated Tuesday 26 June as 'Meridian Day', on the grounds that any outdoor events would be less likely to be affected by the weather.
Commemorative six-inch diameter plastic plaques were offered to any individual who could show that the Meridian passed through the curtilage of their property. Potential claimants were required to write to their regional office of the Ordnance Survey to verify their claim and send this as proof of authenticity to the English Tourist Board who were distributing them. No records of how many were issued can be traced. The locations of just four are known, along with the existence of a fifth.
The National Maritime Museum also arranged for the Enfield Foundry to cast a bronze plaque as a more enduring alternative. At the time, it was stated that they would only be produced if 20 or more orders were received. How many were made is unknown, the Foundry's records having been destroyed. Only three have been located to date. (If you are aware of one of these locations, please informe me, thanks PB)

In 2000, the completion of a working draft reference DNA sequence of the human genome was announced at the White House by President Bill Clinton, and representatives from the Human Genome Project (HGP) and the private company Celera Genomics. Clinton stated that even greater discoveries would follow from the working draft. As a draft, it contained some gaps and errors, but represented about 95% of all genes. HGP expected to use it as a scaffold for generating the high-quality reference genome sequence within three years. This provides knowledge to link genes with particular diseases, of the influence of genetics and to help discover new treatments.
*TIS

BIRTHS
1730 Charles Messier (26 June 1730 – 12 April 1817) French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.

1824 Lord Kelvin (26 June 1824 – 17 December 1907) Born as William Thomson, he became an influential physicist, mathematician and engineer who has been described as a Newton of his era. At Glasgow University, Scotland, he was a professor for over half a century. The name he made for himself was more than just a temperature scale. His activities ranged from being the brains behind the laying of a transatlantic telephone cable, to attempting to calculate the age of the earth from its rate of cooling. In 1892, when raised to the peerage as Baron Kelvin of Largs, he had chosen the name from the Kelvin River, near Glasgow.*TIS

1878 Leopold Löwenheim (26 June 1878 in Krefeld, Germany (also the birthplace of Max Zorn) – 5 May 1957 in Berlin) was a German mathematician who worked on mathematical logic and is best-known for the Löwenheim-Skolem paradox.*SAU

1969 Andrei Yuryevich Okounkov (June 26, 1969 - ) is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions. He is currently a professor at Columbia University. In 2006, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry." *Wik

DEATHS
1274 Nasir al-Tusi (born 18 February 1201 in Ṭūs, Khorasan – died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad), was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.*SAU Among the many wonderful antiquities at the Bodleian Library is a 16th century printing of the 13th century Arabic translation by Nasir al-Din al-Tusi of Euclid's Elements. It was part of the collection donated by Thomas Allen.

1796 David Rittenhouse (April 8, 1732 – June 26, 1796) American astronomer, instrument maker and inventor who was an early observer of the atmosphere of Venus. For observations for the transit of Venus on 3 Jun 1769, he constructed a high precision pendulum clock, an astronomical quadrant, an equal altitude instrument, and an astronomical transit. He was the first one in America to put spider web as cross-hairs in the focus of his telescope. He is generally credited with inventing the vernier compass and possibly the automatic needle lifter. He was professor of astronomy at the University of Pennsylvania. Benjamin Franklin consulted him on various occasions. For Thomas Jefferson he standardized the foot by pendulum measurements in a project to establish a decimal system of weights and measures.*TIS

1810 Joseph Montgolfier (26 August 1740 – 26 June 1810) French ballooning pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world. *TIS

1951 George Udny Yule (18 February 1871 – 26 June 1951) graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU

1967 Henry Thomas Herbert Piaggio (2 June 1884–26 June 1967) graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations.("An Elementary Treatise on Differential Equations and their Applications".) *SAU

1990 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to forsee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-36425949831694184812020-06-25T00:00:00.000+01:002020-06-25T16:13:24.859+01:00On This Day in Math - June 25

Astronomy was the cradle of the natural sciences and the starting point of geometrical theories.
~Cornelius Lanczos

The 177th day of the year; there are 177 graphs with seven edges. *What's So Special About This Number. (only 79 of these are connected graphs)

177 is the smallest magic constant for a 3 x 3 prime magic square

An old idea that was new to me, from John Golden@mathhombre and here. Use two Simple Squares to make a make a third, and I just did one with magic sum of 177.
2 3 1
1 2 3
3 1 2

And
53 61 57
61 57 53
57 53 61

Now add the numbers in same location

55 64 58
62 59 56
60 54 63

More Math Facts for each day here

EVENTS
1641 John Pell begins the work of expanding Walter Warner's table of anti-logarithms from 10,000 to 100,000 entries. Warner felt he was too old to complete the laborious task he had set for himself, and offered Pell 40 GBPounds (appx. worth 5,000 pounds today) to complete the tables and make them ready for printing. *Thomas Harriot's Doctrine of Triangular Numbers, Beery & Stedall, pg 39

1665 René Descartes died on 11 February 1650 in Stockholm, Sweden, where he had been invited as a teacher for Queen Christina of Sweden. The cause of death was said to be pneumonia—accustomed to working in bed until noon, he may have suffered a detrimental effect on his health due to Christina's demands for early morning study (the lack of sleep could have severely compromised his immune system). Others believe that Descartes may have contracted pneumonia as a result of nursing a French ambassador, Dejion A. Nopeleen, ill with the aforementioned disease, back to health. In his recent book, Der rätselhafte Tod des René Descartes (The Mysterious Death of René Descartes), the German philosopher Theodor Ebert asserts that Descartes died not through natural causes, but from an arsenic-laced communion wafer given to him by a Catholic priest. He believes that Jacques Viogué, a missionary working in Stockholm, administered the poison because he feared Descartes's radical theological ideas would derail an expected conversion to Roman Catholicism by the monarch of Protestant Lutheran Sweden.*Wik

After his death in Stockholm, his body was returned to Paris, arriving on 25 Jun 1665 , though the coffin had been looted by his followers for relics in Stockholm. Supposedly, the coffin was shipped overland from Copenhagen to avoid piracy by English admirers! The remains were in Ste. Geneviève, then in Lenoir's Museum of French Monuments, and then finally moved to St‑Germain-des-Prés in 1819. His headstone (or gravestone) is in St‑Germain‑des‑Prés, in the second chapel on the right of the apse. Stephen Jay Gould says the (purported) skull of Descartes is in the Musée de l'Homme, apparently on display. Arjen Dijksman recently advised me that the Musee de l'Homme is closed for another year, and there have been efforts to move the skull to the Pantheon.
Église St-Germain-des-Prés, at 3 Place St-Germain-des-Prés, is the oldest church in Paris. Part of it dates to the 6th century, when a Benedictine abbey was founded on the site by King Childebert, son of Clovis. The church was originally built to house a relic of the True Cross brought from Spain in 542. The Normans destroyed the abbey on multiple occasions and only the marble columns in the triforium remain from the original structure. The carved capitals on the pillars are copies of the originals, which are kept in the Musée National du Moyen-Age. The church was enlarged and reconsecrated by Pope Alexander III in 1163. The abbey was completely destroyed during the Revolution, but the church was spared. The present building is a fine example of Romanesque architecture, with gothic interior elements. The square tower dating from the early 11th century, is topped by a landmark spire, which dates to the 19th century. For a time, the abbey served as a pantheon for Merovingian kings. The Chapelle Saint Symphorien, built during the Middle Ages and restored in 1981, served as the necropolis mérovingienne (crypt of the Merovingians). This is the presumed site of first tomb of Saint Germain, Bishop of Paris, who died in 576. Among the others interred here are King Jean-Casimir of Poland

1712 Brook Taylor suggested that if two glass plates which are clamped together into a "V" are placed into a pan of water then capillary action will draw water up into the shape of a rectangular hyperbola with asymptotes the surface of the water and the point of the "V." This and several similar experiments performed by Francis Hauksbee before the Royal Society caused Newton to rethink his ideas on capillary force. *VFR

