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Arabic numerals

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**Arabic numerals**, also called

**Hinduâ€“Arabic numerals**,{{Citation|last1=Schipp|first1=Bernhard|title=Statistical Inference, Econometric Analysis and Matrix Algebra: Festschrift in Honour of GÃ¶tz Trenkler|url=https://books.google.com/?id=t6XfLJzqO_kC&pg=PA387|page=387|year=2008|publisher=Springer|isbn=9783790821208|last2=KrÃ¤mer|first2=Walter}}{{Citation|last1=Lumpkin|first1=Beatrice|title=Multicultural science and math connections: middle school projects and activities|url=https://books.google.com/?id=2LgG8lsJQmAC&pg=PA118|page=118|year=1995|publisher=Walch Publishing|isbn=9780825126598|last2=Strong|first2=Dorothy}} are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The term often implies a decimal number written using these digits, which is the most common system for the symbolic representation of numbers in the world today. However the term can mean the digits themselves, such as in the statement "octal numbers are written using Arabic numerals."The Hinduâ€“Arabic numeral system (i.e. decimal) was developed by Indian mathematicians around AD 500.BOOK, Richard, Bulliet, Pamela, Crossley, Daniel, Headrick,, Steven, Hirsch, Lyman, Johnson, The Earth and Its Peoples: A Global History, Volume 1, 192, 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, Cengage Learning, 2010,weblink 1439084742, {{better source|date=January 2017}} From India, the system was adopted by Arabic mathematicians in Baghdad and passed on to the Arabs farther west. The Arabic numerals developed in North Africa. 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. European trade, books, and colonialism helped popularize the adoption of Arabic numerals around the world.The term

*Arabic numerals*is ambiguous, it may also be intended to mean the numerals used by Arabs, in which case it generally refers to the Eastern Arabic numerals. 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*,"Arabic",

*Oxford English Dictionary*, 2nd edition which helps to distinguish it from "Arabic numerals" as the Eastern Arabic numerals.Other alternative names are

*Western Arabic numerals*,

*Western numerals*,

*Hindu numerals*, and Unicode calls them

*digits*.Official Unicode Consortium code chart

## History

### Origins

File:Gwalior zeros.jpg|thumb|The numeral "zero" as it appears in two numbers (50 and 270) in an inscription in (Gwalior]]. Dated to the 9th century.BOOK, Smith, David Eugene, Karpinski, Louis Charles, The Hindu-Arabic numerals, 1911, Boston, London, Ginn and Company, 52,weblink For a modern image)The decimal Hinduâ€“Arabic numeral system with zero was developed in India by around AD 700.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. 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. Prior to Brahmagupta, zero was in use various forms but was regarded as a 'blank spot' (

*sunya sthana*) in a positional number. It was only used by mathematicians (

*ganakas*â€”people doing calculations) while the general populace used the traditional Brahmi numerals. After 700 AD, the decimal numbers with zero replaced the Brahmi numerals. The system was revolutionary by limiting the number of individual digits to ten. It is considered an important milestone in the development of mathematics. File:Bakhshali numerals 2.jpg|thumb|right|upright=1.6|The numerals used in the Bakhshali manuscriptBakhshali manuscriptFile:EgyptphoneKeypad.jpg|right|thumb|Modern-day Arab telephone keypad with two forms of Arabic numerals: Western Arabic numerals on the left and Eastern Arabic numeralsEastern Arabic numeralsThe 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.The MacTutor History of Mathematics archiveIn 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 952â€“953. The decimal point notation was introduced by Sind ibn Ali, who also wrote the earliest treatise on Arabic numerals.

#### Origin of the Arabic numeral symbols

According to Al-Beruni, there were multiple forms of numerals in use in India, and "Arabs chose among them what appeared to them most useful".{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=7}} Al-Nasawi wrote in the early eleventh century that the mathematicians had not agreed on the form of numerals, but most of them had agreed to train themselves with the forms now known as Eastern Arabic numerals.{{harvnb|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=7}}: "Les personnes qui se sont occupÃ©es de la science du calcul n'ont pas Ã©tÃ© d'accord sur une partie des formes de ces neuf signes; mais la plupart d'entre elles sont convenues de les former comme il suit." The oldest specimens of the written numerals available from Egypt in 260 A.H. (873â€“874 CE) show three forms of the numeral "2" and two forms of the numeral "3", and these variations indicate the divergence between what later became known as the Eastern Arabic numerals and the (Western) Arabic numerals.{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=5}}Calculations were originally performed using a dust board (*takht*, Latin:

*tabula*) which involved writing symbols with a stylus and erasing them as part of calculations. Al-Uqlidisi then invented a system of calculations with ink and paper "without board and erasing" (

*bi-ghayr takht wa-lÄ maá¸¥w bal bi-dawÄt wa-qirá¹Äs*).{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|pp=7â€“8}} The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called

*á¸¥isÄb al-hindÄ«*in the east, it was called

*á¸¥isÄb al-ghubÄr*in the west (literally, "calculation with dust").{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=8}} The numerals themselves were referred to in the west as

*ashkÄl alâ€ghubÄr*(dust figures, in Ibn al-YÄsamin) or

*qalam al-ghubÃ¥r*(dust letters).{{sfn|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=10}}The western Arabic variants of the symbols came to be used in Maghreb and Al-Andalus, which are the direct ancestor of the modern "Arabic numerals" used throughout the world.{{harvnb|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|pp=12â€“13}}: "While specimens of Western Arabic numerals from the early periodâ€”the tenth to thirteenth centuriesâ€”are still not available, we know at least that Hindu reckoning (called

*á¸¥isÄb al-ghubÄr*) was known in the West from the tenth century onward..."The divergence in the terminology has led some scholars to propose that the Western Arabic numerals had a separate origin in the so-called "

*ghubÄr*numerals" but the available evidence indicates no separate origin.{{harvnb|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|p=10}}: 'I should think that, therefore, it is no longer justified for us to call the Western Arabic forms of the Hindu-Arabic numerals "ghubÄr numerals." Rather we should speak of the Eastern and the Western Arabic forms of the nine numerals.'Woepecke has also 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.{{harvnb|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003|pp=12â€“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."{{citation |last1=Smith |first1=D. E. |authorlink1=D. E. Smith |authorlink2=Louis Charles Karpinski |first2=L. C. |last2=Karpinski |title=The Hindu-Arabic Numerals |publisher=Dover |year= 2013 |origyear=first published in Boston, 1911 |ISBN=0486155110 |url=https://www.gutenberg.org/ebooks/22599#download |at=Chapter V}}{{citation|title=The Origin of the GhubÄr Numerals, or the Arabian Abacus and the Articuli|first=Solomon|last=Gandz|journal=Isis|volume=16|issue=2|date=November 1931|pages=393â€“424|doi=10.1086/346615|jstor=224714}}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.BOOK, Ifrah, Georges, The universal history of numbers: from prehistory to the invention of the computer; translated from the French by David Bellos, 1998, Harvill Press, London, 9781860463242, 356â€“357,

### Adoption in Europe

(File:The Brahmi numeral system and its descendants.png|alt=|thumb|Evolution of Indian numerals into Arabic numerals and their adoption in Europe)File:Petrus Astronomus Astronomical clock in Uppsala Cathedral.jpg|thumb|Woodcut showing the 16th century astronomical clock of Uppsala CathedralUppsala CathedralFile:Ms.Thott.290.2Âº 150v.jpg|thumb|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 astrologyastrology(File:Clock-french-republic.jpg|thumb|right|Late 18th-century French revolutionary "decimal" clockface.)In 825 Al-KhwÄrizmÄ« wrote a treatise in Arabic,*On the Calculation with Hindu Numerals*,Philosophy Of Mathematics Francis, John â€“ 2008 â€“ Page 38 which survives only as the 12th-century Latin translation,

*Algoritmi de numero Indorum*.The Ellipse: A Historical and Mathematical Journey Arthur Mazer â€“ 2011WEB,weblink al-Khwarizmi - Muslim mathematician,

*Algoritmi*, the translator's rendition of the author's name, gave rise to the word

*algorithm*.Models of Computation: An Introduction to Computability Theory â€“ Page 1 Maribel FernÃ¡ndez â€“ 2009The first mentions of the numerals in the West are found in the

