Eastern Arabic numerals

The Eastern Arabic numerals, also called 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), the Arabian Peninsula, and its variant in other countries that use the Persian numerals on the Iranian plateau and in Asia.

The early Hindu–Arabic numeral system used a variety of shapes.^[1] It is unknown when the Western Arabic numeral shapes diverged from those of Eastern Arabic numerals; it is considered that 1, 2, 3, 4, 5, and 9 are related in both versions, but 6, 7 and 8 are from different sources.^[2]

Origin

The numeral system originates from an ancient Indian numeral system, which was re-introduced during the Islamic Golden Age in the book On the Calculation with Hindic Numerals written by the Persian mathematician and engineer al-Khwarizmi, whose name was Latinized as Algoritmi.^{[note 1]}

Other names

These numbers are known as ʾarqām hindiyyah (أَرْقَام هِنْدِيَّة) in Arabic. They are sometimes also called Indic numerals^[3] or Arabic–Indic numerals^[4] in English. However, that is sometimes discouraged as it can lead to confusion with Indian numerals, used in Brahmic scripts of the Indian subcontinent.^[5]

Numerals

Each numeral in the Persian variant has a different Unicode point even if it looks identical to the Eastern Arabic numeral counterpart.^[6] However, the variants used with Urdu, Sindhi, and other Languages of South Asia are not encoded separately from the Persian variants.

Western Arabic	0	1	2	3	4	5	6	7	8	9	10
Eastern Arabic^[a]	٠	١	٢	٣	٤	٥	٦	٧	٨	٩	١٠
Persian^[b]					۴	۵	۶	٧
Urdu^[c]					۴	۵	۶	۷
Abjad numerals			ب	جـ	د	هـ	و	ز	حـ	ط	ى

^ U+0660 to U+0669
^ U+06F0 to U+06F9. The numbers 4, 5, and 6 are different from Eastern Arabic.
^ Same Unicode characters as the Persian, but language is set to Urdu. The numerals 4, 6 and 7 are different from Persian. On some devices, this row may appear identical to Persian. Commonly used in Pakistani languages.

The numerals 23 appear in Ruqʿah style (٢٣) differently from Naskh (٢٣).

Written numerals are arranged with their lowest-value digit to the right, with higher value positions added to the left. That is identical to the arrangement used for Western Arabic numerals, even though Arabic script is read from right-to-left.^[7] Columns of numbers are usually arranged with the decimal points aligned.

Negative signs are written to the right of magnitudes, e.g. −٣ (−3).

In-line fractions are written with the numerator on the left and the denominator on the right of the fraction slash, e.g. ٢/٧ (2⁄7).

The Arabic decimal separator ٫ (U+066B) or the comma , is used as the decimal mark, as in ٣٫١٤١٥٩٢٦٥٣٥٨ (3.14159265358).

The arabic thousands separator ٬ (U+066C) or quote ' or Arabic comma ، (U+060C) may be used as a thousands separator, e.g. ١٬٠٠٠٬٠٠٠٬٠٠٠ (1,000,000,000).

Contemporary use

Modern-day Arab telephone keypad with two forms of Arabic numerals: Western Arabic numerals on the left and Eastern Arabic numerals on the right

Eastern Arabic letters and numerals on the license plate of a car in Iran

Eastern Arabic numerals are in predominant use over Western Arabic numerals in many countries to the east of the Arab world, notably Iran and Afghanistan.

In Arabic-speaking Asia, as well as Egypt and Sudan, both types of numerals are in use (and are often employed alongside each other), though Western Arabic numerals are increasingly used, including in Saudi Arabia. The United Arab Emirates uses both Eastern and Western Arabic numerals.

In Pakistan, Western Arabic numerals are more extensively used digitally. Eastern numerals continue to see use in Urdu publications and newspapers, as well as signboards.^{[clarification needed]}

In the Maghreb, only Western Arabic numerals are commonly used. In medieval times, these areas used a slightly different set (from which, via Italy, Western Arabic numerals derive).

