Misplaced Pages

Latest revision as of 12:17, 3 January 2025

The ten Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) are the most commonly used symbols for writing numbers. The term often also implies a positional notation number with a decimal base, in particular when contrasted with Roman numerals. However the symbols are also used to write numbers in other bases, such as octal, as well as non-numerical information such as trademarks or license plate identifiers.

They are also called Western Arabic numerals, Western digits, European digits, Ghubār numerals, or Hindu–Arabic numerals due to positional notation (but not these digits) originating in India. The Oxford English Dictionary uses lowercase Arabic numerals while using the fully capitalized term Arabic Numerals for Eastern Arabic numerals. In contemporary society, the terms digits, numbers, and numerals often implies only these symbols, although it can only be inferred from context.

Europeans first learned of Arabic numerals c. the 10th century, though their spread was a gradual process. After Italian scholar Fibonacci of Pisa encountered the numerals in the Algerian city of Béjaïa, his 13th-century work Liber Abaci became crucial in making them known in Europe. However, their use was largely confined to Northern Italy until the invention of the printing press in the 15th century. European trade, books, and colonialism subsequently helped popularize the adoption of Arabic numerals around the world. The numerals are used worldwide—significantly beyond the contemporary spread of the Latin alphabet—and have become common in the writing systems where other numeral systems existed previously, such as Chinese and Japanese numerals.

History

Origin

Positional decimal notation including a zero symbol was developed in India, using symbols visually distinct from those that would eventually enter into international use. As the concept spread, the sets of symbols used in different regions diverged over time.

The immediate ancestors of the digits now commonly called "Arabic numerals" were introduced to Europe in the 10th century by Arabic speakers of Spain and North Africa, with digits at the time in wide use from Libya to Morocco. In the east from Egypt to Iraq and the Arabian Peninsula, the 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 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 AD. 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 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's Etymologiae 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 'calculation with dust' in the west. 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 there is no contemporary evidence of this, and the myth is difficult to reconcile with any digits past 4.

Adoption and spread

The first mentions of the numerals from 1 to 9 in the West are found in the 976 Codex Vigilanus, 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 ṣifr (صفر), transliterated into Latin as cifra, which became 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 Computus emendatus.

Italy

Leonardo Fibonacci was a Pisan mathematician who had studied in the Pisan trading colony of Bugia, in what is now Algeria, and he endeavored to promote the 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's analysis highlighting the advantages of positional notation was widely influential. Likewise, Fibonacci's use of the Béjaïa digits in his exposition ultimately led to their widespread adoption in Europe. Fibonacci's work coincided with the European commercial revolution of the 12th and 13th centuries centered in Italy. Positional notation facilitated complex calculations (such as currency conversion) to be completed more quickly than was possible with the Roman system. In addition, the system could handle larger numbers, did not require a separate reckoning tool, and allowed the user to check their work without repeating the entire procedure. Late medieval Italian merchants did not stop using Roman numerals or other reckoning tools: instead, Arabic numerals were adopted for use in addition to their preexisting methods.

Europe

By 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 barriers: although Fibonacci's Liber Abaci was written in Latin, the Italian abacus traditions were predominantly written in Italian vernaculars that circulated in the private collections of abacus schools or individuals.

The European acceptance of the numerals was accelerated by the invention of the printing press, 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 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.

By the mid-16th century, they had been widely adopted in Europe, and by 1800 had almost completely replaced the use of counting boards and Roman numerals in accounting. Roman numerals were mostly relegated to niche uses such as years and numbers on clock faces.

Russia

Prior to the introduction of Arabic numerals, Cyrillic numerals, derived from the Cyrillic alphabet, were used by South and East Slavs. 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 in 1699. Reasons for Peter's switch from the alphanumerical system are believed to go beyond a surface-level 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 also covertly travelled throughout Northern Europe from 1697 to 1698 during his Grand Embassy and was likely informally exposed to Western mathematics during this time. The Cyrillic system was found to be inferior for calculating practical kinematic values, such as the trajectories and parabolic flight patterns of artillery. With its use, it was difficult to keep pace with Arabic numerals in the growing field of ballistics, whereas Western mathematicians such as John Napier had been publishing on the topic since 1614.

China

The Chinese Shang dynasty numerals from the 14th century BC predates the Indian Brahmi numerals by over 1000 years and shows substantial similarity to the Brahmi numerals. Similar to the modern Arabic numerals, the Shang dynasty numeral system was also decimal based and positional.

While positional Chinese numeral systems such as the counting rod system and Suzhou numerals had been in use prior to the introduction of modern Arabic numerals, the externally-developed system was eventually introduced to medieval China by the 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 (and therefore in Unicode encodings) at positions 0x30 to 0x39. Masking all but the four least-significant binary digits gives the value of the decimal digit, a design decision facilitating the digitization of text onto early computers. EBCDIC used a different offset, but also possessed the aforementioned masking property.