*Codex Vigilanus*of 976.WEB,weblink MATHORIGINS.COM_V, www.mathorigins.com, 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 BÃ©jaÃ¯a (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 is the same in Arabic as well as the Indo-European languages.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",{{Citation|url=http://www.unc.edu/~rowlett/units/roman.html|title=Roman and "Arabic" Numerals|last=Rowlett|first=Russ|date=4 July 2004|publisher=University of North Carolina at Chapel Hill|accessdate=22 June 2009}}{{Citation|url=http://www.highbeam.com/doc/1P2-909875.html|archive-url=https://web.archive.org/web/20130518234854weblink|dead-url=yes|archive-date=18 May 2013|title=Article: Take a Number, Please.|last=Achenbach|first=Joel|authorlink=Joel Achenbach|date=16 September 1994|publisher=The Washington Post|accessdate=22 June 2009}} 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 ({{script/Arabic|Ù }} - {{script/Arabic|Ù¡}} - {{script/Arabic|Ù¢}} - {{script/Arabic|Ù£}} -{{script/Arabic|Ù¤}} - {{script/Arabic|Ù¥}} - {{script/Arabic|Ù¦}} - {{script/Arabic|Ù§}} - {{script/Arabic|Ù¨}} - {{script/Arabic|Ù©}}) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ).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,NEWS, 14th century timepiece unearthed in Qld farm shed, ABC News,weblink 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.ErdÃ©lyi: Magyar mÅ±velÅ‘dÃ©stÃ¶rtÃ©net 1-2. kÃ¶tet. KolozsvÃ¡r, 1913, 1918 By the mid-16th century, they were in common use in most of Europe.Mathforum.org 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

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

File:Yuan dynasty iron magic square.jpg|thumb|right|Iron plate with an order 6 magic square in Persian/ Arabic numbers from China, dating to the Yuan DynastyYuan DynastyArabic numerals were introduced to China during the Yuan Dynasty (1271â€“1368) by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.BOOK, Helaine Selin, Helaine Selin, Encyclopaedia of the history of science, technology, and medicine in non-western cultures,weblink 3 March 2012, 31 July 1997, Springer, 978-0-7923-4066-9, 198â€“, BOOK, Meuleman, Johan H., Islam in the era of globalization: Muslim attitudes towards modernity and identity,weblink 3 March 2012, 23 August 2002, Psychology Press, 978-0-7007-1691-3, 272, BOOK, Peng Yoke Ho, Li, Qi and Shu: An Introduction to Science and Civilization in China,weblink 3 March 2012, 16 October 2000, Courier Dover Publications, 978-0-486-41445-4, 106,## Evolution of symbols

The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets are used to represent numbers in the Hinduâ€“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 (AndalucÃa, 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 Arabicâ€“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.

*Histoire de la Mathematique*, which was published in 1757:(File:EuropeanFormOfArabianDigits.png|frameless|upright=2.25|Table of numerals)

### Encoding

The Arabic numerals 0â€“9 are encoded in ASCII at positions 0x30 to 0x39. Masking to the lower 4 binary bits (or taking the last hexadecimal digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in Unicode]weblink and in virtually all other encodings based in any way on ASCII. EBCDIC used different values, but also had the lower 4 bits equal to the digit value.{| class="wikitable"!style="width: 5.5em"|Binary!style="width: 2.5em"|Octal!style="width: 2.5em"|Decimal!style="width: 2.5em"|Hex!Glyph!Unicode|U+0030 DIGIT ZERO |

|U+0031 DIGIT ONE |

|U+0032 DIGIT TWO |

|U+0033 DIGIT THREE |

|U+0034 DIGIT FOUR |

|U+0035 DIGIT FIVE |

|U+0036 DIGIT SIX |

|U+0037 DIGIT SEVEN |

|U+0038 DIGIT EIGHT |

|U+0039 DIGIT NINE |

## See also

{hide}Columns-list|colwidth=30em|- Text figures
- Abjad numerals
- Chinese numerals
- Counting rods â€“ decimal positional numeral system with zero
- Decimal
- Greek numerals
- Japanese numerals
- Maya numerals
- Regional variations in modern handwritten Arabic numerals

