![Hindu-Arabic numerals](https://upload.wikimedia.org/wikipedia/commons/5/5a/Hindu-Arabic_numerals.svg)
Arabic numerals are the ten
numerical digit
A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ...
s: , , , , , , , , and . They are the most commonly used symbols to write
decimal numbers
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
. They are also used for writing numbers in other systems such as
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. This is to say that 10octal represents eight and 100octal represents sixty-four. However, English, like most languages, ...
, and for writing identifiers such as computer symbols, trademarks, or license plates. The term often implies a decimal number, in particular when contrasted with
Roman numerals
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
.
They are also called Western Arabic numerals, Ghubār numerals, Hindu-Arabic numerals,
Western digits, Latin digits, or European digits. The ''
Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a com ...
'' differentiates them with the fully capitalized ''Arabic Numerals'' to refer to the
Eastern digits. The term numbers or numerals or digits often implies only these symbols, however this can only be inferred from context.
It was in the
Algeria
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, map_caption =
, image_map2 =
, capital = Algiers
, coordinates =
, largest_city = capital
, relig ...
n city of
Béjaïa
Béjaïa (; ; ar, بجاية, Latn, ar, Bijāya, ; kab, Bgayet, Vgayet), formerly Bougie and Bugia, is a Mediterranean port city and commune on the Gulf of Béjaïa in Algeria; it is the capital of Béjaïa Province, Kabylia. Béjaïa is ...
that the
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
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 from the Republic of Pisa, considered to be "the most talented Western ...
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 colonies and generally with the aim of economic dominance. In the process of colonisation, colonisers may impose their relig ...
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
This article discusses the geographic spread of the Latin script throughout history, from its archaic beginnings in Latium to the dominant writing system on Earth in modernity.
The Latin letters' ancestors are found in the Phoenician, Greek a ...
, and have become common in the writing systems where other numeral systems existed previously, such as
Chinese
Chinese can refer to:
* Something related to China
* Chinese people, people of Chinese nationality, citizenship, and/or ethnicity
**''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation
** List of ethnic groups in China, people of va ...
and
Japanese
Japanese may refer to:
* Something from or related to Japan, an island country in East Asia
* Japanese language, spoken mainly in Japan
* Japanese people, the ethnic group that identifies with Japan through ancestry or culture
** Japanese diaspor ...
numerals.
History
Origin
![The Brahmi numeral system and its descendants](https://upload.wikimedia.org/wikipedia/commons/f/f4/The_Brahmi_numeral_system_and_its_descendants.png)
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 Spain and North Africa, who were then using the digits from Libya to Morocco. In the eastern part of Arabic Peninsula, Arabs were using the
Eastern Arabic numerals
The Eastern Arabic numerals, also called Arabic-Hindu numerals or Indo–Arabic numerals, are the symbols used to represent numerical digits in conjunction with the Arabic alphabet in the countries of the Mashriq (the east of the Arab world), ...
or "Mashriki" numerals: ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩
Al-Nasawi wrote in the early 11th century that mathematicians had not agreed on the form of the numerals, but most of them had agreed to train themselves with the forms now known as Eastern Arabic numerals. The oldest specimens of the written numerals available are from Egypt and date to 873–874 CE. They 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 numerals came to be used in the
Maghreb
The Maghreb (; ar, الْمَغْرِب, al-Maghrib, lit=the west), also known as the Arab Maghreb ( ar, المغرب العربي) and Northwest Africa, is the western part of North Africa and the Arab world. The region includes Algeria, ...
and
Al-Andalus
Al-Andalus DIN 31635, translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label=Berber languages, Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, ...
from the 10th century onward. Some amount of consistency in the Western Arabic numeral forms endured from the 10th century, found in a Latin manuscript of
Isidore of Seville
Isidore of Seville ( la, Isidorus Hispalensis; c. 560 – 4 April 636) was a Spanish scholar, theologian, and archbishop of Seville. He is widely regarded, in the words of 19th-century historian Montalembert, as "the last scholar of ...
's ''
Etymologiae
''Etymologiae'' (Latin for "The Etymologies"), also known as the ''Origines'' ("Origins") and usually abbreviated ''Orig.'', is an etymological encyclopedia compiled by Isidore of Seville (c. 560–636) towards the end of his life. Isidore was ...