1730 Euler observes in a letter to Goldbach that 104 + 1 is divisible by 37, and that
38 +2 8 is divisible by 17. Euler cannot prove that any number is the sum of four squares. He has found another result by Fermat, namely that 1 is the only triangular number that is a fourth power (Several years earlier, Goldbach had sent an erroneous proof of this claim to D. Bernoulli) *Lemmemeyer, EULER, GOLDBACH, AND "FERMAT'S THEOREM"

1776 Captain Cook sails from Deptford on his third voyage, in the 'Resolution' with the 'Discovery' *Nat. Maritime Museum @NMMGreenwich

1783 Antonie Lavoisier announced to the French Academy of Sciences that water was the product formed by the combination of hydrogen and oxygen. However, this discovery had been made earlier by the English chemist Henry Cavendish *TIS

1795 The Bureau des Longitudes is a French scientific institution, founded by decree of 25 June 1795 and charged with the improvement of nautical navigation, standardization of time-keeping, geodesy and astronomical observation. During the 19th century, it was responsible for synchronizing clocks across the world. It was headed during this time by François Arago and Henri Poincaré. The Bureau now functions as an academy and still meets monthly to discuss topics related to astronomy.
The Bureau was founded by the National Convention after it heard a report drawn up jointly by the Committee of Navy, the Committee of Finances and the Committee of State education. Henri Grégoire had brought to the attention of the National Convention France's failing maritime power and the naval mastery of England, proposing that improvements in navigation would lay the foundations for a renaissance in naval strength. As a result, the Bureau was established with authority over the Paris Observatory and all other astronomical establishments throughout France. The Bureau was charged with taking control of the seas away from the English and improving accuracy when tracking the longitudes of ships through astronomical observations and reliable clocks.
The ten original members of its founding board were:
Geometers:
Joseph-Louis Lagrange;
Pierre-Simon Laplace;
Astronomers:
Joseph Jérôme Lefrançais de Lalande;
Pierre Méchain;
Jean Baptiste Joseph Delambre;
Dominique, comte de Cassini;
Jean-Charles de Borda, who carried out work related to the mechanics of fluids and precursor of Carnot because of his insights on thermodynamics;
Jean-Nicolas Buache, geographer;
Louis Antoine de Bougainville, celebrated navigator; and
Noël Simon Caroché, manufacturer of telescopes.
*Wik

1973 Last total solar eclipse with a maximum duration of totality longer than 7 minutes between year 0 and 4000 was June 30, 1973. The eclipse was visible in Africa. The next total solar eclipse with a duration of totality longer than 7 minutes will be on 25 June 2150 in the Pacific Ocean. Thereafter it will be 5 July 2168 in the Indian Ocean. Ref. More Mathematical AstronomicalMorsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

BIRTHS
1864 Walther Hermann Nernst (25 June 1864 – 18 November 1941) German who was one of the founders of modern physical chemistry. In 1889, he devised his theory of electric potential and conduction of electrolytic solutions (the Nernst Equation) and introduced the solubility product to explain precipitation reactions. In 1906, Nernst showed that it is possible to determine the equilibrium constant for a chemical reaction from thermal data, and in so doing he formulated what he himself called the third law of thermodynamics. This states that the entropy, (a thermodynamic measure of disorder in a system), approaches zero as the temperature goes towards absolute zero. For this, he was awarded the 1920 Nobel Prize in Chemistry. In 1918, he explained the H2-Cl2 explosion on exposure to light as an atom chain reaction. *TIS

1905 Rupert Wildt (/ˈvɪlt/; June 25, 1905 – January 9, 1976) was a German-American astronomer.
He was born in Munich, Germany, and grew up in that country during World War I and its aftermath. In 1927 he was awarded a Ph.D. from the University of Berlin. He joined the University of Göttingen, specializing in the properties of atmospheres.
In 1932 he studied the spectra of Jupiter, and other outer planets, and identified certain absorption bands as belonging to the hydrogen-rich compounds of methane and ammonia. The composition appeared consistent with a composition similar to the sun and other stars.
Assuming that the atmosphere was composed of these gases, during the 1940s and 1950s he constructed a model of the structure of these planets. He believed the core of the planets is solid and composed of a mixture of rock and metal, covered by a thick outer shell of ice, overlaid by a dense atmosphere. His model is still widely accepted.
In 1934 he emigrated to the United States, and became a research assistant at Princeton University from 1937 until 1942. He then became an assistant professor at the University of Virginia until 1947, before joining the faculty of the Yale University.
In 1939 he demonstrated that the major source of optical opacity in the Sun's atmosphere is the H- ion, and thus the main source of visible light for the Sun and stars.
From 1965 until 1968 he was president of the Association of Universities for Research in Astronomy. In the period 1966-1968 he also held the post of the chairman of the department of astronomy at Yale, and from 1973 until his death he was professor emeritus. He died in Orleans, Massachusetts.
His awards include the Eddington Medal in 1966. The Asteroid 1953 Rupertwildt is named after him and the crater Wildt on the Moon is also. *Wik

1928 Alexei Alexeyevich Abrikosov (June 25, 1928; ) is a Soviet and Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.
In two works in 1952 and 1957, Abrikosov explained how magnetic flux can penetrate a class of superconductors. This class of materials is known as type-II superconductors. The accompanying arrangement of magnetic flux lines is called the Abrikosov vortex lattice.
Abrikosov was awarded the Lenin Prize in 1966, the Fritz London Memorial Prize in 1972, and the USSR State Prize in 1982. In 1989 he received the Landau Prize from the Academy of Sciences, Russia. Two years later, in 1991, Abrikosov was awarded the Sony Corporation's John Bardeen Award. The same year he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.[1] He is also a member of the Royal Academy of London, a fellow of the American Physical Society, and in 2000 was elected to the prestigious National Academy of Sciences. He was the co-recipient of the 2003 Nobel Prize in Physics, with Vitaly Ginzburg and Anthony James Leggett, for theories about how matter can behave at extremely low temperatures. *Wik

DEATHS
1671 Giovanni Riccioli (17 April 1598 – 25 June 1671) Italian astronomer who was the first to observe (1650) a double star (two stars so close together that they appear to be one) - Mizar in Ursa Major, the middle star in the handle of the Big Dipper. He also discovered satellite shadows on Jupiter. In 1651, he assigned the majority of the lunar feature names in current use. He named the more prominent features after famous astronomers, scientists and philosophers, while the large dark and smooth areas he called "seas" or "maria". The lunar seas were named after moods (Seas of Tranquillity, Serenity) or terrestrial phenomena (Sea of Rains, Ocean or Storms) His map was published in Almagestum Novum in1651.*TIS
Riccioli studied seventy-seven objections to the Copernican thesis and after studying them Riccioli said that the weight of argument favored a "geo-heliocentric" hypothesis such as that advocated by the great Danish astronomer Tycho Brahe. Riccioli's preference for Tycho's model illustrates something important about how science is done. While today anti-Copernicans are often portrayed as Einstein characterized them (opposed to rational thinking, opposed to science), Riccioli, perhaps the most prominent of the anti-Copernicans, examined the available evidence diligently and rationally. The conclusion he reached was indeed wrong, but wrong because at that time neither the diffraction of light and the Airy disk, nor the details of the Coriolis effect, were understood. Riccioli's anti-Copernican arguments were so solid that they would become subjects of further investigation in physics, long after the Copernican theory had triumphed over the Tychonic theory.*Christopher M. Graney, Teaching Galileo, Physics Teacher V50,1

1879 Sir William Fothergill Cooke (4 May 1806 – 25 June 1879) English inventor who worked with Charles Wheatstone in developing electric telegraphy. Of the pair, Cooke contributed a superior business ability, whereas Wheatstone is generally considered the more important of the two in the history of the telegraph. After Cooke attended a demonstration of the use of wire in transmitting messages, he began his own experiments with telegraphy (1836) and formed a partnership with Wheatstone. Their first patent (1837) was impractical because of cost. They demonstrated their five-needle telegraph on 24 July 1837 when they ran a telegraph line along the railway track from Euston to Camden Town able to transmit and successfully receive a message. In 1845, they patented a single-needle electric telegraph. *TIS

