Arabic numerals are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The term often implies a

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

Development of Hindu Arabic and Traditional Chinese Arithmetic

History of Counting Systems and Numerals

Retrieved 11 December 2005.

16 April 2005. * O'Connor, J. J. and Robertson, E. F

November 2000. * History of the numerals *

Arabic numerals

*

*

*

Gerbert d'Aurillac's early use of Hindu-Arabic numerals

a

Convergence

{{Islamic mathematics Numerals

decimal
The decimal numeral system
A numeral system (or system of numeration) is a writing system
A writing system is a method of visually representing verbal communication
Communication (from Latin ''communicare'', meaning "to share") is t ...

number
A number is a mathematical object
A mathematical object is an abstract concept arising in mathematics.
In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deduct ...

written using these digits (in particular when contrasted with ''Roman numerals
Roman numerals are a that originated in and remained the usual way of writing numbers throughout Europe well into the . Numbers in this system are represented by combinations of letters from the . Modern style uses seven symbols, each with a ...

''). However the term can mean the digits themselves, such as in the statement "octal
The octal numeral system, or oct for short, is the radix, base-8 number system, and uses the Numerical digit, digits 0 to 7, that is to say 10 represents 8 in decimal and 100 represents 64 in decimal. However, English uses a Base 10, base-10 num ...

numbers are written using Arabic numerals."
Although the Hindu–Arabic numeral system
The Hindu–Arabic numeral system or Indo-Arabic numeral system Audun HolmeGeometry: Our Cultural Heritage 2000 (also called the Arabic numeral system or Hindu numeral system) is a positional notation, positional decimal numeral system, and is t ...

(i.e. decimal) was developed by Indian mathematicians
The chronology of Indian mathematicians spans from the Indus Valley Civilization
oxen for pulling a cart and the presence of the chicken
The chicken (''Gallus gallus domesticus''), a subspecies of the red junglefowl, is a type of d ...

around AD 500, quite different forms for the digits were used initially. They were modified into Arabic numerals later in North Africa. It was in the city of that the Italian
Italian may refer to:
* Anything of, from, or related to the country and nation of Italy
** Italians, an ethnic group or simply a citizen of the Italian Republic
** Italian language, a Romance language
*** Regional Italian, regional variants of the ...

scholar Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician
A mathematician is someone who uses an extensive knowledge of mathem ...

first encountered the numerals; his work was crucial in making them known throughout Europe. European trade, books, and colonialism
Colonialism is a practice or policy of control by one people or power over other people or areas, often by establishing colony, colonies and generally with the aim of economic dominance. In the process of colonisation, colonisers may impose the ...

helped popularize the adoption of Arabic numerals around the world. The numerals have found worldwide use significantly beyond the contemporary spread of the Latin alphabet
Spread may refer to:
Places
* Spread, West Virginia
Arts, entertainment, and media
* ''Spread'' (film), a 2009 film.
* ''$pread
''$pread'' was a quarterly magazine by and for sex workers and those who support their rights. The magazine's fo ...

, intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, such as Chinese
Chinese can refer to:
* Something related to China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the List of countries and dependencies by population, world's most populous country, with a populat ...

and Japanese
Japanese may refer to:
* Something from or related to Japan
Japan ( ja, 日本, or , and formally ) is an island country
An island country or an island nation is a country
A country is a distinct territory, territorial body
or ...

writing.
The term ''Arabic numerals'' may be intended to mean the numerals used in Arabic
Arabic (, ' or , ' or ) is a Semitic language
The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East
The Middle East is a list of transcontinental countries, transcontinental region ...

writing, such as the Eastern Arabic numerals
The Eastern Arabic numerals, also called Arabic–Hindu numerals, are the symbols used to represent numerical digits in conjunction with the Arabic alphabet
The Arabic alphabet ( ar, الْأَبْجَدِيَّة الْعَرَبِيَّ ...

. The ''Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the principal historical dictionary
A historical dictionary or dictionary on historical principles is a dictionary which deals not only with the latterday meanings of words but also the historica ...

