Instruct: Given a question, retrieve passages that answer the question.
Query: When did the Arabic numeral system develop?
It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. Influential were the books of Muḥammad ibn Mūsā al-Khwārizmī ("On the Calculation with Hindu Numerals", ) and Al-Kindi ("On the Use of the Hindu Numerals", ). The system later spread to medieval Europe by the High Middle Ages.
Al-Karkhi (953–1029), also known as Al-Karaji, was the successor of Abū al-Wafā' al-Būzjānī (940–998) and he discovered the first numerical solution to equations of the form ax + bx = c. Al-Karkhi only considered positive roots. Al-Karkhi is also regarded as the first person to free algebra from geometrical operations and replace them with the type of arithmetic operations which are at the core of algebra today. His work on algebra and polynomials, gave the rules for arithmetic operations to manipulate polynomials. The historian of mathematics F. Woepcke, in "Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi" (Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle.
Many numbers include hundreds, units and tens. The Roman numeral system being basically decimal, each power of ten is added in descending sequence from left to right, as with Arabic numerals. For example:As each power of ten (or "place") has its own notation there is no need for place keeping zeros, so "missing places" are ignored, as in Latin (and English) speech, thus:Roman numerals for large numbers are nowadays seen mainly in the form of year numbers (other uses are detailed later in this article), as in these examples:The "standard" forms described above reflect typical modern usage rather than an unchanging and universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval times. There is still no official "binding" standard, which makes the elaborate "rules" used in some sources to distinguish between "correct" and "incorrect" forms highly problematic.Although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used , , , , , and for , , , , , and , of which only and happened to be letters in their alphabet.
The first mentions of the numerals in the West are found in the "Codex Vigilanus" of 976.
In print, Arabic numerals are employed in Modern Hebrew for most purposes. Hebrew numerals are used nowadays primarily for writing the days and years of the Hebrew calendar; for references to traditional Jewish texts (particularly for Biblical chapter and verse and for Talmudic folios); for bulleted or numbered lists (similar to "A", "B", "C", "etc.", in English); and in numerology (gematria).
Musical notation was developed before parchment or paper were used for writing. The earliest form of musical notation can be found in a cuneiform tablet that was created at Nippur, in Sumer (today's Iraq) in about 2,000 BC. The tablet represents fragmentary instructions for performing music, that the music was composed in harmonies of thirds, and that it was written using a diatonic scale.
The invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age of the late 4th millennium BC. The Sumerian archaic cuneiform script and the Egyptian hieroglyphs are generally considered the earliest writing systems, both emerging out of their ancestral proto-literate symbol systems from 3400 to 3200 BC with earliest coherent texts from about 2600 BC. It is generally agreed that Sumerian writing was an independent invention; however, it is debated whether Egyptian writing was developed completely independently of Sumerian, or was a case of cultural diffusion.
Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.
Adelard of Bath (; 1080 1152 AD) was a 12th-century English natural philosopher. He is known both for his original works and for translating many important Arabic and Greek scientific works of astrology, astronomy, philosophy and mathematics into Latin from Arabic versions, which were then introduced to Western Europe. He is known as one of the first to introduce the Arabic numeral system to Europe. He stands at the convergence of three intellectual schools: the traditional learning of French schools, the Greek culture of Southern Italy, and the Arabic science of the East.
Al-Khwarizmi's popularizing treatise on algebra ("The Compendious Book on Calculation by Completion and Balancing", c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The term "algebra" itself comes from the title of his book (specifically the word "al-jabr" meaning "completion" or "rejoining"). His name gave rise to the terms "algorism" and "algorithm". His name is also the origin of (Spanish) "guarismo" and of (Portuguese) "algarismo", both meaning digit.
The invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age in the late 4th millennium BC. The Sumerian archaic cuneiform script and the Egyptian hieroglyphs are generally considered to be the earliest writing systems, both emerging out of their ancestral proto-literate symbol systems from 3400–3200 BC with the earliest coherent texts from about 2600 BC. It is generally agreed that Sumerian writing was an independent invention; however, it is debated whether Egyptian writing was developed completely independently of Sumerian, or was a case of cultural diffusion. A similar debate exists for the Chinese script, which developed around 1200 BC. The pre-Columbian Mesoamerican writing systems (including among others Olmec and Maya scripts) are generally believed to have had independent origins.
Writing systems were preceded by proto-writing, systems of ideographic and/or early mnemonic symbols. The best known examples are:The invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age in the late Neolithic of the late 4th millennium BC. The Sumerian archaic cuneiform script and the Egyptian hieroglyphs are generally considered the earliest writing systems, both emerging out of their ancestral proto-literate symbol systems from 3400 to 3200 BC with earliest coherent texts from about 2600 BC. It is generally agreed that Sumerian writing was an independent invention; however, it is debated whether Egyptian writing was developed completely independently of Sumerian, or was a case of cultural diffusion.
During 1909 and 1910 there were movements by Young Turks supporters to adopt an Arabic alphabet, as they considered the Latin script to be un-Islamic. In Elbasan, Muslim clerics led a demonstration for the Arabic script, telling their congregations that using the Latin script would make them infidels. In 1911, the Young Turks dropped their opposition to the Latin script, and the Latin alphabet was invented. In order to eliminate ambiguity in the pronunciation of the Arabic script, Rexhep Voka developed a customized Arabic alphabet consisting of 44 consonants and vowels, which he published in 1911. However, it was hardly used anymore due to the Congress of Monastir. Tiranli Fazli then used this script to publish a thirty-two page grammar. Only one Albanian newspaper at the time ever appeared in Arabic script, and it lasted a brief period. Regardless of what script appeared, such material raised Albanian national consciousness.