1941 Alfred Pringsheim  (2 September 1850 – 25 June 1941). His work in Fourier series, analytic function theory, and continued fractions was a model of the Weierstrassian approach, although he was not a student of Weierstrass. *VFR
In mathematical analysis, Pringsheim studied real and complex functions, following the power-series-approach of the Weierstrass school. Pringsheim published numerous works on the subject of complex analysis, with a focus on the summability theory of infinite series and the boundary behavior of analytic functions.
Pringsheim's theorem concerns the convergence of a power series with non-negative real coefficients. However, Pringsheim's original proof had a flaw (related to uniform convergence), and a correct proof was provided by Ralph P. Boas. Pringsheim's theorem is used in analytic combinatorics and the Perron–Frobenius theory of positive operators on ordered vector spaces.
Besides his research in analysis, Pringsheim also wrote articles for the Encyclopedia of Mathematical Sciences on the fundamentals of arithmetic and on number theory. He published papers in the Annals of Mathematics. As an officer of the Bavarian Academy of Sciences, he recorded the minutes of its scientific meetings.
Pringsheim and Ivan Śleszyński, working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions.*Wik

1960 Walter Baade (24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

1974 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU Lanczos served as assistant to Albert Einstein during the period of 1928–29.*Wik

1978 Hsien Chung Wang (April 18, 1918 — June 25, 1978.)worked on algebraic topology and discovered the 'Wang sequence', an exact sequence involving homology groups associated with fibre bundles over spheres. These discoveries were made while he worked with Newman in Manchester. Wang also solved, at that time, an important open problem in determining the closed subgroups of maximal rank in a compact Lie group *SAU

1997 Jacques-Yves Cousteau (11 June 1910 – 25 June 1997) French naval officer, oceanographer, marine biologist and ocean explorer, known for his extensive underseas investigations. He was co-inventor of the aqualung which made SCUBA diving possible (1943). Cousteau developed the Conshelf series of manned habitats, the Diving Saucer, a process of underwater television and numerous other platforms and specialized instruments of ocean science. In 1945 he founded the French Navy's Undersea Research Group. He modified a WWII wooden hull minesweeper into the research vessel Calypso, in 1950. An observation dome added to the foot of Calypso's bow was found to increase the ship's stability, speed and fuel efficiency. *TIS

2006 Irving "Kap" Kaplansky (March 22, 1917, Toronto – June 25, 2006, Los Angeles) was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act.
He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-3584056763213203922020-06-24T00:00:00.000+01:002020-06-24T00:00:03.977+01:00On This Day in Math - June 24

"For example" is not a proof.
Jewish proverb,

The 176th day of the year; 176 and its reversal 671 are both divisible by 11. ( Students should confirm that the reverse of any number that is divisible by 11 will also be divisible by 11.)

176 is a happy number, repeatedly iterating the sum of the squares of the digits will lead to 1, 12 + 72 + 62= 86, 82 + 62 = 100 and 12 + 02 + 02 = 1

The number 15 can be partitioned in 176 ways.

EVENTS

1497 The name America is first used for the newly discovered continent, or at least part of it. Named by John Cabot in honor of his Bristol sponsor, Welshman Robert Ameryk, a prosperous merchant. According to accounts from the period, a record for that year in the Bristol calendar stated, "... on Saint Johns Day, the land of America was found by merchants of Bristowe, in a ship of Bristowe called the Mathew."
 The first use of the name on a map was on the Waldseemuller map of 1507. As was common at the time, the map was accompanied by a cosmographia explaining the basics of cartography and how to use the map. In his Cosmographiae Introductio Waldseemuller makes clear that it is named for Vespucci. Its full title translates to, "Introduction to Cosmography With Certain Necessary Principles of Geometry and Astronomy To which are added The Four Voyages of Amerigo Vespucci A Representation of the Entire World, both in the Solid and Projected on the Plane, Including also lands which were Unknown to Ptolemy, and have been Recently Discovered".
While Cabot certainly discovered the mainland of the Americas before Vespucci, it seems that the weight of evidence for why we use the name America is weighted heavily toward the Amerigo Vespucci theory. An excellent analysis of the evidence on that side, and the lack of evidence in support of Ameryk, is given by The Renaissance Mathematicus here. *PB combined notes from many sources.

1634 Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Coll`ege Royal in Paris. Thereafter, he kept his mathematical discoveries secret so that he could continue to win the competition and keep the chair. As a consequence he lost credit for many of his discoveries. *VFR
He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented.
Another of Roberval's discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines."

1644 In a letter to Torricelli, Fr. Marin Mersenne gives a method to find a number with any number of factors. He explained; since 60 = 2*2*3*5 subtract one from each factor (1,1,2, 4) and make them the exponents of any primes.. he used 24*32*5*7= 5040.. Of course Plato knew much earlier that 5040 had sixty factors.In Laws, Plato suggests that 5040 is the optimal number of citizens in a state because a) It is the product of 12, 20, and 21; b) the 12th part of it can still be divided by 12; and c) it has 59 proper divisors, including all numbers for 1 to 12 except 11, and 5038--which is very close to 5040--is divisible by 11.

1687 In a letter to Huygens, Fatio de Dullier used an integrating factor to solve the differential equation 3x dy − 2y dx = 0. No earlier instance of an integrating factor is known. The fundamental conception of integrating factors was due to Euler (1734) and further developed by Clairaut (1739). *VFR

In 1778, David Rittenhouse observed a total solar eclipse in Philadelphia. In a letter to him, dated 17 Jul 1778, Thomas Jefferson wrote that "We were much disappointed in Virginia generally on the day of the great eclipse, which proved to be cloudy." Rittenhouse (1732-1796) was not only an American astronomer, but also a mathematician and public official. He is reputed to have built the first American-made telescope and was the first director of the U.S. Mint (1792-1795).*TIS Jefferson was an excellent applied mathematician and had contacted Rittenhouse on another occasion. Travelling through France ten years later, " in 1788, he noticed peasants near Nancy ploughing, and fell to wondering about the design of the moldboard, that is, the surface which turns the earth: he spent the next ten years working on this, on and off, wondering how to achieve the most efficient design, both offering least frictional resistance, and which also would be easy for farmers out in the frontiers to construct, far from technical help. He consulted the Pennsylvania mathematician Robert Patterson (born in Ireland in 1743), and consulted also another Philadelphia luminary, the self-taught astronomer and mathematical instrument-maker David Rittenhouse (1732-1796)." Jefferson also communicated with Thomas Paine about bridge design, suggesting the use of catenary arches. Jefferson is believed to be the first person ever to use the term "catenary" in English.

1847 The first observation with the Great Refractor at Harvard was of the Moon on the afternoon of June 24, 1847. A number of significant achievements quickly followed. The eighth satellite of Saturn was discovered in 1848 by W.C. Bond and his son, George P. Bond, who was to succeed his father as Director in 1859. In 1850, Saturn's crape, or inner, ring was first observed, again by the Bonds. That same year, the first daguerreotype ever made of a star, the bright Vega, was taken by J.A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes. One of the earliest photographs of a double star, Mizar and Alcor in the handle of the Big Dipper, was achieved in 1857, using the wet-plate collodion process. *Observatory web page... The 15 inch Great Refractor was "once the biggest and best telescope in the United States, perhaps the world." *Frederik Pohl, Chasing Science, pg 42.