'' uses lowercase ''Arabic numerals'' to refer to Western digits, and capitalized ''Arabic Numerals'' to refer to the Eastern digits.
Other alternative names are ''Western Arabic numerals'', ''Western numerals'' and ''Hindu–Arabic numerals''. Unicode
Unicode, formally the Unicode Standard, is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expressed in most of the world's wri ...

just uses the unadorned term ''digits''.
History

Origins

The decimal Hindu–Arabic numeral system was developed in India by around 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
Brahmagupta ( – ) was an Indian mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures ...

's formulation of zero
0 (zero) is a number
A number is a mathematical object
A mathematical object is an abstract concept arising in mathematics.
In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and ...

as a numeral in 628.
The numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using Numerical digit, digits or other symbols in a consistent manner.
The same s ...

came to be known to the , where mathematicians such as the Persian
Persian may refer to:
* People and things from Iran, historically called ''Persia'' in the English language
** Persians, Persian people, the majority ethnic group in Iran, not to be conflated with the Iranian peoples
** Persian language, an Iranian ...

Al-Khwarizmi
Muḥammad ibn Mūsā al-Khwārizmī ( fa, محمد بن موسی خوارزمی, Moḥammad ben Musā Khwārazmi; ), Arabized as al-Khwarizmi and formerly Latinized as ''Algorithmi'', was a Persian polymath
A polymath ( el, πολυμα ...

, whose book ''On the Calculation with Hindu Numerals'' ( ''Al-Jam` wal-Tafrīq bil-Ḥisāb al-Hindī'') was written about 825 in Arabic
Arabic (, ' or , ' or ) is a Semitic language
The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East
The Middle East is a list of transcontinental countries, transcontinental region ...

, and then the Arab mathematician Al-Kindi
Abu Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab
The Arabs (singular Arab ; singular ar, عَرَب ...

, who wrote four volumes, ''On the Use of the Indian Numerals'' ( ar, كتاب في استعمال الأعداد الهندية ''Kitāb fī Isti`māl al-'A`dād al-Hindīyyah'') in about 830. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West.
Middle-East
The Middle East ( ar, الشرق الأوسط, ISO 233: ) is a geopolitical term that commonly refers to the region spanning the Levant, Arabian Peninsula, Anatolia (including modern Turkey and Cyprus), Egypt, Iran and Iraq. The term came in ...

ern mathematicians extended the decimal numeral system to include fractions
A fraction (from Latin ', "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, ...

, as recorded in a treatise by the Arab mathematician Abu'l-Hasan al-UqlidisiAbu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi ( ar, أبو الحسن أحمد بن ابراهيم الإقليدسي) was a Muslim
Muslims () are people who follow or practice Islam, a Monotheism, monotheistic Abrahamic religions, Abrahamic religi ...

in 952–953. The decimal point
A decimal separator is a symbol used to separate the integer
An integer (from the Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spok ...

notation was introduced by Sind ibn AliAbu al-Tayyib Sanad ibn Ali al-Yahudi (died c. 864 C.E.), was an eighth-century Iraqi Jewish astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. T ...

, who also wrote the earliest treatise on Arabic numerals.
Origin of the Arabic numeral symbols

According toAl-Biruni
Abu Rayhan al-Biruni (973 – after 1050) was an Iranian
Iranian may refer to:
* Iran
Iran ( fa, ایران ), also called Persia and officially the Islamic Republic of Iran ( fa, جمهوری اسلامی ایران ), is a co ...

, there were multiple forms of numerals in use in India, and "Arabs chose among them what appeared to them most useful". 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
The Eastern Arabic numerals, also called Arabic–Hindu numerals, are the symbols used to represent numerical digits in conjunction with the Arabic alphabet
The Arabic alphabet ( ar, الْأَبْجَدِيَّة الْعَرَبِيَّ ...

