Instruct: Given a question, retrieve passages that can help answer the question.
Query: When was the Arabic numeral system introduced in Europe?
From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo. Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th  century. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's "Liber Abaci" of 1201. In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.
Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication and division) first appear in the archaeological record. The Babylonians also possessed a place-value system, and used a sexagesimal numeral system, still in use today for measuring angles and time.
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.
The first mentions of the numerals in the West are found in the "Codex Vigilanus" of 976.
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.
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.
Algebra was also pioneered by Persian Scientist Muhammad ibn Mūsā al-Khwārizmī during this time in his landmark text, Kitab al-Jabr wa-l-Muqabala, from which the term algebra is derived. He is thus considered to be the father of algebra. The terms algorism and algorithm are also derived from the name of al-Khwarizmi, who was responsible for introducing the Arabic numerals and Hindu-Arabic numeral system beyond the Indian Subcontinent.
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).
Writing was introduced by the Greeks and from there also brought to the Romans (6th century BC). There are five alphabets in regular use in the areas generally considered Europe. The Latin alphabet was developed into several scripts. In the early years of Europe, the Carolingian minuscules were the most important variety of the Latin script. From this two branches developed, the Gothic/Fracture/German tradition, which Germans used well into the 20th century, and the Italian/Italic/Antiqua/Latin tradition, still used. For some nations the integration into Europe meant giving up older scripts, e.g. the Germanic gave up the runes (Futhark) (3rd to 17th centuries), the Irish the Ogham script (4th to 7th centuries). The Cyrillic script is the second most widespread alphabet in Europe, and was developed in the 9th century under the influence of the Greek, Latin and Glagolitic alphabets. Both the Latin and Cyrillic alphabets are used for multiple languages in multiple states, both inside and outside Europe. As well as these two, there are three alphabets used primarily for a single language, although they are occasionally applied to minority languages in the states from which they originate. The oldest of these alphabets is the Greek alphabet, which could be considered the progenitor of all the surviving alphabets of Europe, with the earliest recorded inscriptions appearing in the 9th century BC. The other two are both found in the Caucasus, both originating in the 5th century. The Georgian alphabet is used primarily to write Georgian, though it is also used to write the other Kartvelian languages, Svan, Mingrelian and Laz, all of which are found largely within the borders of Georgia. The Armenian alphabet is used to write the Armenian language, which has two dialects, and has been used to write Turkish in the past.
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.
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.
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.
For central Arabia, especially Mecca, there is a lack of epigraphical evidence but details are found in the writings of Muslim authors of the Abbasid era. Inscriptions of the ancient South Arabian calendars reveal the use of a number of local calendars. At least some of these South Arabian calendars followed the lunisolar system. Both al-Biruni and al-Mas'udi suggest that the ancient Arabs used the same month names as the Muslims, though they also record other month names used by the pre-Islamic Arabs.
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.
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.
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.
The currency was introduced in non-physical form (traveller's cheques, electronic transfers, banking, etc.) at midnight on 1 January 1999, when the national currencies of participating countries (the eurozone) ceased to exist independently. Their exchange rates were locked at fixed rates against each other. The euro thus became the successor to the European Currency Unit (ECU). The notes and coins for the old currencies, however, continued to be used as legal tender until new euro notes and coins were introduced on 1 January 2002.
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.
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.
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).
The currency was introduced in non-physical form (traveller's cheques, electronic transfers, banking, etc.) at midnight on 1 January 1999, when the national currencies of participating countries (the eurozone) ceased to exist independently in that their exchange rates were locked at fixed rates against each other, effectively making them mere non-decimal subdivisions of the euro. The euro thus became the successor to the European Currency Unit (ECU). The notes and coins for the old currencies, however, continued to be used as legal tender until new notes and coins were introduced on 1 January 2002 (having been distributed in small amounts in the previous December). Beginning on 1 January 1999, all bonds and other forms of government debt by eurozone nations were denominated in euros.
The Hindu-Arabic numerals were invented by mathematicians in India. Perso-Arabic mathematicians called them "Hindu numerals" (where "Hindu" meant Indian). Later they came to be called "Arabic numerals" in Europe, because they were introduced to the West by Arab merchants.
The reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were then using the digits from Libya to Morocco. Arabs, on the other hand, call the base-10 system (not just these digits) "Hindu numerals", referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabic numerals ( - - - - - - - - - ) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ).
The familiar shape of the Western Arabic glyphs as now used with the Latin alphabet (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they enter early typesetting.
Muslim scientists used the Babylonian numeral system, and merchants used the Abjad numerals, a system similar to the Greek numeral system and the Hebrew numeral system. Similarly, 's introduction of the system to Europe was restricted to learned circles.
The credit for first establishing widespread understanding and usage of the decimal positional notation among the general population goes to , an author of the German Renaissance, whose 1522 " was targeted at the apprentices of businessmen and craftsmen.
In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in "Brahma-sphuta-siddhanta", he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu–Arabic numeral system. It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as Arabic numerals. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, all of which evolved from the Brahmi numerals. Each of the roughly dozen major scripts of India has its own numeral glyphs. In the 10th century, Halayudha's commentary on Pingala's work contains a study of the Fibonacci sequence and Pascal's triangle, and describes the formation of a matrix.