In 1898, a U.S. commemorative stamp was first used that carried the design of a major engineering construction project, the Mississippi River Bridge, a triple-arch steel bridge between East St. Louis, Illinois and St. Louis,

Missouri. Each span was roughly 500 feet and rested on piers resting on bedrock some 100 feet beneath the river bottom. Opened on 4 Jul 1874, the bridge was named after its designer, the self-trained engineer, James Eads. The upper level road also carried streetcars, which are seen in the stamp design along with steam ships on the river below. The trains that ran on its lower level are hidden from view at this angle. (Although still in use, the bridge no longer carries rail traffic.) The design was reissued in 1998.*TIS

In 1975, a moon tremour, caused by a strike of Taurid meteors, was detected by the seismometer network left on the Moon's surface by American astronauts. The major series of lunar impacts between 22 - 26 Jun 1975 represented 5% of the total number of impacts detected during the eight years of the network's operation, and included numerous 1-ton meteorites. The impacts were detected only when the nearside of the Moon (where the astronauts landed) was facing the Beta Taurid radiant. At the same time, there was a lot of activity detected in Earth's ionosphere, which has been linked with meteor activity. The Taurid meteor storm crosses the Earth orbit twice a year, during the period 24 Jun to 6 Jul and the period 3 Nov to 15 Nov.*TIS

1978  Charon first suggested for the name of Pluto's moon. Charon was originally known by the temporary designation S/1978 P 1, according to the then recently instituted convention. On June 24, 1978, U.S. Naval Observatory astronomer James Christy who had discovered the moon, first suggested the name Charon as a scientific-sounding version of his wife Charlene's nickname, "Char."
Although colleagues at the Naval Observatory proposed Persephone, Christy stuck with Charon after discovering it coincidentally refers to a Greek mythological figure: Charon is the ferryman of the dead, closely associated in myth with the god Hades, whom the Romans identified with their god Pluto. Official adoption of the name by the IAU waited until late 1985 and was announced on January 3, 1986.
There is minor debate over the preferred pronunciation of the name. The practice of following the classical pronunciation established for the mythological ferryman Charon is used by major English-language dictionaries such as the Merriam-Webster and Oxford English Dictionary.[19][20] These indicate only one pronunciation of "Charon" when referring specifically to Pluto's moon: with an initial "k" sound. Speakers of languages other than English, and many English-speaking astronomers as well, follow this pronunciation.
However, Christy himself pronounced the ch in the moon's name as sh, after his wife Charlene. *Wik

2012 Lonesome George, the last Pinta Island tortoise dies. Also known as the Pinta giant tortoise, Abingdon Island tortoise, or Abingdon Island giant tortoise, was a subspecies of Galápagos tortoise native to Ecuador's Pinta Island.
The subspecies was described by Albert Günther in 1877 after specimens arrived in London. By the end of the 19th century, most of the Pinta Island tortoises had been wiped out due to hunting. By the mid-20th century, it was assumed that the species was extinct until a single male was discovered on the island in 1971. Efforts were made to mate the male, named Lonesome George, with other subspecies, but no viable eggs were produced. Lonesome George died on June 24, 2012. The subspecies is believed to have become extinct; however, there has been at least one first-generation hybrid individual found outside Pinta Island *Wik

BIRTHS

1880 Oswald Veblen, (June 24, 1880 – August 10, 1960) American mathematician, born in Decorah, Iowa, who made important contributions to differential geometry and early topology. Many of his contributions found application to atomic physics and relativity. Along with his interest in the foundations of geometry he developed an interest in algebraic topology, or analysis situs as it was then called and by 1912 was writing papers on this subject. Gradually he became more interested in differential geometry. From l922 onward most of his papers were in this area and in its connections with relativity. His work on axioms for differentiable manifolds and differential geometry contributed directly to the field.*TIS

1909 William Penney (24 Jun 1909, 3 Mar 1991 at age 81)(Baron Penney of East Hendred) British nuclear physicist who led Britain's development of the atomic bomb. Penney was to Britain as Robert Oppenheimer was to the U.S. He was a prominent part of the British Mission at Los Alamos during WW II, where his principal assignment was studying the damage effects from the blast wave of the atomic bomb, but he became involved in implosion studies as well. Penney's combination of expertise, analytical skill, effective communication, and the ability to translate them into practical application soon made him one of the five members of the Los Alamos "brain trust" that made key decisions. He was the only Briton to be part of the ten man Target Committee that drew up the list of targets for the atomic bombing of Japan. *TIS

1912 Wilhelm Cauer (June 24, 1900 – April 22, 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter. *Wik
By the end of World War II, he was, like millions of less-distinguished countrymen and -women, merely a person in the way of a terrible conflagration.
Cauer succeeded in evacuating his family west, where the American and not the Soviet army would overtake it — but for reasons unclear he then returned himself to Berlin. His son Emil remembered the sad result.

The last time I saw my father was two days before the American Forces occupied the small town of Witzenhausen in Hesse, about 30 km from Gottingen. We children were staying there with relatives in order to protect us from air raids. Because rail travel was already impossible, my father was using a bicycle. Military Police was patrolling the streets stopping people and checking their documents. By that time, all men over 16 were forbidden to leave towns without a permit, and on the mere suspicion of being deserters, many were hung summarily in the market places. Given this atmosphere of terror and the terrible outrages which Germans had inflicted on the peoples of the Soviet Union, I passionately tried to persuade my father to hide rather than return to Berlin, since it was understandable that the Red Army would take its revenge. But he decided to go back, perhaps out of solidarity with his colleagues still in Berlin, or just due to his sense of duty, or out of sheer determination to carry out what he had decided to do.
Seven months after the ending of that war, my mother succeeded in reaching Berlin and found the ruins of our house in a southern suburb of the city. None of the neighbors knew about my father's fate. But someone gave identification papers to my mother which were found in a garden of the neighborhood. The track led to a mass grave with eight bodies where my mother could identify her husband and another man who used to live in our house. By April 22, 1945, the Red Army had crossed the city limits of Berlin at several points. Although he was a civilian and not a member of the Nazi Party, my father and other civilians were executed by soldiers of the Red Army. The people who witnessed the executions were taken into Soviet captivity, and it was not possible to obtain details of the exact circumstances of my father's death.
*ExecutedToday.com

1915 Sir Fred Hoyle (24 June 1915 – 20 August 2001) English mathematician and astronomer, best known as the foremost proponent and defender of the steady-state theory of the universe. This theory holds both that the universe is expanding and that matter is being continuously created to keep the mean density of matter in space constant. He became Britain's best-known astronomer in 1950 with his broadcast lectures on The Nature of the Universe, and he recalled coining the term "Big Bang" in the last of those talks. Although over time, belief in a "steady state" universe as Hoyle had proposed was shared by fewer and fewer scientists because of new discoveries, Hoyle never accepted the now most popular "Big Bang" theory for the origin of the universe.

1927 Martin Lewis Perl (June 24, 1927 – September 30, 2014) was an American physicist who won the Nobel Prize in Physics in 1995 for his discovery of the tau lepton.
He received his Ph.D. from Columbia University in 1955, where his thesis advisor was I.I. Rabi. Perl's thesis described measurements of the nuclear quadrupole moment of sodium, using the atomic beam resonance method that Rabi had won the Nobel Prize in Phyics for in 1944.
Following his Ph.D., Perl spent 8 years at the University of Michigan, where he worked on the physics of strong interactions, using bubble chambers and spark chambers to study the scattering of pions and later neutrons on protons.[1] While at Michigan, Perl and Lawrence W. Jones served as co-advisors to Samuel C. C. Ting, who earned the Nobel Prize in Physics in 1976.
Seeking a simpler interaction mechanism to study, Perl started to consider electron and muon interactions. He had the opportunity to start planning experimental work in this area when he moved in 1963 to the Stanford Linear Accelerator Center (SLAC), then being built in California. He was particularly interested in understanding the muon: why it should interact almost exactly like the electron but be 206.8 times heavier, and why it should decay through the route that it does. Perl chose to look for answers to these questions in experiments on high-energy charged leptons. In addition, he considered the possibility of finding a third generation of lepton through electron-positron collisions. He died after a heart attack at Stanford University Hospital on September 30, 2014 at the age of 87. *Wik

DEATHS

1832 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

1880 Jules Lissajous (March 4, 1822, Versailles – June 24, 1880, Plombières-<wbr></wbr>les-Bains) was a French mathematician best known for the Lissajous figures produced from a pair of sine waves. *SAU The curves are also called Bowditch curves for the early American mathematician, Nathanial Bowditch, who worked with them earlier. In general, a parametric curve with equations x= A sin(k t ); y= B sin(m t), the curves can describe things as simple as a circle or ellipse to more complex open and closed curves. If the ratio of k/m is rational, the curve will eventually close.