'' from 976 and the Gerbertian abacus, into the 12th and 13th centuries, in early manuscripts of translations from the city of
Toledo.
Calculations were originally performed using a dust board (''takht'', Latin: ''tabula''), which involved writing symbols with a stylus and erasing them. 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") or ''qalam al-ghubår'' ("dust letters").
Al-Uqlidisi Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi ( ar, أبو الحسن أحمد بن ابراهيم الإقليدسي) was a Muslim Arab mathematician, who was active in Damascus and Baghdad. He wrote the earliest surviving book on the positional us ...
later invented a system of calculations with ink and paper "without board and erasing" (''bi-ghayr takht wa-lā maḥw bal bi-dawāt wa-qirṭās'').
A popular myth claims that the symbols were designed to indicate their numeric value through the number of angles they contained, but no evidence exists of this, and the myth is difficult to reconcile with any digits past 4.
Adoption and spread
![Codex Vigilanus Primeros Numeros Arabigos](https://upload.wikimedia.org/wikipedia/commons/3/3b/Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg)
The first mentions of the numerals from 1 to 9 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, an
illuminated
Illuminated may refer to:
* "Illuminated" (song), by Hurts
* Illuminated Film Company, a British animation house
* ''Illuminated'', alternative title of Black Sheep (Nat & Alex Wolff album)
* Illuminated manuscript
See also
* Illuminate (disambi ...
collection of various historical documents covering a period from antiquity to the 10th century in
Hispania
Hispania ( la, Hispānia , ; nearly identically pronounced in Spanish, Portuguese, Catalan, and Italian) was the Roman name for the Iberian Peninsula and its provinces. Under the Roman Republic, Hispania was divided into two provinces: Hispania ...
.
Other texts show that numbers from 1 to 9 were occasionally supplemented by a placeholder known as
''sipos'', represented as a circle or wheel, reminiscent of the eventual symbol for
zero
0 (zero) is a number representing an empty quantity. In place-value notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or ...
. The Arabic term for zero is ''sifr'' (), transliterated into Latin as ''cifra'', and the origin of the English word ''cipher''.
From the 980s, Gerbert of
Aurillac
Aurillac (; oc, Orlhac ) is the prefecture of the Cantal department, in the Auvergne-Rhône-Alpes region of France. The inhabitants of the commune are known as ''Aurillacois'' or ''Aurillacoises''.
Geography
Aurillac is at above sea leve ...
(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 Gre ...
) 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 inclin ...
from
Lupitus of Barcelona Lupitus of Barcelona, identified with a Christian archdeacon called Sunifred, was an astronomer in late 10th century Barcelona, then part of the ''Marca Hispanica'' between Islamic Al-Andalus and Christian Western Francia, France (in 985 changing f ...
after he had returned to France.
The reception of Arabic numerals in the West was gradual and lukewarm, as other numeral systems circulated in addition to the older Roman numbers. As a discipline, the first to adopt Arabic numerals as part of their own writings were astronomers and astrologists, evidenced from manuscripts surviving from mid-12th-century Bavaria. Reinher of Paderborn (1140–1190) used the numerals in his calendrical tables to calculate the dates of
Easter
Easter,Traditional names for the feast in English are "Easter Day", as in the '' Book of Common Prayer''; "Easter Sunday", used by James Ussher''The Whole Works of the Most Rev. James Ussher, Volume 4'') and Samuel Pepys''The Diary of Samuel ...
more easily in his text ''Compotus emendatus''.
Italy
Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western ...
, a mathematician from the
Republic of Pisa
The Republic of Pisa ( it, Repubblica di Pisa) was an independent state centered on the Tuscan city of Pisa, which existed from the 11th to the 15th century. It rose to become an economic powerhouse, a commercial center whose merchants dominated ...
who had studied in
Béjaïa
Béjaïa (; ; ar, بجاية, Latn, ar, Bijāya, ; kab, Bgayet, Vgayet), formerly Bougie and Bugia, is a Mediterranean port city and commune on the Gulf of Béjaïa in Algeria; it is the capital of Béjaïa Province, Kabylia. Béjaïa is ...
(Bugia),
Algeria
)
, image_map = Algeria (centered orthographic projection).svg
, map_caption =
, image_map2 =
, capital = Algiers
, coordinates =
, largest_city = capital
, relig ...
