Arabic numerals

Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, one of several sets of glyphs used to write numbers in the Hindu–Arabic numeral system.^[1] This is the most common symbolic representation of numbers in the world today, having found worldwide use together with the Latin alphabet, and even significantly intruding into regions where other numerals had been in use (see Chinese numerals, Japanese numerals).

They are also called Hindu–Arabic numerals,^[2]^[3] Indo–Arabic numerals, or Hindu numerals since the Arabs themselves called them "Hindu numerals".^[4]^{[note 1]} However this is also the European name for the entire family of related numerals of Arabic and Indian numerals.

The term Arabic numerals is ambiguous, as it may also be intended to mean the numerals used by Arabs — generally the Eastern Arabic numerals. To avoid confusion the terms European digits, Western numerals or Western Arabic numerals have been used. Unicode calls these digits.^[5]

From India, the system was adopted by Arabic mathematicians in Baghdad and passed on to the Arabs farther west. The current form of the numerals developed in North Africa, distinct in form from the Indian and Eastern Arabic numerals. It was in the North African city of Bejaia that the Italian scholar Fibonacci first encountered the numerals; his work was crucial in making them known throughout Europe. The use of Arabic numerals spread around the world through European trade, books and colonialism.

History[edit]

Origins[edit]

The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700.^[4] The development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten. 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 varied regionally.

The glyphs most commonly used in conjunction with the Latin script since early modern times are 0 1 2 3 4 5 6 7 8 9. The first universally accepted inscription containing the use of the 0 glyph in India is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD, but their dates are uncertain. Inscriptions in Indonesia and Cambodia dating to AD 683 have also been found.^[6]

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

The numerals used in the Bakhshali manuscript, dated to sometime between the 3rd and 7th century AD.

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

The numeral system came to be known to the court of Baghdad, where mathematicians such as the Persian Al-Khwarizmi, whose book On the Calculation with Hindu Numerals was 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, propagated it in the Arab world. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.^[7]

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 952–953. The decimal point notation was introduced by Sind ibn Ali, who also wrote the earliest treatise on Arabic numerals.

A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus (sometimes called ghubar numerals, though the term is not always accepted), which are the direct ancestor of the modern "Arabic numerals" used throughout the world.^[8] Woepecke has proposed that the Western Arabic numerals were already in use in Spain before the arrival of the Moors, purportedly received via Alexandria, but this theory is not accepted by scholars.^[9]^[10]^[11]

Popular myths[edit]

Some popular myths have argued that the original forms of these symbols indicated their numeric value through the number of angles they contained, but no evidence exists of any such origin.^[12]

Adoption in Europe[edit]

Adoption of the Hindu numerals through the Arabs by Europe

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

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.

Late 18th-century French revolutionary "decimal" clockface.

In 825 Al-Khwārizmī wrote a treatise in Arabic, On the Calculation with Hindu Numerals,^[13] which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum.^[14]^[15] Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm.^[16]

The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.^[17]

From the 980s, Gerbert of Aurillac (later, Pope Sylvester II) used his position 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.

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

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 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 system "Hindu numerals",^[18]^[19] 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).^[12]

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 evidence of their use in Britain includes: an equal hour horary quadrant from 1396,^[20] in England, 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 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 the use of Arabic numerals, which appear for the first time in a royal document of 1456.^[21] By the mid-16th century, they were in common use in most of Europe.^[22] Roman numerals remained in use mostly for the notation of Anno Domini years, and for numbers on clockfaces.

Today, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical enumeration), for sequential volumes, to differentiate monarchs or family members with the same first names, and (in lower case) to number pages in prefatory material in books.

Adoption in Russia[edit]

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.

Adoption in China[edit]

Iron plate with an order 6 magic square in Persian/ Arabic numbers from China, dating to the Yuan Dynasty (1271–1368).

Eastern Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.^[23]^[24]^[25]

Evolution of symbols[edit]

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, potentially including both symbols that evolved from the Brahmi numerals, and symbols that developed independently. 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 script, in the table below labelled European, descended from the West Arabic numerals developed in al-Andalus (Andalucía, Spain) and the Maghreb. Spanish scholars, because of the geographic proximity, trade, and constant warfare with the Muslim kingdoms of Southern Spain, saw a potential in the simplicity of Arabic numbers, and decided to adopt those symbols, and later other Europeans followed suit. 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 script, developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals used in the Persian and Urdu languages is shown below as East Arabic-Indic.
The Devanagari numerals used with Devanagari and related variants are grouped as Indian numerals.