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell email@example.com:blogger.com,1999:blog-2433841880619171855.post-46904041423626787492020-06-23T02:00:00.000+01:002020-06-23T02:00:10.420+01:00Sums of Cubes as Square of Sum with a Why? and More.

Like many teachers at the upper level high school math classes, over the years I've presented the sum of the Cubes of the natural numbers formula above many dozens of times. Then, perhaps like many others, I would point out how nice it is that it turns out to be the square of the nth triangular number, a happy coincidence that would make it easier to remember. Usually then, we would challenge them to extend the idea to fourth powers and see if they could do the induction proof, even though there was no really nice simplification (to my knowledge) of the sums of fourth powers.

But then I reread a book that has been in my library for about six years, and realized that many of those teachers may have known a different approach to sums of cubes equaling square of sums that I had been completely unaware of. In case there are other teachers who somehow also didn't know, I share my newfound ancient knowledge.

The book was David Wells', Games and Mathematics, Subtle Connections, and as I reread it, I came across a theorem by Joseph Liouville (1809-1882) It is most easily understood if you illustrate with an example I think, so, as Wells did in his book, I'll use the number 15, although you can you any integer and it's still true.

If you write down all the divisors of the number, including 1 and the number, you see that there are four such divisors, 1, 3, 5, and 15. Now the unusual step, we want to write down the number of divisors each of the divisors has, so one has only 1 divisor, three has 2 divisors, five has 2 divisors, and fifteen has 4 divisors. Now let's make a set of these four new numbers, {1,2,2,4} What Liouville discovered was that the sum of the cubes of these four numbers, \( (1^3 + 2^3 + 2^3 + 4^3) = 81\(; is equal to the square of their sum. (1 + 2 + 2 + 4 )^2 .

And then, he goes on to explain why that is meaningful in relation to the natural numbers, the WHY of the fact I thought was just a coincidence. Take any prime to a power, for example 64 = 26. Now the divisors of 64 are 1, 2, 4, 8, 16, 32, and 64. When we take the number of divisors of each of these divisors, we get 1, 2, 3, 4, 5, 6, 7,

When I played around with the idea, I realized that all the strings of natural numbers (powers of a prime) summed to a triangular number (64 above sums to 28, the 7th triangular number), but no others. Semiprimes always produce {1,2,2,4} which has a sum of nine, (one less than a triangular number. A pattern?)
Fifteen is a pronic or oblong number, the product of two primes. If you try any other pronic, you will get the same result as for 15, the sum of the cubes of the set of divisors (and the square of their sum) will be 81.

Numbers like 2*3*5=30 are called sphenic numbers. They should, like pronic numbers, all have the same Louiville sets for their divisors. The eight divisors of 30, (1, 2, 3, 5, 6, 10,15, 30) have a divisors set of (1, 2, 2, 2, 4, 4, 4, 8) . The sum of the set is 27 (also one less than a triangular number) so the sum of the cubes should be 27^2 = 729, and it is.

I haven't yet tried 210. Will return later unless one of you beats me to it.

Sets that have multiple factors, other than powers of a prime seem not to form such sets. Try 12 for instance.

There is another sort of multiplication of the sets that I found on another paper on line (now lost it seems) that allows you to take any two sets and make another that also has the Liouville property. For example the set for three is {1,2} and the set for 10 is (1, 2, 2, 4} . You can form a type of cross product by multiplying each number of one set by each number of the other set independently, so we could get {1*1, 1*2, 1*2, 1*4, 2*1, 2*2, 2*2, 2*4} or {1,2,2,4,2,4,4,8} or in preferred order, {1,2,2,2,4,4,4,8} . The cubes sum to 729 and the sum (27) also squares to 729. And if you walk through the process of producing the Liouville set for 3*10 = 30, you will find it matches....but then so would 105, or in general, any sphenic number, the product of three distinct primes.

So for 210, we can multiply the Louisville set of 30, {(1, 2, 2, 2, 4, 4, 4, 8) by the set for 7 (1,2), so we just add in a double for all of these and for a product of four primes we get, in order (1, 2, 2, 2, 4, 4, 4, 8) conjoined with (2, 4, 4, 4, 8, 8, 8, 16) So I'm counting a 1, four 2's, six 4's, four 8's, and a 16 . 1^3 + 4*2^3 + 6*4^3 + 4*8^3 + 16^3 = 6561, and 1 + 4*2 + 6*4 + 4*8 +16 = 81 and 81^2 (drum roll please...da da da.. ) is 6561. (End of hoped for pattern of sum as one more than a triangular number, but I now see a binomial of the terms. For a semi-prime we had 1, 2, and 1 0f the numbers 1, 2, 4. For a product of three primes we got 1, 3, 6, 3, and 1 of the values 1, 2, 4, 6, 8, & 16.

Looking at the first four cubes we got 9, 81, 729 and 6561 which are the squares of 3, 9, 27, and 81; so hoping for 243 for the Liouville sum for this one, fingers crossed...

and on that I will predict the Liouville series for the product of five prime factors to have 1*1^3 + 5*2^3 + 10*4^3 + 10 * 8^3 + 5*16^3 + 1*32^3 = (Eureka, 59049 or 81^2.

The open question remaining is, Are there any sets that have this property that are NOT derived from divisors of a natural number? I am right where David Wells left me on that question. I would really be surprised if there were, but then I was surprised when I found out all the above.

email@example.com:blogger.com,1999:blog-2433841880619171855.post-30698304135429860312020-06-23T00:00:00.000+01:002020-06-23T00:00:05.102+01:00On This Day in Math - June 23

We can only see a short distance ahead,
but we can see plenty there that needs to be done.

Alan Turing, From his paper on the Turing test

The 175th day of the year; 175 is the smallest number n greater than 1 such that n6
\(\pm 6\) are both prime. *Prime Curios & Derek Orr

175 is the number of partitions of 35 into prime parts.

From Jim Wilder @wilderlab : \( 175 = 1^1 + 7^2 + 5^3 \)

EVENTS

1191 "In the month of June, the Vigil of the Nativity of St John the Baptist (June 23), the 9 th day before the Kalends of July, on the 27 th day of the Moon, at the 9 th hour of the day, the Sun was eclipsed and it lasted for three hours; the Sun was so obscured that the darkness arose over the Earth and stars appeared in the sky. And when the eclipse withdrew, the Sun returned to its
original beauty." This was an annular solar eclipse.

1585 Thomas Harriot arrived off the coast of Virginia (actually Cape Lookout, NC). He was the first substantial mathematician to visit North America. [John W. Shirley in Thomas Harriot: A Biography, 1983, p. 129; Thanks to Kullman] *VFR Thomas Harriot's name was once synonymous with a common method of solving quadratics taught in nearly every high school. Once commonly called Harriot's Method, today it is simply referred to as factoring.
And how did he come to be in the exploration of Virginia?? Here is the story from Encyclopedia Virginia, 2010:

Thomas Hariot (often spelled Harriot) was an English mathematician, astronomer, linguist, and experimental scientist. During the 1580s, he served as Sir Walter Raleigh's primary assistant in planning and attempting to establish the English colonies on Roanoke Island off the coast of present-day North Carolina. He taught Raleigh's sea captains to sail the Atlantic Ocean using sophisticated navigational methods not well understood in England at the time. He also learned the Algonquian language from two Virginia Indians, Wanchese and Manteo. In 1585, Hariot joined the expedition to Roanoke, which failed and returned to England the next year. During his stay in America, Hariot helped to explore the present-day Outer Banks region and, farther north, the Chesapeake Bay. He also collaborated with the artist John White in producing several maps notable at the time for their accuracy. Although Hariot left extensive papers, the only work published during his lifetime was "A Briefe and True Report of the New Found Land of Virginia", which evaluated the economic potential of Virginia. The report appeared most impressively in Theodor de Bry's 1590 edition that included etchings based on the White-Hariot maps and White's watercolors of Indian life. After a brief imprisonment in connection to the Gunpowder Plot (1605), Hariot calculated the orbit of Halley's Comet, sketched and mapped the moon, and observed sunspots. He died in 1621.