Sumer in Mesopotamia, the Indus valley civilization and ancient Egypt were the first civilizations to develop their own scripts, and to keep historical records; this took place already during the early Bronze Age. Neighboring civilizations were the first to follow. Most other civilizations reached the end of prehistory during the Iron Age. The three-age system of division of prehistory into the Stone Age, followed by the Bronze Age and Iron Age, remains in use for much of Eurasia and North Africa, but is not generally used in those parts of the world where the working of hard metals arrived abruptly with contact with Eurasian cultures, such as the Americas, Oceania, Australasia and much of Sub-Saharan Africa. These areas also, with some exceptions in Pre-Columbian civilizations in the Americas, did not develop complex writing systems before the arrival of Eurasians, and their prehistory reaches into relatively recent periods; for example 1788 is usually taken as the end of the prehistory of Australia.
Year zero does not exist in the anno Domini system usually used to number years in the Gregorian calendar and in its predecessor, the Julian calendar. In this system, the year is followed by . However, there is a year zero in astronomical year numbering (where it coincides with the Julian year ) and in ISO 8601:2004 (where it coincides with the Gregorian year ) as well as in all Buddhist and Hindu calendars.
More complete writing systems were preceded by proto-writing. Early examples are the Jiahu symbols (c. 6600 BCE), Vinča signs (c. 5300 BCE), early Indus script (c. 3500 BCE) and Nsibidi script (c. before 500 CE). There is disagreement concerning exactly when prehistory becomes history, and when proto-writing became "true writing" However, invention of the first writing systems is roughly contemporary with the beginning of the Bronze Age in the late Neolithic of the late 4th millennium BCE. The Sumerian archaic cuneiform script and the Egyptian hieroglyphs are generally considered the earliest writing systems, both emerging out of their ancestral proto-literate symbol systems from 3400–3200 BCE with earliest coherent texts from about 2600 BCE.
The "Brāhmasphuṭasiddhānta" of Brahmagupta (598–668) is the earliest known text to treat zero as a number in its own right and to define operations involving zero. The author could not explain division by zero in his texts: his definition can be easily proven to lead to algebraic absurdities. According to Brahmagupta,
Its numerical value is 800 (see Abjad numerals).
ISO 8601:2004 (and previously ISO 8601:2000, but not ISO 8601:1988) explicitly uses astronomical year numbering in its date reference systems. Because it also specifies the use of the proleptic Gregorian calendar for all years before 1582, some readers incorrectly assume that a year zero is also included in that proleptic calendar, but it is not used with the BC/AD era. The "basic" format for year 0 is the four-digit form 0000, which equals the historical year 1 BC. Several "expanded" formats are possible: −0000 and +0000, as well as five- and six-digit versions. Earlier years are also negative four-, five- or six-digit years, which have an absolute value one less than the equivalent BC year, hence -0001 = 2 BC. Because only ISO 646 (7-bit ASCII) characters are allowed by ISO 8601, the minus sign is represented by a hyphen-minus.
The notation is similar to the older Roman numerals for numbers 1 to 9 "(I,II,III,IV,V,VI,VII,VIII,IX)". Unlike the Roman notation, there are only symbols for numbers one ("I") and five ("U"). In inscriptions the notches are placed vertically on the stem or "stav" of the rune. The number 4 is represented by four horizontal lines on the stem, 5 is represented by what looks like an inverted letter U. 10 is represented by two U's opposing each other. Numbers up to 19, or even 20, can be represented by a combination of I's and U's, just like the Roman numerals are represented by combinations of I's and V's. (A Roman 10 is represented by two V's opposing each other).
Group D
Numbers should be distinguished from numerals, the symbols used to represent numbers. The Egyptians invented the first ciphered numeral system, and the Greeks followed by mapping their counting numbers onto Ionian and Doric alphabets. Roman numerals, a system that used combinations of letters from the Roman alphabet, remained dominant in Europe until the spread of the superior Arabic numeral system around the late 14th century, and the Arabic numeral system remains the most common system for representing numbers in the world today. The key to the effectiveness of the system was the symbol for zero, which was developed by ancient Indian mathematicians around 500 AD.
The numeral system came to be known to both the Persian mathematician Khwarizmi, who wrote a book, "On the Calculation with Hindu Numerals" in about 825, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Use of the Hindu Numerals" ( ["kitāb fī isti'māl al-'adād al-hindī"]) around 830. These earlier texts did not use the Hindu numerals. Kushyar ibn Labban who wrote "Kitab fi usul hisab al-hind (Principles of Hindu Reckoning)" is one of the oldest surviving manuscripts using the Hindu numerals. These books are principally responsible for the diffusion of the Hindu system of numeration throughout the Islamic world and ultimately also to Europe.
Al-Uqlidisi developed a notation to represent decimal fractions.
The numerals came to fame due to their use in the pivotal work of the Persian mathematician Al-Khwarizmi, whose book "On the Calculation with Hindu Numerals" was written about 825, and the Arab mathematician Al-Kindi, who wrote four volumes (see [2]) "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. They, amongst other works, contributed to the diffusion of the Indian system of numeration in the Middle-East and the West.
Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used in the First Bulgarian Empire and by South and East Slavic peoples. The system was used in Russia as late as the early 18th century, when Peter the Great replaced it with Arabic numerals as part of his civil script reform initiative. Cyrillic numbers played a role in Peter the Great's currency reform plans, too, with silver wire kopecks issued after 1696 and mechanically minted coins issued between 1700 and 1722 inscribed with the date using Cyrillic numerals. By 1725, Russian Imperial coins had transitioned to Arabic numerals. The Cyrillic numerals may still be found in books written in the Church Slavonic language.