Arabic numerals
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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 using the numerals, as well as the use of a decimal base, in particular when contrasted with other systems such as Roman numerals. However, the symbols are also used to write numbers in other bases such as octal, as well as for writing non-numerical information such as trademarks or license plate identifiers.
They are also called Western Arabic numerals, Ghubār numerals, Hindu–Arabic numerals,[1] Western digits, Latin digits, or European digits.[2] The Oxford English Dictionary differentiates them with the fully capitalized Arabic Numerals to refer to the Eastern digits.[3] The term numbers or numerals or digits often implies only these symbols, however this can only be inferred from context.
Europeans first learned of Arabic numerals about the 10th century, though their spread was a gradual process. Two centuries later, in the
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 eastern part of the Arabian Peninsula, the Arabs were using the Eastern Arabic numerals or "Mashriki" numerals: ٠, ١, ٢, ٣, ٤, ٥, ٦, ٧, ٨, ٩.[5]
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").[9] The numerals themselves were referred to in the west as ashkāl al‐ghubār ("dust figures") or qalam al-ghubår ("dust letters").[10] 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).[11]
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.[12]
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.[13] 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.[13]
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.[14]
Italy
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 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.[16]
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.[16] 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.[16]
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.[16] This may in part have been due to language barriers: 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
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 (“A.D.”) years, and for numbers on clock faces.[citation needed] Other digits (such as Eastern Arabic) were virtually unknown.[citation needed]
Russia
Prior to the introduction of Arabic numerals,
China
The Chinese Shang dynasty numerals from the 14th century B.C. 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.[26] [27]
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,[28][29] 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.[30][31][32]
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[33]) 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.
ASCII | Unicode | EBCDIC hex | ||||
---|---|---|---|---|---|---|
binary | octal | decimal | 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 with other digits
Symbol | Used with scripts | Numerals | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | many | Arabic numerals |
𑁦 | 𑁧 | 𑁨 | 𑁩 | 𑁪 | 𑁫 | 𑁬 | 𑁭 | 𑁮 | 𑁯 | Brahmi | Brahmi numerals |
० | १ | २ | ३ | ४ | ५ | ६ | ७ | ८ | ९ | Devanagari | Devanagari numerals |
০ | ১ | ২ | ৩ | ৪ | ৫ | ৬ | ৭ | ৮ | ৯ | Bengali–Assamese | Bengali numerals
|
੦ | ੧ | ੨ | ੩ | ੪ | ੫ | ੬ | ੭ | ੮ | ੯ | Gurmukhi | Gurmukhi numerals
|
૦ | ૧ | ૨ | ૩ | ૪ | ૫ | ૬ | ૭ | ૮ | ૯ | Gujarati | Gujarati numerals |
୦ | ୧ | ୨ | ୩ | ୪ | ୫ | ୬ | ୭ | ୮ | ୯ | Odia | Odia numerals |
᱐ | ᱑ | ᱒ | ᱓ | ᱔ | ᱕ | ᱖ | ᱗ | ᱘ | ᱙ | Santali | Santali numerals |
𑇐 | 𑇑 | 𑇒 | 𑇓 | 𑇔 | 𑇕 | 𑇖 | 𑇗 | 𑇘 | 𑇙 | Sharada | Sharada numerals |
௦ | ௧ | ௨ | ௩ | ௪ | ௫ | ௬ | ௭ | ௮ | ௯ | Tamil | Tamil numerals |
౦ | ౧ | ౨ | ౩ | ౪ | ౫ | ౬ | ౭ | ౮ | ౯ | Telugu | Telugu script § Numerals |