See also

• Arabic numeral variations
• Regional variations in modern handwritten Arabic numerals
• Seven-segment display
• Text figures

Footnotes

1. Terminology for Digits Archived 26 October 2021 at the Wayback Machine. Unicode Consortium.
2. "Arabic numeral". American Heritage Dictionary. Houghton Mifflin Harcourt. 2020. Archived from the original on 21 November 2021. Retrieved 21 November 2021.
3. "Arabic", Oxford English Dictionary, 2nd edition
4. Danna, Raffaele (13 January 2021). "Figuring Out: The Spread of Hindu–Arabic Numerals in the European Tradition of Practical Mathematics (13th–16th Centuries)". Nuncius. 36 (1): 5–48. doi:10.1163/18253911-bja10004. ISSN 0394-7394.
5. ^ Burnett, Charles (2002). Dold-Samplonius, Yvonne; Van Dalen, Benno; Dauben, Joseph; Folkerts, Menso (eds.). From China to Paris: 2000 Years Transmission of Mathematical Ideas. Franz Steiner Verlag. pp. 237–288. ISBN 978-3-515-08223-5.
6. Kunitzsch 2003, p. 7: "Les personnes qui se sont occupées de la science du calcul n'ont pas été 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."
7. Kunitzsch 2003, p. 5.
8. Kunitzsch 2003, pp. 12–13: "While specimens of Western Arabic numerals from the early period—the tenth to thirteenth centuries—are still not available, we know at least that Hindu reckoning (called ḥisāb al-ghubār) was known in the West from the 10th century onward..."
9. Kunitzsch 2003, p. 8.
10. Kunitzsch 2003, p. 10.
11. Kunitzsch 2003, pp. 7–8.
12. Ifrah, Georges (1998). The universal history of numbers: from prehistory to the invention of the computer. Translated by Bellos, David. London: Harvill. pp. 356–357. ISBN 978-1-860-46324-2.
13. ^ Nothaft, C. Philipp E. (3 May 2020). "Medieval Europe's satanic ciphers: on the genesis of a modern myth". British Journal for the History of Mathematics. 35 (2): 107–136. doi:10.1080/26375451.2020.1726050. ISSN 2637-5451. S2CID 213113566.
14. Herold, Werner (2005). "Der "computus emendatus" des Reinher von Paderborn". ixtheo.de (in German). Archived from the original on 30 July 2022. Retrieved 29 July 2022.
15. Tung, K. K. (2016). Topics in Mathematical Modeling. Princeton University Press. p. 1. ISBN 978-1-4008-8405-6.
16. ^ Danna, Raffaele (12 July 2021). The Spread of Hindu–Arabic Numerals in the European Tradition of Practical Arithmetic: a Socio-Economic Perspective (13th–16th centuries) (PhD thesis). University of Cambridge. doi:10.17863/cam.72497. Archived from the original on 27 July 2021. Retrieved 29 July 2022.
17. Danna, Raffaele; Iori, Martina; Mina, Andrea (22 June 2022). "A Numerical Revolution: The Diffusion of Practical Mathematics and the Growth of Pre-modern European Economies". SSRN 4143442.
18. "14th century timepiece unearthed in Qld farm shed". ABC News. Archived from the original on 29 February 2012. Retrieved 10 November 2011.
19. See G. F. Hill, The Development of Arabic Numerals in Europe, for more examples.
20. Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918.
21. Conatser Segura, Sylvia (26 May 2020). Orthographic Reform and Language Planning in Russian History (Honors thesis). Archived from the original on 30 July 2022. Retrieved 29 July 2022.
22. Brown, Peter B. (2012). "Muscovite Arithmetic in Seventeenth-Century Russian Civilization: Is It Not Time to Discard the "Backwardness" Label?". Russian History. 39 (4): 393–459. doi:10.1163/48763316-03904001. ISSN 0094-288X. Archived from the original on 30 July 2022. Retrieved 29 July 2022.
23. Lockwood, E. H. (October 1978). "Mathematical discoveries 1600-1750, by P. L. Griffiths. Pp 121. £2·75. 1977. ISBN 0 7223 1006 4 (Stockwell)". The Mathematical Gazette. 62 (421): 219. doi:10.2307/3616704. ISSN 0025-5572. JSTOR 3616704. Archived from the original on 30 July 2022. Retrieved 29 July 2022.
24. ^ Campbell, Douglas M.; Higgins, John C. (1984). Mathematics: People, Problems, Results. Taylor & Francis. ISBN 978-0-534-02879-4.
25. ^ The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, Table 20, p. 6, Cambridge University Press ISBN 0-521-23582-0
26. Shell-Gellasch, Amy (2015). Algebra in context : introductory algebra from origins to applications. J. B. Thoo. Baltimore. ISBN 978-1-4214-1728-8.{{cite book}}: CS1 maint: location missing publisher (link)
27. Uy, Frederick L. (January 2003). "The Chinese Numeration System and Place Value". Teaching Children Mathematics. 9 (5): 243–247. doi:10.5951/tcm.9.5.0243. ISSN 1073-5836.
28. Selin, Helaine, ed. (1997). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. p. 198. ISBN 978-0-7923-4066-9. Archived from the original on 27 October 2015. Retrieved 18 October 2015.
29. Meuleman, Johan H. (2002). Islam in the era of globalization: Muslim attitudes towards modernity and identity. Psychology Press. p. 272. ISBN 978-0-7007-1691-3. Archived from the original on 27 October 2015. Retrieved 18 October 2015.
30. Peng Yoke Ho (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Mineola, NY: Courier Dover Publications. p. 106. ISBN 978-0-486-41445-4. Archived from the original on 27 October 2015. Retrieved 18 October 2015.
31. "The Unicode Standard, Version 13.0" (PDF). unicode.org. Archived (PDF) from the original on 2 June 2001. Retrieved 1 September 2021.