. The oldest specimens of the written numerals available from Egypt in 873–874 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.
The western Arabic variants of the symbols came to be used in Maghreb
The Maghreb (; ar, المغرب, al-Maghrib, lit=the west), also known as Northwest Africa, is the western part of North Africa and the Arab world. The region includes Algeria, Libya, Mauritania (also considered part of West Africa), Morocco and ...

and , which are the direct ancestor of the modern Arabic numerals.
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-lā maḥw bal bi-dawāt wa-qirṭās''). The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called ''ḥisāb al-hindī'' in the east, it was called ''ḥisāb al-ghubār'' in the west (literally, "calculation with dust"). The numerals themselves were referred to in the west as ''ashkāl al‐ghubār'' (dust figures, in Ibn al-Yāsamin) or ''qalam al-ghubår'' (dust letters). The divergence in the terminology has led some scholars to propose that the Western Arabic numerals had a separate origin in the so-called "''ghubār'' numerals" but the available evidence indicates no separate origin.
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.
Some popular myths argue 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.
Adoption in Europe

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 were also using theEastern Arabic numerals
The Eastern Arabic numerals, also called Arabic–Hindu numerals, are the symbols used to represent numerical digits in conjunction with the Arabic alphabet
The Arabic alphabet ( ar, الْأَبْجَدِيَّة الْعَرَبِيَّ ...

(٠١٢٣٤٥٦٧٨٩) in other areas.
In 825 Al-Khwārizmī
Muḥammad ibn Mūsā al-Khwārizmī ( fa, محمد بن موسی خوارزمی, Moḥammad ben Musā Khwārazmi; ), Arabization, Arabized as al-Khwarizmi and formerly Latinisation of names, Latinized as ''Algorithmi'', was a Persians, Persian ...

wrote a treatise in Arabic, ''On the Calculation with Hindu Numerals'', which survives only as the 12th-century Latin translation, ''Algoritmi de numero Indorum''. ''Algoritmi'', the translator's rendition of the author's name, gave rise to the word ''algorithm
In and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always and are used as specifications for performing s, , , and other ...

''.
The first mentions of the numerals in the West are found in the ''Codex Vigilanus
The ''Codex Vigilanus'' or ''Codex Albeldensis'' (Spanish: ''Códice Vigilano'' or ''Albeldense'') is an illuminated compilation of various historical documents accounting for a period extending from antiquity to the 10th century in Hispania
...

'' of 976.
From the 980s, Gerbert of Aurillac
Aurillac (; oc, Orlhac ) is the Prefectures in France, prefecture of the Cantal Departments of France, department, in the Auvergne-Rhône-Alpes Regions of France, region of France. The inhabitants of the commune are known as ''Aurillacois'' or ...

(later, Pope Sylvester II
Pope Sylvester II ( – 12 May 1003), originally known as Gerbert of Aurillac, was a French-born scholar and teacher who served as the bishop of Rome and ruled the Papal States from 999 to his death. He endorsed and promoted study of Arab and Grec ...

) used his position to spread knowledge of the numerals in Europe. Gerbert studied in Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...

in his youth. He was known to have requested mathematical treatises concerning the astrolabe
An astrolabe ( grc, ἀστρολάβος ; ar, ٱلأَسْطُرلاب ; persian, ستارهیاب ) is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclinom ...

from Lupitus of Barcelona after he had returned to France.
Leonardo Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician
A mathematician is someone who uses an extensive knowledge of mathem ...

( Leonardo of Pisa), a mathematician born in the Republic of Pisa
The Republic of Pisa ( it, Repubblica di Pisa) was an independent state centered on the Tuscan
Tuscan may refer to:
Places
* A person from, or something of, from, or related to Tuscany, a region of Italy
* Tuscan Archipelago
Currency
* Tuscan p ...

who had studied in Béjaïa
Béjaïa (; ar, بِجَايَة, ''Bijayah''; ber, Bgayet, Bgayeth), formerly Bougie and Bugia, is a Mediterranean
The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin
In biogeography, ...

