Arabic numerals

This article is about the symbols only. For numerical system, see Hindu–Arabic numeral system. For other uses, see Arabic numerals (disambiguation). For Numeric system in Arab Script, see Eastern Arabic numerals.

Arabic numerals set in Source Sans typeface

Arabic numerals are the ten numerical digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. They are also called Western Arabic numerals, Ghubār numerals, Hindu-Arabic numerals, ASCII digits, Western digits, Latin digits, or European digits. The Oxford English Dictionary differentiates them with the fully capitalized Arabic Numerals to refer to the Eastern digits. Arabic numerals are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other bases such as octal, and for writing identifiers such as license plates.

The term often implies a decimal number, in particular when contrasted with Roman numerals. The decimal numeral system, however, was developed centuries before the Arabic numerals in the Asian subcontinent, using other symbols.

It was in the Algerian city of Béjaïa 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 numerals have found worldwide use significantly beyond the contemporary spread of the Latin alphabet, and have become commonly used in the writing systems in where other numeral systems existed previously, such as Chinese and Japanese numerals.

Origin of the Arabic numeral symbols

Evolution of Indian numerals into Arabic numerals and their 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 tenth 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 or "Mashriki" numerals: ٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩

Al-Nasawi wrote in the early eleventh 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 and Al-Andalus from the tenth century onward.

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 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

The first Arabic numerals in the West appeared in the Codex Albeldensis in Spain.

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.

The first mentions of the numerals from 1 to 9 in the West are found in the Codex Vigilanus of 976, an illuminated collection of various historical documents covering a period from antiquity to the 10th century in 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. The Arabic term for zero is sifr (صفر), transliterated into Latin as cifra, and the origin of the English word cipher.

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.

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 more easily in his text Compotus emendatus.

Italy

Leonardo Fibonacci (also known as Leonardo of Pisa), a mathematician born in the Republic of Pisa who had studied in Béjaïa (Bougie), Algeria, promoted the Hindu-Arabic 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 Liber Abaci showed how the positional numeral system functioned, gave a thorough overview of the contemporary state of Hindu-Arabic mathematics, and detailed several examples on how type of mathematics could be used in Europe to solve both practical and commercial problems. Conversion and exchange rates from the numerous circulating, and largely unstandardized, currencies was at the core of the growing international trade. The fractions, decimals, and proportions more easily allowed by Arabic numerals were fundamental for financial and economic practices, ultimately leading to their widespread adoption. Arabic numerals introduced modern mathematical symbolism that is still used to represent fractions.

Fibonacchi's introduction coincided with Europe's commercial revolution of the 12th and 13th centuries, centered in Italy. Commercial centers were developing new corporate structures and financial instruments - insurance contracts, bills of exchange, and double-entry bookkeeping. These burgeoning technologies allowed for the development of the first international merchant-banking companies in Europe to develop during the 14th century - the companies then required high levels of literacy and numeracy. Arabic numerals were a useful tool in this process because they could be used for quicker and more complex mathematical operations than Roman and other numeric systems could allow. The positional numeral system 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 Arabic numerals 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.

Due to the written character of Arabic numerals, a community of highly literate users was necessary to implement them commercially. It was therefore necessary to provide aspiring merchants and bankers with necessary training, which developed into the Italian practical arithmetic tradition of abacus mathematics, a misnomer as reckoning tables were not documented as being used. Abacus mathematics then developed into abacus schools, where children ages 11 to 13 were taught by abacus masters. Then the capital of international commercial banking, Florence was the most important center for abacus mathematics, with over 70 abacus masters teaching in over 20 abacus schools. By the 14th century, almost every practitioner in Florence had attended an abacus school; in the 15th century, abacus school educations were widespread among economic agents. They were attended not only by future merchants and bankers, but also by engineers, artists, and architects.

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, 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. 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. Between the late 14th and early 15th century, the first texts using Arabic numerals and the positional numeral system began appearing outside of Italy, but without the continuity or scale of abacus mathematics centered in Florence and other Italian commercial centers. 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.

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 years, and for numbers on clock faces.

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

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

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

Chinese numeral systems that used positional notation (such as the counting rod system and Suzhou numerals) were in use in China previous to the introduction of Arabic numerals. The Arabic numeral system was first introduced to medieval China by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.

Encoding

The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such as Morse code.

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

	ASCII Binary	ASCII Octal	ASCII Decimal	ASCII Hex	Unicode	EBCDIC Hex
0	0011 0000	060	48	30	U+0030 DIGIT ZERO	F0
1	0011 0001	061	49	31	U+0031 DIGIT ONE	F1
2	0011 0010	062	50	32	U+0032 DIGIT TWO	F2
3	0011 0011	063	51	33	U+0033 DIGIT THREE	F3
4	0011 0100	064	52	34	U+0034 DIGIT FOUR	F4
5	0011 0101	065	53	35	U+0035 DIGIT FIVE	F5
6	0011 0110	066	54	36	U+0036 DIGIT SIX	F6
7	0011 0111	067	55	37	U+0037 DIGIT SEVEN	F7
8	0011 1000	070	56	38	U+0038 DIGIT EIGHT	F8
9	0011 1001	071	57	39	U+0039 DIGIT NINE	F9

Comparison of different numerals

Western Arabic	0	1	2	3	4	5	6	7	8	9	10
Eastern Arabic	٠	١	٢	٣	٤	٥	٦	٧	٨	٩	١٠
Persian	۰	۱	۲	۳	۴	۵	۶	۷	۸	۹	۱۰
Urdu	۰	۱	۲	۳	۴	۵	۶	۷	۸	۹	۱۰

See also

• Abjad numerals
• Armenian numerals
• Chinese numerals
• Counting rods – decimal positional numeral system with zero
• Decimal
• Greek numerals
• Japanese numerals
• Maya numerals
• Regional variations in modern handwritten Arabic numerals
• Seven-segment display
• Text figures

Sources

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

Further reading

• 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, 34 (1–2), Springer-Netherlands: 15–30, doi:10.1007/s10781-005-8153-z, S2CID 170783929.
• Encyclopædia Britannica (Kim Plofker) (2007), "mathematics, South Asian", Encyclopædia Britannica Online, 189 (4761): 1–12, Bibcode:1961Natur.189S.273., doi:10.1038/189273c0, S2CID 4288165, 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, ISBN 0471393401.
• 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 978-0691114859.

External links

• 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
  • Arabic numerals
  • Hindu-Arabic numerals
  • Numeral & Numbers' history and curiosities
  • Gerbert d'Aurillac's early use of Hindu-Arabic numerals at Convergence