Arabic numerals

Numerals sans-serif

The Arabic numerals or Hindu numerals^[1][2] or Hindu-Arabic numerals^[2][3] are the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, by which a sequence of numerals such as "975" is read as a whole number. The Indian numerals were adopted by the Persian mathematicians in India, and passed on to the Arabs further west. From there they were transmitted to Europe in the Middle Ages. The use of Arabic numerals spread around the world through European trade, books and colonialism. Today they are the most common symbolic representation of numbers in the world.

As befitting their history, the digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are more appropriately known as Hindu or Hindu-Arabic numerals. The reason that they are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the tenth century from Arabs of North Africa, who were then using the digits from Libya to Morocco.^[4] Europeans did not know about the numerals' roots in ancient India, so they named them "Arabic numerals".^[5] Arabs, on the other hand, call the system "Hindu numerals",^[6][7] 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 (٠.١.٢.٣.٤.٥.٦.٧.٨.٩) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ०.१.२.३.४.५.६.७.८.९).^[8]

In English, the term Arabic numerals can be ambiguous. It most commonly refers to the numeral system widely used in Europe and the Americas. Arabic numerals is the conventional name for the entire family of related systems of Arabic and Indian numerals. It may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals.

The decimal Hindu-Arabic numeral system was invented in India around 500 AD.^[8][9] The system was revolutionary in that it included a zero and positional notation. It is considered an important milestone in the development of mathematics. One may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which vary regionally. The glyphs most commonly used in conjunction with the Latin alphabet since early modern times are 0 1 2 3 4 5 6 7 8 9.

Although the phrase "Arabic numeral" is frequently capitalized, it is sometimes written in lower case: for instance, in its entry in the Oxford English dictionary.^[10] This helps distinguish it from "Arabic numerals" as the East Arabic numerals specific to the Arabs.

History

Origins

The digits 1 to 9 in the Hindu-Arabic numeral system evolved from the Brahmi numerals. Buddhist inscriptions from around 300 BC use the symbols which became 1, 4 and 6. One century later, their use of the symbols which became 2, 7 and 9 was recorded.

The first universally accepted inscription containing the use of the 0 glyph is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. By this time, the use of the glyph had already reached Persia, and was mentioned in Al-Khwarizmi's descriptions of Indian numerals. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD.^[11]

Brahmi numerals (lower row) in India in the 1st century AD

Modern-day Arab telephone keypad with two forms of Hindu-Arabic numerals: Western Arabic/European numerals on the left and Eastern Arabic numerals on the right

The numeral system came to be known to both the Persian mathematician Al-Khwarizmi, whose book On the Calculation with Hindu Numerals written about 825 in Arabic, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Use of the Indian Numerals" (Ketab fi Isti'mal al-'Adad al-Hindi) about 830. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.^[12] In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–53.

A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus, called ghubar ("sand-table" or "dust-table") numerals, which is the direct ancestor to the modern Western Arabic numerals used throughout the world.^[13]

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.^[14] From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his office to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona in his youth. He was known to have requested mathematical treatises concerning the astrolabe from Lupitus of Barcelona after he had returned to France.

Common misconceptions

Despite evidence to the contrary, some folkloric explanations for the origin of modern Arabic numerals persist. While these hypotheses continue to propagate due to their seemingly well-constructed arguments, they were based entirely on speculation by individuals who, while genuinely intrigued by the subject, were either ignorant of the relevant archeological facts, or simply lived in an era preceding much of their modern rediscovery. One popular example of such myths claims that the original forms of these symbols indicated their value through the quantity of angles they contained.^[15][16][17]

Adoption in Europe

A German manuscript page teaching use of Arabic numerals (Talhoffer Thott, 1459). At this time, knowledge of the numerals was still widely seen as esoteric, and Talhoffer presents them with the Hebrew alphabet and astrology.

Woodcut showing the 16th century astronomical clock of Uppsala Cathedral, with two clockfaces, one with Arabic and one with Roman numerals.

Late 18th century French revolutionary "decimal" clockface.

In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals, which was translated into Latin from Arabic in the 12th century as Algoritmi de numero Indorum, where Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm (Latin algorithmus, "calculation method").