1676 Newton, via Oldenburg, sent his famous Epistola prior to Leibniz. It contained the first use of fractional exponents as well as the newly discovered binomial theorem.*VFR

In 1775, the first American-made book was advertised in Philadelphia, Penn. Titled Impenetrable Secret, the book was printed and sold by Story and Humphreys. Their advertisement in the Pennsylvania Mercury announced it was "printed with types, paper and ink manufactured in this Province."*TIS

1783 In June 1783, Charles Blagden, then assistant to Henry Cavendish, visited Antoine Lavoisier in Paris and described how Cavendish had created water by burning "inflammable air". Lavoisier's dissatisfaction with the Cavendish's "dephlogistinization" theory led him to the concept of a chemical reaction, which he reported to the Royal Academy of Sciences on 24 June 1783, effectively founding modern chemistry. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1789 *wik

1835 Mobius receives a letter from Bellavitis with a method for adding and subtracting non-collinear vectors. (A history of vector analysis: the evolution of the idea of a vectorial system By Michael J. Crowe) A geometrical work by Bellavitis was published in 1832 which also contains vector type quantities. His basic objects are line segments AB and he considers AB and BA as two distinct objects. He defines two line segments as 'equipollent' if they are equal and parallel, so, in modern notation, two line segments are equipollent if they represent the same vector. Bellavitis then defines the 'equipollent sum of line segments' and obtains an 'equipollent calculus' which is essentially a vector space. *SAU

1868 Christopher Latham Sholes receives a patent for an invention he calls the "Type-Writer." *OnThisDay & Facts @NotableHistory (Sholes was an American inventor who invented the first practical typewriter and the QWERTY keyboard still in use today. He was also a newspaper publisher and Wisconsin politician.)

1993 Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards. After announcing his results, (Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

1988  Global warming became more widely popular after 23 June, 1988 when NASA climate scientist James Hansen used the term in a testimony to Congress. He said: "global warming has reached a level such that we can ascribe with a high degree of confidence a cause and effect relationship between the greenhouse effect and the observed warming." His testimony was widely reported and afterward global warming was commonly used by the press and in public discourse. *Wik

2013 The Moon will make its closest approach to the Earth (at perigee) for the year on Sunday, 23 June, at 11:11 (UTC), and at this time the Moon will be 356,989 km from the Earth (that means 221,823 miles for us non-geeks). *Bob Mrotek

BIRTHS
1612 André Tacquet (23 June 1612 Antwerp – 22 December 1660 Antwerp, also referred to by his Latinized name Andrea Tacquet) was a Flemish mathematician and Jesuit Priest. His work prepared ground for the eventual discovery of the calculus.
He was born in Antwerp, and entered the Jesuit Order in 1629. From 1631 to 1635, he studied mathematics, physics and logic at Leuven. Two of his teachers were Saint-Vincent and Francois d'Aguilon.
Tacquet became a brilliant mathematician of international fame and his works were often reprinted and translated (into Italian and English). He helped articulate some of the preliminary concepts necessary for Isaac Newton and Gottfried Leibniz to recognize the inverse nature of the quadrature and the tangent. He was one of the precursors of the infinitesimal calculus, developed by John Wallis. His most famous work, which influenced the thinking of Blaise Pascal and his contemporaries, is Cylindricorum et annularium (1651). In this book Tacquet presented how a moving point could generate a curve and the theories of area and volume. *Wik

1756 Thomas Jones (23 June 1756 – 18 July 1807) was Head Tutor at Trinity College, Cambridge for twenty years and an outstanding teacher of mathematics. He is notable as a mentor of Adam Sedgwick.
He was born at Berriew, Montgomeryshire, in Wales. On completing his studies at Shrewsbury School, Jones was admitted to St John's College, Cambridge on 28 May 1774, as a 'pensioner' (i.e. a fee-paying student, as opposed to a scholar or sizar). He was believed to be an illegitimate son of Mr Owen Owen, of Tyncoed, and his housekeeper, who afterwards married a Mr Jones, of Traffin, County Kerry, Thomas then being brought up as his son.
On 27 June 1776, Jones migrated from St John's College to Trinity College. He became a scholar in 1777 and obtained his BA in 1779, winning the First Smith's Prize and becoming Senior Wrangler. In 1782, he obtained his MA and became a Fellow of Trinity College in 1781. He became a Junior Dean, 1787–1789 and a Tutor, 1787-1807. He was ordained a deacon at the Peterborough parish on 18 June 1780. Then he was ordained priest, at the Ely parish on 6 June 1784, canon of Fen Ditton, Cambridgeshire, in 1784, and then canon of Swaffham Prior, also 1784. On 11 December 1791, he preached before the University, at Great St Mary's, a sermon against duelling (from Exodus XX. 13), which was prompted by a duel that had lately taken place near Newmarket between Henry Applewhaite and Richard Ryecroft, undergraduates of Pembroke, in which the latter was fatally wounded. Jones died on 18 July 1807, in lodgings in Edgware Road, London. He is buried in the cemetery of Dulwich College. A bust and a memorial tablet are in the ante-chapel of Trinity College. *Wik

1775 Étienne-Louis Malus (23 Jun 1775, 24 Feb 1812 at age 36)French physicist who discovered that light, when reflected, becomes partially plane polarized; i.e., its rays vibrate in the same plane. He served in Napoleon's corps of engineers, fought in Egypt, and contracted the plague during Napoleon's aborted campaign in Palestine. Posted to Europe after 1801, he began research in optics. In 1808, he discovered that light rays may be polarized by reflection, while looking through a crystal of Iceland spar at the windows of a building reflecting the rays of the Sun. He noticed that on rotating the crystal the light was extinguished in certain positions. Applying corpuscular theory, he argued that light particles have sides or poles and coined the word "polarization." *TIS

1824 Johann Martin Zacharias Dase (June 23, 1824, Hamburg – September 11, 1861, Hamburg) was a German mental calculator.
He used to spend a lot of time playing dominoes, and suggested that this played a significant role in developing his calculating skills. Dase suffered from epilepsy from early childhood throughout his life.

At age 15 he began to travel extensively, giving exhibitions in Germany, Austria and England. Among his most impressive feats, he multiplied 79532853 × 93758479 in 54 seconds. He multiplied two 20-digit numbers in 6 minutes; two 40-digit numbers in 40 minutes; and two 100-digit numbers in 8 hours 45 minutes. The famous mathematician Carl Friedrich Gauss commented that someone skilled in calculation could have done the 100-digit calculation in about half that time with pencil and paper.

These exhibitions however did not earn him enough money, so he tried to find other employments. In 1844 he obtained a position in the Railway Department of Vienna, but this didn't last long since in 1845 he was reported in Mannheim and in 1846 in Berlin.

In 1844, Dase calculated π to 200 decimal places over the course of approximately two months, a record for the time, from the Machin-like formula:

\( \frac{\pi}{4} = \arctan \frac{1}{2} + \arctan \frac{1}{5} + \arctan \frac{1}{8} \)

He also calculated a 7-digit logarithm table and extended a table of integer factorizations from 7,000,000 to 10,000,000.

Dase had very little knowledge of mathematical theory. The mathematician Julius Petersen tried to teach him some of Euclid's theorems, but gave up the task once he realized that their comprehension was beyond Dase's capabilities. Gauss however was very impressed with his calculating skill, and he recommended that the Hamburg Academy of Sciences should allow Dase to do mathematical work on a full-time basis, but Dase died shortly thereafter.