(Bougie), Algeria
)
, image_map = Algeria (centered orthographic projection).svg
, map_caption =
, image_map2 =
, capital = Algiers
, coordinates =
, largest_city = capital
, religion =
, official_languages =
, languages_type = Oth ...

, promoted the Indian numeral system in Europe with his 1202 book ''Liber Abaci
''Liber Abaci'' (also spelled as ''Liber Abbaci''; "The Book of Calculation") is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci.
''Liber Abaci'' was among the first Western books to describe ...

'':
When my father, who had been appointed by his country as public notary in the customs at acting for theThe European acceptance of the numerals was accelerated by the invention of thePisa Pisa ( , or ) is a city and ''comune The (; plural: ) is a Administrative division, local administrative division of Italy, roughly equivalent to a township or municipality. Importance and function The provides essential public ser ...n 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.

printing press
A printing press is a mechanical device for applying pressure to an ink
Ink is a gel, sol, or solution
Image:SaltInWaterSolutionLiquid.jpg, Making a saline water solution by dissolving Salt, table salt (sodium chloride, NaCl) in water ...

, and they became widely known during the 15th century. Early evidence of their use in Britain
Britain usually refers to:
* United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain,Usage is mixed. The Guardian' and Telegraph' use Britain as a synonym for the United ...

includes: an equal hour horary quadrant
Quadrant may refer to:
Companies
* Quadrant Cycle Company, 1899 manufacturers in Britain of the Quadrant motorcar
* Quadrant (motorcycles), one of the earliest British motorcycle manufacturers, established in Birmingham in 1901
* Quadrant Private ...

from 1396, in England, a 1445 inscription on the tower of Heathfield Church, Sussex
Sussex (), from the Old English
Old English (, ), or Anglo-Saxon, is the earliest recorded form of the English language
English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, e ...

; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire
Berkshire ( ; in the 17th century sometimes spelt phonetically as Barkeshire; abbreviated Berks.) is a county
A county is a geographical region of a country used for administrative or other purposesChambers Dictionary
The ''Chambers ...

; and a 1487 inscription on the belfry door at Piddletrenthide
Piddletrenthide () is a village and Civil parishes in England, civil parish in the English county of Dorset. It is sited by the small River Piddle in a valley on the Escarpment, dip slope of the Dorset Downs, north of Dorchester, Dorset, Dorches ...

church, Dorset
Dorset (; archaically
In language
A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) and writing. Most languages have a writing system compose ...

; and in Scotland
Scotland ( sco, Scotland, gd, Alba
Alba (Scottish Gaelic
Scottish Gaelic ( gd, Gàidhlig or Scots Gaelic, sometimes referred to simply as Gaelic) is a Goidelic language (in the Celtic languages, Celtic branch of the Indo-European ...

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
The King of Hungary ( hu, magyar király) was the ruling head of state
A head of state (or chief of state) is the public persona
A persona (plural personae or personas), depending on the context, can refer to either the public imag ...

Ladislaus the Posthumous
Ladislaus the Posthumous ( hu, Utószülött László; hr, Ladislav Posmrtni; cs, Ladislav Pohrobek; german: Ladislaus Postumus; 22 February 144023 November 1457) was Duke of Austria and King of Hungary, King of Croatia, Croatia and King of Bo ...

, started the use of Arabic numerals, which appear for the first time in a royal document of 1456. By the mid-16th century, they were in common use in most of Europe. Roman numerals
Roman numerals are a that originated in and remained the usual way of writing numbers throughout Europe well into the . Numbers in this system are represented by combinations of letters from the . Modern style uses seven symbols, each with a ...

remained in use mostly for the notation of anno Domini
The terms (AD) and before Christ (BC) are used to label or number years in the Julian and Gregorian calendar
The Gregorian calendar is the used in most of the world. It was introduced in October 1582 by as a modification of the , r ...

years, and for numbers on clockfaces.
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 (5 September 1725 – 18 December 1799) was a French mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topic ...

in his ''Histoire de la Mathematique'', which was published in 1757:
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, as well as on clockfaces.
Adoption in Russia

Cyrillic numerals
Cyrillic numerals are a numeral system derived from the Cyrillic script, developed in the First Bulgarian Empire in the late 10th century. It was used in the First Bulgarian Empire and by South Slavs, South and East Slavs, East Slavic peoples. Th ...

were a numbering system derived from the Cyrillic alphabet
, bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця
, fam1 = Egyptian hieroglyphs
Egyptian hieroglyphs () were the formal writing system
A writing system is ...