Fibonacci, a mathematician born in the Republic of Pisa who had studied in Bejaia (Bougie), Algeria, promoted the Indian numeral system in Europe with his book Liber Abaci, which was written in 1202:

"When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.."

The numerals are arranged with their lowest value digit to the right, with higher value positions added to the left. This arrangement was adopted identically into the numerals as used in Europe. Languages written in the Latin alphabet run from left to right, unlike languages written in the Arabic alphabet. Hence, from the point of view of the reader, numerals in Western texts are written with the highest power of the base first whereas numerals in Arabic texts are written with the lowest power of the base first.

The European acceptance of the numerals was accelerated by the invention of the printing press, and they became widely known during the 15th century. Early uses in Britain include a 1445 inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription on the tomb of the first Earl of Huntly in Elgin, (Elgin, Moray) Cathedral. (See G.F. Hill, The Development of Arabic Numerals in Europe for more examples.) In central Europe, the King of Hungary Ladislaus the Posthumous, started using the Arabic numerals, appearing for the first time in a royal document of 1456.^[18] By the mid-16th century, they were in common use in most of Europe.^[19] Roman numerals remained in use mostly for the notation of Anno Domini years, and for numbers on clockfaces. Sometimes, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), and numbering pages in prefatory material in books.

Adoption in Russia

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 1700s when Peter the Great replaced it with Arabic numerals.

Adoption in China

During Ming and Qing dynasties (when Arabic numerals were first introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After Qing dynasty, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.

Evolution of symbols

The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hindu-Arabic numeral system, all of which evolved from the Brahmi numerals. The symbols used to represent the system have split into various typographical variants since the Middle Ages:

• The widespread Western Arabic numerals used with the Latin alphabet, in the table below labelled European, descended from the West Arabic numerals developed in al-Andalus and the Maghreb. (There are two typographic styles for rendering European numerals, known as lining figures and text figures).
• The Arabic-Indic or Eastern Arabic numerals used with the Arabic alphabet developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in the Persian and Urdu languages is shown as East Arabic-Indic. There is substantial variation in usage of glyphs for the Eastern Arabic-Indic digits, especially for the digits four, five, six, and seven.^[20]
• The Devanagari numerals used with Devanagari and related variants are grouped as Indian numerals.

The evolution of the numerals in early Europe is shown on a table created by the French scholar J.E. Montucla in his Histoire de la Mathematique, which was published in 1757:

The Arabic numerals are encoded in ASCII (and Unicode) at positions 48 to 57:

See also

• Hindu-Arabic numeral system
• Numeral system
• Numerical digit
• Decimal
• Positional numeral system
• Counting rods - decimal positional numeral system with zero
• Chinese numerals
• Japanese numerals
• Roman numerals

Notes

References

• Ore, Oystein (1988), "1", Number theory and its history, Dover, pp. 19–24, ISBN 0486656209, http://store.doverpublications.com/0486656209.html 
• Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic, Greek and Latin", Journal of Indian Philosophy, (Springer-Netherlands) 34 (1-2): 15–30, doi:10.1007/s10781-005-8153-z .
• Encyclopaedia Britannica (Kim Plofker) (2007), "mathematics, South Asian", Encyclopædia Britannica Online: 1–12, http://www.britannica.com/eb/article-9389286, retrieved May 18, 2007 .
• Hayashi, Takao (1995), The Bakhshali Manuscript, An ancient Indian mathematical treatise, Groningen: Egbert Forsten, ISBN 906980087X .
• Ifrah, Georges (2000), A Universal History of Numbers: From Prehistory to Computers, New York: Wiley, ISBN 0471393401, http://www.amazon.com/Universal-History-Numbers-Prehistory-Invention/dp/0471393401/ .
• Katz, Victor J. (ed.) (July 20, 2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, NJ: Princeton University Press,, ISBN 0691114854 .

External links

• History of Counting Systems and Numerals. Retrieved 11 December 2005.
• The Evolution of Numbers. 16 April 2005.
• O'Connor, J. J. and Robertson, E. F. Indian numerals. November 2000.
• History of the Numerals
  • Arabic numerals:
  • Hindu-Arabic numerals:
  • Numeral & Numbers' history and curiosities:
  • Gerbert d'Aurillac's early use of Hindu-Arabic numerals at Convergence

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