The evolution of the numerals in early Europe is shown here in a table created by the French scholar Jean-Étienne Montucla in his Histoire de la Mathematique, which was published in 1757:

The Arabic numeral glyphs 0–9 are encoded in ASCII and Unicode at positions 0x30 to 0x39, matching up with the second hexadecimal digit for convenience:

Binary	Octal	Decimal	Hexadecimal	Glyph
0011 0000	060	48	30	0
0011 0001	061	49	31	1
0011 0010	062	50	32	2
0011 0011	063	51	33	3
0011 0100	064	52	34	4
0011 0101	065	53	35	5
0011 0110	066	54	36	6
0011 0111	067	55	37	7
0011 1000	070	56	38	8
0011 1001	071	57	39	9

Notes[edit]

^ Hindu was the Persian name for "Indian" in the 10th century, when the Arabs adopted the number system. The connotation of "Hindu" as a religion was a later development.

References[edit]

^ Bulliet, Richard; Crossley, Pamela; Headrick,, Daniel; Hirsch, Steven; Johnson, Lyman (2010). The Earth and Its Peoples: A Global History, Volume 1. Cengage Learning. p. 192. ISBN 1439084742. Indian mathematicians invented the concept of zero and developed the "Arabic" numerals and system of place-value notation used in most parts of the world today ^{[better source needed]}
^ Schipp, Bernhard; Krämer, Walter (2008), Statistical Inference, Econometric Analysis and Matrix Algebra: Festschrift in Honour of Götz Trenkler, Springer, p. 387, ISBN 9783790821208
^ Lumpkin, Beatrice; Strong, Dorothy (1995), Multicultural science and math connections: middle school projects and activities, Walch Publishing, p. 118, ISBN 9780825126598
^ ^a ^b O'Connor, J. J. and Robertson, E. F. Arabic Numerals. January 2001. Retrieved on 2007-02-20.
^ Official Unicode Consortium code chart
^ Plofker 2009, p. 45.
^ The MacTutor History of Mathematics archive
^ Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered 2003, pp. 12–13: "While specimens of Western Arabic numerals from the early period—the tenth to thirteenth centuries—are still not available, we know at least that Hindu reckoning (called ḥisāb al-ghubār) was known in the West from the tenth century onward..."
^ Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered 2003, pp. 12–13: "Since edition of and research on the Pseudo-Boethius[41] we now know that the texts running under his name and carrying Arabic numerals date from the eleventh century. Thus the assumed way of transmission from Alexandria to Spain is impossible and this theory can no longer be taken as serious."
^ Smith, D. E.; Karpinski, L. C. (2013) [first published in Boston, 1911], The Hindu-Arabic Numerals, Dover, Chapter V, ISBN 0486155110
^ Gandz, Solomon (November 1931), "The Origin of the Ghubār Numerals, or the Arabian Abacus and the Articuli", Isis, 16 (2): 393–424, doi:10.1086/346615, JSTOR 224714
^ ^a ^b Ifrah, Georges (1998). The universal history of numbers: from prehistory to the invention of the computer; translated from the French by David Bellos. London: Harvill Press. pp. 356–357. ISBN 9781860463242.
^ Philosophy Of Mathematics Francis, John – 2008 – Page 38
^ The Ellipse: A Historical and Mathematical Journey Arthur Mazer – 2011
^ "al-Khwarizmi - Muslim mathematician".
^ Models of Computation: An Introduction to Computability Theory – Page 1 Maribel Fernández – 2009
^ "MATHORIGINS.COM_V". www.mathorigins.com.
^ Rowlett, Russ (4 July 2004), Roman and "Arabic" Numerals, University of North Carolina at Chapel Hill, retrieved 22 June 2009
^ Achenbach, Joel (16 September 1994), Article: Take a Number, Please., The Washington Post, retrieved 22 June 2009
^ "14th century timepiece unearthed in Qld farm shed". ABC News.
^ Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918
^ Mathforum.org
^ Helaine Selin, ed. (31 July 1997). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. pp. 198–. ISBN 978-0-7923-4066-9. Retrieved 3 March 2012.
^ Meuleman, Johan H. (23 August 2002). Islam in the era of globalization: Muslim attitudes towards modernity and identity. Psychology Press. p. 272. ISBN 978-0-7007-1691-3. Retrieved 3 March 2012.
^ Peng Yoke Ho (16 October 2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Courier Dover Publications. p. 106. ISBN 978-0-486-41445-4. Retrieved 3 March 2012.

Sources[edit]

Kunitzsch, Paul (2003), "The Transmission of Hindu-Arabic Numerals Reconsidered", in J. P. Hogendijk; A. I. Sabra, The Enterprise of Science in Islam: New Perspectives, MIT Press, pp. 3–22, ISBN 978-0-262-19482-2
Plofker, Kim (2009), Mathematics in India, Princeton University Pres, ISBN 978-0-691-12067-6