The Thaana writing system used for the Maldivian language adopted its first nine letters (haa, shaviyani, noonu, raa, baa, lhaviyani, kaafu, alifu, and vaavu) from Perso-Arabic digits.^[8]

Notes

^ Other Latin transliterations include Algaurizin.^{[citation needed]}

References

^ 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. This leads to the question of the shape of the nine numerals. Still after the year 1000 al-Biruni reports that the numerals used in India had a variety of shapes and that the Arabs chose among them what appeared to them most useful. And al-Nasawi (early eleventh century) in his al-Muqni' fi l-hisåb al-hindi writes at the beginning, when describing the forms of the nine signs, "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" (then follow the common Eastern Arabic forms of the numerals). Among the early arithmetical writings that are edited al-Baghdådi mentions that for 2, 3, and 8 the Iraqis would use different forms. This seems to be corroborated by the situation in the Sijzi manuscript. Further, the Latin adaptation of al-Khwårizmi's book says that 5, 6, 7, and 8 may be written differently. If this sentence belongs to al-Khwårizmi's original text, that would be astonishing. Rather one would be inclined to assume that this is a later addition made either by Spanish-Muslim redactors of the Arabic text or by the Latin translator or one of the adapters of the Latin translation, because it is in these four signs (or rather, in three of them) that the Western Arabic numerals differ from the Eastern Arabic ones.
^ 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. That the Eastern Arabic numerals were also known in al-Andalus is demonstrated by several Latin manuscripts that clearly show the Eastern forms… Unfortunately, the documentary evidence on the side of Western Arabic numerals is extremely poor. So far, the oldest specimen of Western Arabic numerals that became known to me occurs in an anonymous treatise on automatic water-wheels and similar devices in MS Florence… dated to 1265 and 1266… Here we have the symbols for 1, 2, 3, 4, 5, 8, and 9. The figures for 2 and 3 look like the corresponding Eastern Arabic forms and are not turned by 90o as in other, more recent, Maghrebi documents… When one compares the Eastern and the Western Arabic forms of the numerals, one finds that they are not completely different. The Western forms of 1, 2, 3, 4, 5, and 9 can be recognized as being related to, or derived from, the corresponding Eastern forms. Major difficulty arises with 6, 7, and 8. It may not be accidental that the oldest existing Latin re-working made from the translation of al-Khwårizmi's Arithmetic mentions just these three figures (plus 5) as being differently written. As I have already said earlier, this notice can hardly stem from al-Khwårizmi himself; rather it may have been added by a Spanish-Arabic redactor of al-Khwårizmi's text. He would have been best equipped to recognize this difference. The Latin translator, or Latin adapters, would less probably have been able to notice the difference between the Eastern and Western Arabic forms of these four numerals. We cannot explain why, and how, the three Western figures were formed, especially since we have no written specimens of Western Arabic numerals before the thirteenth century.
^ "Glossary of Unicode terms". IBM. Retrieved 2 September 2015.
^ "Arabic–Indic Numerals / أرقام هندية - Learn Arabic with Polly Lingual". pollylingu.al. Retrieved 2023-03-15.
^ "Glossary". Retrieved 2 September 2015.
^ About numbers in Iran (2021-01-25). "Persian numbers". en-US.
^ Menninger, Karl (1992). Number words and number symbols: a cultural history of numbers. Courier Dover Publications. p. 415. ISBN 0-486-27096-3.
^ Gippert, Jost (2013). Chen, Shu-Fen; Slade, Benjamin (eds.). "An Outline of the History of Maldivian Writing" (PDF). Grammatica et Verba Glamor and Verve - Studies in South Asian, Historical, and Indo-Europea Linguistics in Honor O Hans Henrich Hock on the Occasion of His Seventy-fifth Birthday. Ann Arbor: Beech Stave Press: 96–98. ISBN 978-0-9895142-0-0. OCLC 852488593 – via Maldives National University.