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.

Further reading

• 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.
• Hayashi, Takao (1995). The Bakhshālī Manuscript: An Ancient Indian Mathematical Treatise. Groningen, Netherlands: 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.
• "Mathematics in South Asia". Nature. 189 (4761): 273. 1961. Bibcode:1961Natur.189S.273.. doi:10.1038/189273c0. S2CID 4288165.
• Ore, Oystein (1988). "Hindu–Arabic numerals". Number Theory and Its History. Dover. pp. 19–24. ISBN 0486656209.

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.
• The Evolution of Numbers. 16 April 2005.
• O'Connor, J. J., and E. F. Robertson, Indian numerals Archived 6 July 2015 at the Wayback Machine. 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

v t e Mathematics in the medieval Islamic world
Mathematicians	9th century 'Abd al-Hamīd ibn Turk Sanad ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Qusta ibn Luqa Al-Mahani al-Dinawari Banū Mūsā brothers Hunayn ibn Ishaq Al-Khwarizmi Yusuf al-Khuri Ishaq ibn Hunayn Na'im ibn Musa Thābit ibn Qurra al-Marwazi Abu Said Gorgani 10th century Abu al-Wafa al-Khazin Al-Qabisi Abu Kamil Ahmad ibn Yusuf Aṣ-Ṣaidanānī Sinān ibn al-Fatḥ al-Khojandi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus al-Uqlidisi Al-Battani Sinan ibn Thabit Ibrahim ibn Sinan Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud Al-Sijzi Al-Karaji al-Majriti al-Jabali 11th century Abu Nasr Mansur Alhazen Kushyar Gilani Al-Biruni Ibn al-Samh Abu Mansur al-Baghdadi Avicenna al-Jayyānī al-Nasawī al-Zarqālī ibn Hud Al-Isfizari Omar Khayyam Muhammad al-Baghdadi 12th century Jabir ibn Aflah Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi al-Hassar Sharaf al-Din al-Tusi Ibn al-Yasamin 13th century Ibn al‐Ha'im al‐Ishbili Ahmad al-Buni Ibn Munim Alam al-Din al-Hanafi Ibn Adlan al-Urdi Nasir al-Din al-Tusi al-Abhari Muhyi al-Din al-Maghribi al-Hasan al-Marrakushi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Ibn al-Banna' Kamāl al-Dīn al-Fārisī 14th century Nizam al-Din al-Nisapuri Ibn al-Shatir Ibn al-Durayhim Al-Khalili al-Umawi 15th century Ibn al-Majdi al-Rūmī al-Kāshī Ulugh Beg Ali Qushji al-Wafa'i al-Qalaṣādī Sibt al-Maridini Ibn Ghazi al-Miknasi 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi
Mathematical works	The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Book on the Measurement of Plane and Spherical Figures Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij
Concepts	Alhazen's problem Islamic geometric patterns
Centers	Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi ad-Din Madrasa Maragheh observatory University of al-Qarawiyyin
Influences	Babylonian mathematics Greek mathematics Indian mathematics
Influenced	Byzantine mathematics European mathematics Indian mathematics
Related	Hindu–Arabic numeral system Arabic numerals (Eastern Arabic numerals, Western Arabic numerals) Trigonometric functions History of trigonometry History of algebra

• Numerals