೦ | ೧ | ೨ | ೩ | ೪ | ೫ | ೬ | ೭ | ೮ | ೯ | Kannada | Kannada script § Numerals |
൦ | ൧ | ൨ | ൩ | ൪ | ൫ | ൬ | ൭ | ൮ | ൯ | Malayalam | Malayalam numerals |
෦ | ෧ | ෨ | ෩ | ෪ | ෫ | ෬ | ෭ | ෮ | ෯ | Sinhala | Sinhala numerals |
၀ | ၁ | ၂ | ၃ | ၄ | ၅ | ၆ | ၇ | ၈ | ၉ | Burmese | Burmese numerals |
༠ | ༡ | ༢ | ༣ | ༤ | ༥ | ༦ | ༧ | ༨ | ༩ | Tibetan | Tibetan numerals |
᠐ | ᠑ | ᠒ | ᠓ | ᠔ | ᠕ | ᠖ | ᠗ | ᠘ | ᠙ | Mongolian | Mongolian numerals |
០ | ១ | ២ | ៣ | ៤ | ៥ | ៦ | ៧ | ៨ | ៩ | Khmer | Khmer numerals |
๐ | ๑ | ๒ | ๓ | ๔ | ๕ | ๖ | ๗ | ๘ | ๙ | Thai | Thai numerals |
໐ | ໑ | ໒ | ໓ | ໔ | ໕ | ໖ | ໗ | ໘ | ໙ | Lao | Lao script § Numerals |
᮰ | ᮱ | ᮲ | ᮳ | ᮴ | ᮵ | ᮶ | ᮷ | ᮸ | ᮹ | Sundanese | Sundanese numerals |
꧐ | ꧑ | ꧒ | ꧓ | ꧔ | ꧕ | ꧖ | ꧗ | ꧘ | ꧙ | Javanese | Javanese numerals |
᭐ | ᭑ | ᭒ | ᭓ | ᭔ | ᭕ | ᭖ | ᭗ | ᭘ | ᭙ | Balinese | Balinese numerals |
٠ | ١ | ٢ | ٣ | ٤ | ٥ | ٦ | ٧ | ٨ | ٩ | Arabic | Eastern Arabic numerals |
۰ | ۱ | ۲ | ۳ | ۴ | ۵ | ۶ | ۷ | ۸ | ۹ | Persian / Dari / Pashto | |
۰ | ۱ | ۲ | ۳ | ۴ | ۵ | ۶ | ۷ | ۸ | ۹ | Urdu / Shahmukhi | |
- | ፩ | ፪ | ፫ | ፬ | ፭ | ፮ | ፯ | ፰ | ፱ | Ethio-Semitic
|
Ge'ez numerals
|
〇 | 一 | 二 | 三 | 四 | 五 | 六 | 七 | 八 | 九 | East Asia | Chinese numerals |
See also
- Arabic numeral variations
- Regional variations in modern handwritten Arabic numerals
- Seven-segment display
- Text figures
Citations
- American Heritage Dictionary. Houghton Mifflin Harcourt Publishing Company. 2020. Archivedfrom the original on 21 November 2021. Retrieved 21 November 2021.
- ^ Terminology for Digits Archived 26 October 2021 at the Wayback Machine. Unicode Consortium.
- ^ "Arabic", Oxford English Dictionary, 2nd edition
- ISSN 0394-7394.
- ^ ISBN 978-3-515-08223-5. Archivedfrom the original on 30 July 2022. Retrieved 29 July 2022.
- ^ 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."
- ^ Kunitzsch 2003, p. 5.
- ^ 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..."
- ^ Kunitzsch 2003, p. 8.
- ^ Kunitzsch 2003, p. 10.
- ^ Kunitzsch 2003, pp. 7–8.
- ISBN 9781860463242.
- ^ S2CID 213113566.
- ^ 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.
- ISBN 978-1-4008-8405-6.
- ^ from the original on 27 July 2021. Retrieved 29 July 2022.
- SSRN 4143442.
- ^ "14th century timepiece unearthed in Qld farm shed". ABC News. Archived from the original on 29 February 2012. Retrieved 10 November 2011.
- ^ See G. F. Hill, The Development of Arabic Numerals in Europe, for more examples.
- ^ Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918.
- ^ 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.
- from the original on 30 July 2022. Retrieved 29 July 2022.
- from the original on 30 July 2022. Retrieved 29 July 2022.
- ISBN 978-0-534-02879-4.
- ISBN 0-521-23582-0
- ISBN 978-0-534-02879-4.
- ISBN 0-521-23582-0
- )
- from the original on 30 July 2022. Retrieved 29 July 2022.
- ISBN 978-0-7923-4066-9. Archivedfrom the original on 27 October 2015. Retrieved 18 October 2015.
- ISBN 978-0-7007-1691-3. Archivedfrom the original on 27 October 2015. Retrieved 18 October 2015.
- ISBN 978-0-486-41445-4. Archivedfrom the original on 27 October 2015. Retrieved 18 October 2015.
- ^ "The Unicode Standard, Version 13.0" (PDF). unicode.org. Archived (PDF) from the original on 2 June 2001. Retrieved 1 September 2021.
General and cited 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. S2CID 170783929.
- Hayashi, Takao (1995). The Bakhshālī Manuscript: An Ancient Indian Mathematical Treatise. Groningen, Netherlands: Egbert Forsten. ISBN 906980087X.
- 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. 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