The book "Gödel, Escher, Bach" by Douglas Hofstadter mentions his calculating abilities. "... he also had an uncanny sense of quantity. That is, he could just 'tell', without counting, how many sheep were in a field, or words in a sentence, and so forth, up to about 30." *Wik

1902 Dr. Howard T. Engstrom (23 Jun 1902, 9 Mar 1962 at age 59 American computer designer who promoted the first commercially available digital computer, the Univac. As a Yale professor he had written a paper on the mathematical basis for cryptanalysis techniques. During WW II he was called to the Navy and placed in command of the OP-20-G automated machines "Research Section" for message decryption. After the war, he was a co-founder of Engineering Research Associates, a private company to work on electronic digital circuit technology for the Navy on a contract basis, with former Navy researchers. ERA delivered its first Atlas computer to the National Security Agency in Dec 1950. As vice president for research, Engstrom took the initiative to make a commercial version, renamed Univac.*TIS

1912 Alan Mathison Turing (23 June 1912 – 7 June 1954) born. This British mathematician was one of the founders of recursion theory, invented the Turing machine (an abstract model of a computer), did important work in cryptography, and invented the computer. *Alan Turing. The Enigma by Andrew Hodges, 1983.

1941 Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics.
He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission for the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. In 2010, he was elected an Honorary Member of the Bertrand Russell Society.
He spent much of his career at Middlesex University. He was a fellow at the Institute for Advanced Study in Princeton, New Jersey, and is a member of the Académie Internationale d'Histoire des Sciences. *Wik

1944 Richard Peter Stanley (June 23, 1944; New York City, New York - ) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.
Stanley is known for his two-volume book Enumerative Combinatorics (1986–1999). He is also the author of Combinatorics and Commutative Algebra (1983) and well over 100 research articles in mathematics. He has served as thesis advisor to more than 45 doctoral students, many of whom have had distinguished careers in combinatorial research.
Stanley's distinctions include membership in the National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition, the 2003 Schock Prize, a plenary lecture at the 2006 meeting of the ICM (in Madrid, Spain), and election in 2012 as a fellow of the American Mathematical Society
Stanley created the symbol \( (\binom{n}{k}) = \binom {n+k-1}{k} \) for binomial selection with replacement. *John D Cook, Wik

DEATHS

1891 Wilhelm Eduard Weber (24 October 1804 – 23 June 1891)  German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

1891 Norman Robert Pogson (23 Mar 1829; 23 Jun 1891 at age 62) English astronomer who devised the magnitude scale of the brightness of stars (1850) now in use. He divided the classical scale in which a first magnitude star is one hundred times brighter than a sixth magnitude star using five integer steps. Each step represents a fifth-root of 100 (about 2.512) increase in brightness. The Sun's magnitude on this scale is -26.91, whereby negative numbers denote objects brighter than first magnitude. Sirius is magnitude -1.58, Aldebaran is 1 and the faintest star detected is 30. His interest in astronomy began in his youth; by age 18 he had calculated orbits for two comets. He discovered 8 asteroids, 21 new variable stars and compiled a massive star catalogue. In 1860 he moved to India for the remainder of his life's work.*TIS

1892 Pierre Ossian Bonnet (22 December 1819, Montpellier – 23 June 1892, Paris)died. He worked on minimal surfaces, geodesics, and integral geometry. *VFR Bonnet made major contributions introducing the notion of geodesic curvature. A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss-Bonnet theorem. Gauss published a special case.

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & firstname.lastname@example.com:blogger.com,1999:blog-2433841880619171855.post-89638631723328238752020-06-22T00:00:00.000+01:002020-06-22T00:00:04.144+01:00On This Day in Math - June 22

The mathematical education of the young physicist [Albert Einstein ] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
~Hermann Minkowski

The 174th day of the year; there are 174 twin prime pairs among the first 1000 integers.

174 = 72 + 53 and is also the sum of four consecutive squares.

174 is the smallest number that begins a string of four numbers so that none of them is a palindrome in any base, b, \( 2 \leq b \leq 10 \)

EVENTS

1633 Galileo, under threat of torture from the inquisition, was forced to "abjure, curse, and detest" his Copernican heliocentric views.
The recantation of GALILEO took place in the Great Hall of the former monastery of Santa Maria sopra Minerva, then the headquarters of the Dominican order. This is where he supposedly said "E pur si muove" (Nevertheless, it does move). For a long time, these words were believed to be a much later invention, but they probably date back to c1643 [Fahie, pp. 72 75]. Galileo was never officially imprisoned except for the few hours between his trial and the sentencing. In 1992, the Vatican officially declared that Galileo had been the victim of an error.

Galileo before the Holy Office, a 19th-century painting by Joseph-Nicolas Robert-Fleury

In 1675, the Royal Greenwich Observatory was created by Royal Warrant in England by Charles II. Building designed by Sir Christopher Wren (who was also a Professor of Astronomy) was commenced 10 Aug 1675 and finished the following year by John Flamsteed was appointed as the first Astronomer Royal. Its primary uses were in practical astronomy - navigation, timekeeping, determination of star positions. In 1767 the observatory began publishing The Nautical Almanac, which established the longitude of Greenwich as a baseline for time calculations. The almanac's popularity among navigators led in part to the adoption (1884) of the Greenwich meridian as the Earth's prime meridian (0° longitude) and the international time zones.*TIS

1714 second reading of the Longitude Bill in British Parliament *@Lordoflongitude

1799 France adopted the metric system of weights and measures. *VFR

1902 In response to a letter from Bertrand Russell dated 16 June 1902, Gottlob Frege responded with characteristic scientific honesty that "your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic." [van Heijenoort, From Frege to G¨odel, 125–128] *VFR
Russell had found a class of contradictions to Frege's 1879 Begriffsschrift. This contradiction can be stated as "the class of all classes that do not contain themselves as elements".

1959 According to Steven Krantz's Mathematical Apocrypha Redux, it was Marshall McLuhan who created the phrase, "Publish or Perish." In a letter to Ezra Pound he wrote about "beaneries", which was Pound's favorite term for a university:

"The beaneries are on their knees to these gents (foundation administrators). They regard them as Santa Claus. They will do 'research on anything' that Santa approves. They will think his thoughts as long as he will pay the bill for getting them before the public signed by the profesorry-rat. 'Publish or perish' is the beanery motto."

1978 evidence of the first moon of Pluto was discovered by astronomer James W. Christy of the Naval Observatory in Flagstaff, Ariz. when he obtained a photograph of Pluto that showed the orb to be distinctly elongated.. Furthermore, the elongations appeared to change position with respect to the stars over time. After eliminating the possibility that the elongations were produced by plate defects and background stars, the only plausible explanation was that they were caused by a previously unknown moon orbiting Pluto at a distance of about 19,600 kilometers (12,100 miles) with a period of 6.4 days. The moon was named Charon, after the boatman in Greek mythology who took the souls of the dead across the River Styx to Pluto's underworld. *TIS (actually Christy created the name in honor of his wife, whose nickname was Char. He did not know the mythical name when he proposed it. It is said he still persists in pronouncing the moon with a "sh" sound rather than the hard k sound used in mythology.)