, used by South
South is one of the cardinal directions or compass points. South is the opposite of north and is perpendicular to the east and west.
Etymology
The word ''south'' comes from Old English ''sūþ'', from earlier Proto-Germanic language, Proto-Germa ...

and East Slavic peoples
Slavs are an ethno-linguistic group of people who speak the various Slavic languages of the larger Balto-Slavic language, Balto-Slavic linguistic group of the Indo-European languages. They are native to Eurasia, stretching from Central Europe, ...

. The system was used in Russia as late as the early 18th century when Peter the Great
Peter the Great ( rus, Пётр Вели́кий, Pyotr Velíkiy, ˈpʲɵtr vʲɪˈlʲikʲɪj), Peter I ( rus, Пётр Первый, Pyotr Pyervyy, ˈpʲɵtr ˈpʲɛrvɨj) or Pyotr Alekséyevich ( rus, Пётр Алексе́евич, p=ˈp ...

replaced it with Arabic numerals.
Adoption in China

Positional notation was introduced to China during theYuan Dynasty
The Yuan dynasty (), officially the Great Yuan (; xng, , , literally "Great Yuan State"), was a successor state
Successor is someone who, or something which succeeds or comes after (see success and succession)
Film and TV
* ''The Succ ...

(1271–1368) by the Muslim Hui people
The Hui people ( zh, c=, p=Huízú, w=Hui2-tsu2, Xiao'erjing: , dng, Хуэйзў, ) are an East Asian ethnoreligious group which is predominantly composed of Islam in China, Chinese-speaking adherents of Islam who are distributed throughout ...

. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits
The Society of Jesus ( la, Societas Iesu; abbreviated SJ), also known as the Jesuits (; la, Iesuitæ), is a religious order (Catholic), religious order of the Catholic Church headquartered in Rome. It was founded by Ignatius of Loyola and six co ...

.
Encoding

The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such asMorse code
Morse code is a method used in telecommunication
Telecommunication is the transmission of information by various types of technologies over wire
A wire is a single usually cylindrical
A cylinder (from Greek
Greek may refer to: ...

.
They are encoded in ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding
In computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the stu ...

at positions 0x30 to 0x39. Masking to the lower 4 binary bits (or taking the last hexadecimal
In mathematics and computing, the hexadecimal (also base 16 or hex) numeral system is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system repres ...

digit) gives the value of the digit, a great help in converting text to numbers on early computers. These positions were inherited in Unicode
Unicode, formally the Unicode Standard, is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expressed in most of the world's wri ...

.https://www.unicode.org/charts/PDF/U0000.pdf EBCDIC
Extended Binary Coded Decimal Interchange Code (EBCDIC; ) is an eight-bit character encoding used mainly on IBM mainframe and IBM midrange computer operating systems. It descended from the code used with punched cards and the corresponding six-b ...

used different values, but also had the lower 4 bits equal to the digit value.
See also

Notes

References

Sources

* *Further reading

*. *. *. *. *. *.External links

Development of Hindu Arabic and Traditional Chinese Arithmetic

History of Counting Systems and Numerals

Retrieved 11 December 2005.

16 April 2005. * O'Connor, J. J. and Robertson, E. F

November 2000. * History of the numerals *

Arabic numerals

*

*

*

Gerbert d'Aurillac's early use of Hindu-Arabic numerals

a

Convergence

{{Islamic mathematics Numerals