, promoted the Hindu-Arabic 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 Bugia acting for the Pisa
Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the cit ...
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.
The ''Liber Abaci'' introduced the huge advantages of a positional numeric system, and was widely influential. As Fibonacci used the symbols from Béjaïa for the digits, these symbols were also introduced in the same instruction, ultimately leading to their widespread adoption.
Fibonacci's introduction coincided with Europe's commercial revolution of the 12th and 13th centuries, centered in Italy. Positional notation could be used for quicker and more complex mathematical operations (such as currency conversion) than Roman and other numeric systems could. They could also handle larger numbers, did not require a separate reckoning tool, and allowed the user to check a calculation without repeating the entire procedure.
Although positional notation opened possibilities that were hampered by previous systems, late medieval Italian merchants did not stop using Roman numerals (or other reckoning tools). Rather, Arabic numerals became an additional tool that could be used alongside others.
Europe
![Ms](https://upload.wikimedia.org/wikipedia/commons/7/79/Ms.Thott.290.2%C2%BA_150v.jpg)
In the late 14th century only a few texts using Arabic numerals appeared outside of Italy. This suggests that the use of Arabic numerals in commercial practice, and the significant advantage they conferred, remained a virtual Italian monopoly until the late 15th century.
This may in part have been due to language – although Fibonacci's ''Liber Abaci'' was written in Latin, the Italian abacus traditions was predominantly written in Italian vernaculars that circulated in the private collections of abacus schools or individuals. It was likely difficult for non-Italian merchant bankers to access comprehensive information.
The European acceptance of the numerals was accelerated by the invention of the
printing press
A printing press is a mechanical device for applying pressure to an inked surface resting upon a printing, print medium (such as paper or cloth), thereby transferring the ink. It marked a dramatic improvement on earlier printing methods in wh ...
, and they became widely known during the 15th century. Their use grew steadily in other centers of finance and trade such as Lyon. Early evidence of their use in
Britain
Britain most often refers to:
* The United Kingdom, a sovereign state in Europe comprising the island of Great Britain, the north-eastern part of the island of Ireland and many smaller islands
* Great Britain, the largest island in the United King ...
includes: an equal hour horary
quadrant from 1396, in England, a 1445 inscription on the tower of
Heathfield Church,
Sussex
Sussex (), from the Old English (), is a historic county in South East England that was formerly an independent medieval Anglo-Saxon kingdom. It is bounded to the west by Hampshire, north by Surrey, northeast by Kent, south by the English ...
; 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 historic county in South East England. One of the home counties, Berkshire was recognised by Queen Elizabeth II as the Royal County of Berk ...
; and a 1487 inscription on the belfry door at
Piddletrenthide
Piddletrenthide () is a village and civil parish in the English county of Dorset. It is sited by the small River Piddle in a valley on the dip slope of the Dorset Downs, north of Dorchester. In the 2011 census the parish—which includes the ...
church,
Dorset
Dorset ( ; archaically: Dorsetshire , ) is a county in South West England on the English Channel coast. The ceremonial county comprises the unitary authority areas of Bournemouth, Christchurch and Poole and Dorset (unitary authority), Dors ...
; and in
Scotland
Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the ...
a 1470 inscription on the tomb of the first Earl of Huntly in
Elgin Cathedral. In central Europe, the
King of Hungary
The King of Hungary ( hu, magyar király) was the ruling head of state of the Kingdom of Hungary from 1000 (or 1001) to 1918. The style of title "Apostolic King of Hungary" (''Apostoli Magyar Király'') was endorsed by Pope Clement XIII in 1758 ...
Ladislaus the Posthumous
Ladislaus the Posthumous( hu, Utószülött László; hr, Ladislav Posmrtni; cs, Ladislav Pohrobek; german: link=no, Ladislaus Postumus; 22 February 144023 November 1457) was Duke of Austria and King of Hungary, Croatia and Bohemia. He was the ...
, 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 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 calendars. The term is Medieval Latin and means 'in the year of the Lord', but is often presented using "our Lord" instead of "the Lord", ...
years, and for numbers on clock faces. Other digits (such as Eastern Arabic) were virtually unknown.
Russia
Prior to the introduction of Arabic numerals,
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 and East Slavic peoples. The system was used ...
