The Info List - Arabic Numerals

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numerals, also called Hindu– Arabic
numerals,[1][2] are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, based on the Hindu– Arabic
numeral system,[3] the most common system for the symbolic representation of numbers in the world today. In this numeral system, a sequence of digits such as "975" is read as a single number, using the position of the digit in the sequence to interpret its value. They are descended from the Hindu- Arabic
numeral system developed by Indian mathematicians around AD 500.[3] The system was adopted by Arabic
mathematicians in Baghdad
and passed on to the Arabs farther west. There is some evidence to suggest that the numerals in their current form developed from Arabic
letters in the Maghreb, the western region of the Arab
world.[4] 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. The term Arabic
numerals is ambiguous. It most commonly refers to the numerals widely used in Europe and the Americas; to avoid confusion, Unicode
calls these European digits. Arabic
numerals is also the European name for the entire family of related numerals 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. It would be more appropriate to refer to the Arabic
numeral system, where the value of a digit in a number depends on its position. 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,[5] which helps to distinguish it from " Arabic
numerals" as the East Arabic
numerals specific to the Arabs.


1 History

1.1 Origins

1.1.1 Popular myths

1.2 Adoption in Europe 1.3 Adoption in Russia 1.4 Adoption in China

2 Evolution of symbols 3 See also 4 References 5 Sources 6 Further reading 7 External links

History[edit] Origins[edit] Main article: History of the Hindu– Arabic
numeral system The decimal Hindu–Arabic numeral system
Hindu–Arabic numeral system
was developed in India by around AD 700.[6] 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
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.[7]

Brahmi numerals
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.[8] 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, called ghubar ("sand-table" or "dust-table") numerals, which are the direct ancestor of the modern Western Arabic
numerals used throughout the world. Some scholars have proposed that the ghubar numerals themselves are possibly of Roman origin.[9][10] 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.[11] 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,[12] which survives only as the 12th-century Latin translation, Algoritmi de numero Indorum.[13][14] Algoritmi, the translator's rendition of the author's name, gave rise to the word algorithm.[15] The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.[16] 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
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",[17][18] 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
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).[11] 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,[19] 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.[20] By the mid-16th century, they were in common use in most of Europe.[21] Roman numerals
Roman numerals
remained in use mostly for the notation of Anno Domini years, and for numbers on clockfaces. Today, Roman numerals
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
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
Yuan Dynasty

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.[22][23][24] Evolution of symbols[edit] Main article: Algorism 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
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
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

See also[edit]

Abjad numerals Chinese numerals Counting rods
Counting rods
– decimal positional numeral system with zero Decimal Greek numerals Japanese numerals Maya numerals Regional variations in modern handwritten Arabic


^ 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 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] ^ On the Origin of Arabic
Numerals - A. Boucenna - Université Ferhat Abbas Setif
(in French) ^ "Arabic", Oxford English Dictionary, 2nd edition ^ O'Connor, J. J. and E. F. Robertson. 2000. Indian Numerals, MacTutor History of Mathematics Archive, School of Mathematics and Statistics, University of St. Andrews, Scotland. ^ Plofker 2009, p. 45. ^ The MacTutor History of Mathematics archive ^ 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. 


Plofker, Kim (2009), Mathematics in India, Princeton University Pres, ISBN 978-0-691-12067-6 

Further reading[edit]

Ore, Oystein (1988), "Hindu- Arabic
numerals", Number
Theory and Its History, Dover, pp. 19–24, ISBN 0486656209 . 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 . Encyclopædia Britannica (Kim Plofker) (2007), "mathematics, South Asian", Encyclopædia Britannica Online, 189 (4761): 1–12, Bibcode:1961Natur.189S.273., doi:10.1038/189273c0, retrieved 18 May 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, ASIN 0471393401, ISBN 0471393401 CS1 maint: ASIN uses ISBN (link) . Katz, Victor J. (ed.) (20 July 2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton, New Jersey: Princeton University Press, ISBN 0691114854 CS1 maint: Extra text: authors list (link) .

External links[edit]

Wikimedia Commons
Wikimedia Commons
has media related to: Arabic
numerals (category)

Development of Hindu
and Traditional Chinese Arithmetic 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

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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Ṯāʾ Ǧīm Ḥāʾ Ḫāʾ Dāl Ḏāl Rāʾ Zāy Sīn Šīn Ṣād Ḍād Ṭāʾ Ẓāʾ ʿAyn Ġayn Fāʾ Qāf Kāf Lām Mīm Nūn Hāʾ

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