## Notes

{{Notelist}}## References

{{Reflist|30em}}## Sources

- {{citation |first=Paul |last= Kunitzsch |chapter=The Transmission of Hindu-Arabic Numerals Reconsidered |editor1=J. P. Hogendijk |editor2=A. I. Sabra |title=The Enterprise of Science in Islam: New Perspectives |chapter-url=https://books.google.com/books?id=_AUtLNtg3nsC&pg=PA3 |year=2003 |publisher=MIT Press |isbn=978-0-262-19482-2 |pages=3â€“22 |ref={{sfnref|Kunitzsch, The Transmission of Hindu-Arabic Numerals Reconsidered|2003}}}}
- {{citation |last=Plofker |first=Kim |authorlink=Kim Plofker |title=Mathematics in India |publisher=Princeton University Pres |year=2009 |isbn=978-0-691-12067-6}}

## Further reading

- {hide}Citation

|last=Ore

|first=Oystein

|title=Number Theory and Its History

|publisher=Dover

|year=1988

|pages=19â€“24

|chapter=Hindu-Arabic numerals

|isbn=0486656209

{edih}.

|first=Oystein

|title=Number Theory and Its History

|publisher=Dover

|year=1988

|pages=19â€“24

|chapter=Hindu-Arabic numerals

|isbn=0486656209

{edih}.

- {{Citation

| last=Burnett

| first=Charles

| title=The Semantics of Indian Numerals in Arabic, Greek and Latin

| journal=Journal of Indian Philosophy

| publisher=Springer-Netherlands

| volume=34

| issue=1â€“2

| year=2006

| pages=15â€“30

| doi=10.1007/s10781-005-8153-z

}}.

| first=Charles

| title=The Semantics of Indian Numerals in Arabic, Greek and Latin

| journal=Journal of Indian Philosophy

| publisher=Springer-Netherlands

| volume=34

| issue=1â€“2

| year=2006

| pages=15â€“30

| doi=10.1007/s10781-005-8153-z

}}.

- {{Citation

| last=EncyclopÃ¦dia Britannica (Kim Plofker)

| first=

| title=mathematics, South Asian

| journal=EncyclopÃ¦dia Britannica Online

| volume=189

| issue=4761

| year=2007

| pages=1â€“12

| url=http://www.britannica.com/eb/article-9389286

| accessdate=18 May 2007

| bibcode=1961Natur.189S.273.

| doi=10.1038/189273c0

}}.

| first=

| title=mathematics, South Asian

| journal=EncyclopÃ¦dia Britannica Online

| volume=189

| issue=4761

| year=2007

| pages=1â€“12

| url=http://www.britannica.com/eb/article-9389286

| accessdate=18 May 2007

| bibcode=1961Natur.189S.273.

| doi=10.1038/189273c0

}}.

- {hide}Citation

| last1=Hayashi

| first1=Takao

| year=1995

| title=The Bakhshali Manuscript, An ancient Indian mathematical treatise

| place=Groningen

| publisher=Egbert Forsten

| isbn=906980087X

| url=

{edih}.

| first1=Takao

| year=1995

| title=The Bakhshali Manuscript, An ancient Indian mathematical treatise

| place=Groningen

| publisher=Egbert Forsten

| isbn=906980087X

| url=

{edih}.

- {hide}Citation

| last1=Ifrah

| first1=Georges

| authorlink=Georges Ifrah

| year=2000

| title=A Universal History of Numbers: From Prehistory to Computers

| place=New York

| publisher=Wiley

| isbn=0471393401

{edih}.

| first1=Georges

| authorlink=Georges Ifrah

| year=2000

| title=A Universal History of Numbers: From Prehistory to Computers

| place=New York

| publisher=Wiley

| isbn=0471393401

{edih}.

- {{Citation

| last1=Katz

| first1=Victor J. (ed.)

| date=20 July 2007

| title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook

| volume=

| place=Princeton, New Jersey

| publisher=Princeton University Press

| publication-year=

| isbn=0691114854

}}.

| first1=Victor J. (ed.)

| date=20 July 2007

| title=The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook

| volume=

| place=Princeton, New Jersey

| publisher=Princeton University Press

| publication-year=

| isbn=0691114854

}}.

## External links

{{Commons+cat|Arabic numerals}}- weblink" title="web.archive.org/web/20120321111930weblink">Development of Hindu Arabic 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
- weblink" title="web.archive.org/web/20160429163458weblink">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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