2004 Humans are officially slow learners... In 2004, a study led by Richard Doll was published in the British Medical Journal, the first research that quantified the damage over the lifetime of a generation, based on a 50-year study of a group of almost 35,000 British doctors who smoked. The study found that almost half of persistent cigarette smokers were killed by their habit, and a quarter died before age 70. Further, those who quit by age 30 had the same life expectancy as a nonsmoker. Even quitting at age 50 saved six more years of life over those who continued smoking. At age 80, 65% of non-smokers were still alive, but only 32% of smokers. Fifty years before, Doll published in the same journal the first report of a study that linked cigarette smoking to lung cancer*TIS

2011 One of the 15th century copies of a manuscript of Fibonacci's Liber Abacci that was owned by Boncompagni and was until recently in Brown University Maths library is for sale, by auction, on June 22, 2011, in New York and is estimated to fetch in excess of \( $120,000\). (It seems it brought even more,"Fibonacci, manuscript copy of the Liber Flos, \($338,000\) at Bonhams New York on June 22. "

BIRTHS

1837 Paul Gustav Heinrich Bachmann born (22 June 1837 – 31 March 1920). He wrote (1892–1923) a five volume survey of the state of number theory including an evaluation of the various methods of proof. He also devoted time to composing, playing the piano, and serving as a music critic for various newspapers. *VFR

1860 Mario Pieri (22 June 1860 in Lucca, Italy - 1 March 1913 in S Andrea di Compito (near Lucca), Italy) Pieri's main area was projective geometry and he is an important member of the Italian School of Geometers. However, after he moved to Turin, Pieri became influenced by Peano at the University and Burali-Forti who was a colleague at the Military Academy. This influence led Pieri to study the foundations of geometry.
In 1895 he set up an axiomatic system for projective geometry with three undefined terms, namely points, lines and segments. He improved on results of Pasch and Peano and then, in 1905, Pieri gave the first axiomatic definition of complex projective geometry which does not build on real projective geometry.
In 1898 Pieri published the memoir The principles of the geometry of position through the Academy of Sciences of Turin. Russell was impressed by this memoir and wrote, in his Principia, "This is, in my opinion, the best work on the present subject." *SAU

1864 Herman Minkowski born (June 22, 1864 – January 12, 1909) . The motto on his Akademie-Schrift was "Rien n'est beau que le vrai, le vrai seul est aimable" (Nothing is beautiful but the truth, only the truth is lovable). *VFR He developed the geometrical theory of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity. By 1907, Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-euclidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional "space-time continuum". Minkowski worked out a four-dimensional treatment of electrodynamics. His idea of a four-dimensional space (since known as "Minkowski space"), combining the three dimensions of physical space with that of time, laid the mathematical foundation of Albert Einstein's general theory of relativity.*TIS My favorite Minkowski story from Constance Reid's Hilbert, Once in a topology lecture he brought up the Four-color theorem. "This theorem has not been proved, but that is because only mathematicians of the third rank have occupied themselves with it" he announced with unusual arrogance. "I belive I can prove it." He began on the spot to work out the problem and continued over several classes to develop the work. After several weeks he entered one rainy day and a crash of thunder accompanied his entrance. Turning to his students he announced, "Heaven is angered by my arrogance, My proof is defective."

1866 Kazimierz Żorawski (June 22, 1866 – January 23, 1953) was a Polish mathematician. His work earned him an honored place in mathematics alongside such Polish mathematicians as Wojciech Brudzewski, Jan Brożek (Broscius), Nicolas Copernicus, Samuel Dickstein, Stefan Banach, Stefan Bergman, Marian Rejewski, Wacław Sierpiński, Stanisław Zaremba and Witold Hurewicz.[citation needed]
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these disciplines was to prove important in other fields of mathematics and science, such as differential equations, geometry and physics (especially astrophysics and cosmology).*Wik

1880 Alfred Rosenblatt born. He worked in analysis and probability theory. *VFR

1906 Ott-Heinrich Keller was a German mathematician who worked on algebraic geometry and topology*SAU

1910 Konrad Zuse, (22 June 1910
Berlin, German Empire - 18 December 1995 (aged 85) Hünfeld, Germany) inventor of the first fully functional programmable digital computer. *VFR a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941.

Zuse was also noted for the S2 computing machine, considered the first process-controlled computer. He founded one of the earliest computer businesses in 1941, producing the Z4, which became the world's first commercial computer. In 1946, he designed the first high-level programming language, Plankalkül. In 1969, Zuse suggested the concept of a computation-based universe in his book Rechnender Raum (Calculating Space).
Much of his early work was financed by his family and commerce, but after 1939 he was given resources by the Nazi German government. Due to World War II, Zuse's work went largely unnoticed in the United Kingdom and the United States. Possibly his first documented influence on a US company was IBM's option on his patents in 1946. *Wik

1920 James H. Pomerene (June 22, 1920 – December 7, 2008) American computer pioneer. In Apr 1946 he joined John von Neumann and Herman Goldstine in their newly organized Electronic Computer Project at the Institute for Advanced Study in Princeton, New Jersey. This project was to build a parallel stored-program computer. He designed the adder portion of the arithmetic unit and then was entirely responsible for the development and construction of the electrostatic (Williams tube) memory and became the chief engineer of the project 1951-56. Then he joined IBM to assist development of the HARVEST computer, a special system built for the National Security Agency. It had two levels of program control and also had a tape and tape library system that was fully automatic and of great capacity.*TIS

1940 Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He is renowned for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
Quillen was a Putnam Fellow in 1959.
Quillen retired at the end of 2006. He died from complications of Alzheimer's disease on April 30, 2011, aged 70, in Florida. *Wik

1950 Benedict Hyman Gross (June 22, 1950; ) is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College.
He is known for his work in number theory, particularly the Gross–Zagier theorem on L-functions of elliptic curves, which was work with Don Zagier. *Wik

DEATHS

1388 Giovanni Dondi died (1330–1388). In 1381 he built one of the earliest geared equatoria driven by clockwork. There is a model of it in the Smithsonian. It has a heptagonal frame with a planet on each face. Dials show the time of sunrise, sunset, movable feasts, and the nodes of the moon's orbit. *VFR He is remembered today as a pioneer in the art of clock design and construction. The Astrarium, which he designed and built over a period of 16 years, was a highly complex astronomical clock and planetarium, constructed only 60 or so years after the very first mechanical clocks had been built in Europe, and demonstrated an ambitious attempt to describe and model the solar system with mathematical precision and technological sophistication. *Wik

1429 Jamshid al-Kashi (1380 - 22 June 1429 (several different dates are given for his death)
was an Islamic mathematician who published some important teaching works and anticipated Stevin's work on decimals.*SAU
Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, in central Iran. This region was controlled by Tamurlane, better known as Timur. Al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.

The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Persian princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world's greatest mathematicians.

Eight years after he came into power in 1409, their son, Ulugh Beg, founded an institute in Samarkand which soon became a prominent university. Students from all over the Middle East, and beyond, flocked to this academy in the capital city of Ulugh Beg's empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists of the Muslim world. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king's favourite student.

Al-Kashi was still working on his book, called "Risala al-watar wa'l-jaib" meaning "The Treatise on the Chord and Sine", when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are unclear. *Wik

1925 Felix Klein died. Curiously, this was the birthday of his dear friend Minkowski. *VFR German mathematician whose synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm, profoundly influenced mathematical development. He created the Klein bottle, a one-sided closed surface. A Klein bottle cannot be constructed in Euclidean space. It is best pictured as a cylinder looped back through itself to join with its other end. However this is not a continuous surface in 3-space as the surface cannot go through itself without a discontinuity. It is possible to construct a Klein bottle in non-Euclidean space.*TIS

1936 Moritz Schlick, philosopher of science and leader of the Vienna Circle, was murdered by a deranged former student, on the steps of an academic building. *VFR

1977 Harold Calvin Marston Morse developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis*SAU

1990 Ilya Mikhaylovich Frank Russian physicist who, with Tamm, theoretically explained the mechanism of Cherenkov radiation. In 1934, Cherenkov discovered that a peculiar blue light is emitted by charged particles traveling at very high speeds through water. Frank and Tamm provided the theoretical explanation of this effect, which occurs when the particles travel through an optically transparent medium at speeds greater than the speed of light in that medium. This discovery resulted in the development of new methods for detecting and measuring the velocity of high-speed particles and became of great importance for research in nuclear physics. For this, Frank received the Nobel Prize for Physics in 1958 (jointly with Pavel A. Cherenkov and Igor Y. Tamm).*TIS

1994 Julius Adams Stratton (May 18, 1901 – June 22, 1994) was a U.S. electrical engineer and university administrator. He attended the University of Washington for one year, then transferred to the Massachusetts Institute of Technology (MIT), from which he graduated with a bachelor's degree in 1923 and a master's degree in electrical engineering (EE) in 1926. He then followed graduate studies in Europe and the Technische Hochschule of Zurich (ETH Zurich), Switzerland, awarded him the degree of Doctor of Science in 1927. *Wik He worked with the blind-landing research program during WWII to help develop Glide-slope-approach radar.

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & email@example.com