, derived from the
Cyrillic alphabet
, bg, кирилица , mk, кирилица , russian: кириллица , sr, ћирилица, uk, кирилиця
, fam1 = Egyptian hieroglyphs
, fam2 = Proto-Sinaitic
, fam3 = Phoenician
, fam4 = G ...
, were used by
South
South is one of the cardinal directions or Points of the compass, compass points. The direction is the opposite of north and is perpendicular to both east and west.
Etymology
The word ''south'' comes from Old English ''sūþ'', from earlier Pro ...
and
East
East or Orient is one of the four cardinal directions or points of the compass. It is the opposite direction from west and is the direction from which the Sun rises on the Earth.
Etymology
As in other languages, the word is formed from the fa ...
Slavic peoples
Slavs are the largest European ethnolinguistic group. They speak the various Slavic languages, belonging to the larger Balto-Slavic language, Balto-Slavic branch of the Indo-European languages. Slavs are geographically distributed throughout ...
. The system was used in Russia as late as the early 18th century, although it was formally replaced in official use by
Peter the Great
Peter I ( – ), most commonly known as Peter the Great,) or Pyotr Alekséyevich ( rus, Пётр Алексе́евич, p=ˈpʲɵtr ɐlʲɪˈksʲejɪvʲɪtɕ, , group=pron was a Russian monarch who ruled the Tsardom of Russia from t ...
in 1699. Reasons for Peter's switch from the alphanumerical system are believed to go beyond his desire to imitate the West. Historian Peter Brown makes arguments for sociological, militaristic, and pedagogical reasons for the change. At a broad, societal level, Russian merchants, soldiers, and officials increasingly came into contact with counterparts from the West and became familiar with the communal use of Arabic numerals. Peter the Great also travelled incognito throughout Northern Europe from 1697 to 1698
during his Grand Embassy and was likely exposed to Western mathematics, if informally, during this time. The Cyrillic numeric system was also inferior in terms of calculating properties of objects in motions, such as the trajectories and parabolic flight patterns of artillery. It was unable to keep pace with Arabic numerals in the growing science of
ballistics
Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing and a ...
, whereas Western mathematicians such as
John Napier
John Napier of Merchiston (; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioann ...
had been publishing on the topic since 1614.
China
Chinese numeral systems that used
positional notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...
(such as the
counting rod system and
Suzhou numerals
The Suzhou numerals, also known as ' (), is a numeral system used in China before the introduction of Arabic numerals. The Suzhou numerals are also known as ' (), ' (), ' (), ' () and ' ().
History
The Suzhou numeral system is the only survivin ...
) were in use in China previous to the introduction of Arabic numerals, some were introduced to medieval China 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 predominantly composed of Chinese-speaking adherents of Islam. They are distributed throughout China, mainly in the ...
. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese
Jesuits
The Society of Jesus ( la, Societas Iesu; abbreviation: SJ), also known as the Jesuits (; la, Iesuitæ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rom ...
.
Encoding
The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such as
Morse code
Morse code is a method used in telecommunication to encode text characters as standardized sequences of two different signal durations, called ''dots'' and ''dashes'', or ''dits'' and ''dahs''. Morse code is named after Samuel Morse, one of ...
.
They are encoded in
ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...
at positions 0x30 to 0x39.
Masking to the lower four binary bits (or taking the last
hexadecimal
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...
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,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ...
.
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- ...
used different values, but also had the lower 4 bits equal to the digit value.
Comparison with other digits
See also
*
Arabic numeral variations
*
Regional variations in modern handwritten Arabic numerals
*
Seven-segment display
A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays.
Seven-segment displays are widely used in digital clocks, electronic meters, basic ...
*
Text figures
Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...
Explanatory notes
Citations
General and cited sources
*
Further reading
*
*
*
*
*
*
External links
* Lam Lay Yong
"Development of Hindu Arabic and Traditional Chinese Arithmetic" ''Chinese Science'' 13 (1996): 35–54.
"Counting Systems and Numerals" ''Historyworld''. Retrieved 11 December 2005.
16 April 2005.
* O'Connor, J. J., and E. F. Robertson
. November 2000.
* History of the numerals
*
Arabic numerals*
*
*
Gerbert d'Aurillac's early use of Hindu-Arabic numeralsa
Convergence
{{Islamic mathematics
Numerals