[8] U+0660 to U+0669

[9] U+06F0 to U+06F9. The numbers 4, 5, and 6 are different from Eastern Arabic.

[10] Same Unicode characters as the Persian, but language is set to Urdu. The numerals 4, 6 and 7 are different from Persian. On some devices, this row may appear identical to Persian. Commonly used in Pakistani languages.

[3] Other Latin transliterations include Algaurizin.^{[citation needed]}

[1] 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. This leads to the question of the shape of the nine numerals. Still after the year 1000 al-Biruni reports that the numerals used in India had a variety of shapes and that the Arabs chose among them what appeared to them most useful. And al-Nasawi (early eleventh century) in his al-Muqni' fi l-hisåb al-hindi writes at the beginning, when describing the forms of the nine signs, "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" (then follow the common Eastern Arabic forms of the numerals). Among the early arithmetical writings that are edited al-Baghdådi mentions that for 2, 3, and 8 the Iraqis would use different forms. This seems to be corroborated by the situation in the Sijzi manuscript. Further, the Latin adaptation of al-Khwårizmi's book says that 5, 6, 7, and 8 may be written differently. If this sentence belongs to al-Khwårizmi's original text, that would be astonishing. Rather one would be inclined to assume that this is a later addition made either by Spanish-Muslim redactors of the Arabic text or by the Latin translator or one of the adapters of the Latin translation, because it is in these four signs (or rather, in three of them) that the Western Arabic numerals differ from the Eastern Arabic ones.

[2] 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. That the Eastern Arabic numerals were also known in al-Andalus is demonstrated by several Latin manuscripts that clearly show the Eastern forms… Unfortunately, the documentary evidence on the side of Western Arabic numerals is extremely poor. So far, the oldest specimen of Western Arabic numerals that became known to me occurs in an anonymous treatise on automatic water-wheels and similar devices in MS Florence… dated to 1265 and 1266… Here we have the symbols for 1, 2, 3, 4, 5, 8, and 9. The figures for 2 and 3 look like the corresponding Eastern Arabic forms and are not turned by 90o as in other, more recent, Maghrebi documents… When one compares the Eastern and the Western Arabic forms of the numerals, one finds that they are not completely different. The Western forms of 1, 2, 3, 4, 5, and 9 can be recognized as being related to, or derived from, the corresponding Eastern forms. Major difficulty arises with 6, 7, and 8. It may not be accidental that the oldest existing Latin re-working made from the translation of al-Khwårizmi's Arithmetic mentions just these three figures (plus 5) as being differently written. As I have already said earlier, this notice can hardly stem from al-Khwårizmi himself; rather it may have been added by a Spanish-Arabic redactor of al-Khwårizmi's text. He would have been best equipped to recognize this difference. The Latin translator, or Latin adapters, would less probably have been able to notice the difference between the Eastern and Western Arabic forms of these four numerals. We cannot explain why, and how, the three Western figures were formed, especially since we have no written specimens of Western Arabic numerals before the thirteenth century.

[4] "Glossary of Unicode terms". IBM. Retrieved 2 September 2015.

[5] "Arabic–Indic Numerals / أرقام هندية - Learn Arabic with Polly Lingual". pollylingu.al. Retrieved 2023-03-15.

[6] "Glossary". Retrieved 2 September 2015.

[7] About numbers in Iran (2021-01-25). "Persian numbers". en-US.

[karl-11] Menninger, Karl (1992). Number words and number symbols: a cultural history of numbers. Courier Dover Publications. p. 415. ISBN 0-486-27096-3.

[12] Gippert, Jost (2013). Chen, Shu-Fen; Slade, Benjamin (eds.). "An Outline of the History of Maldivian Writing" (PDF). Grammatica et Verba Glamor and Verve - Studies in South Asian, Historical, and Indo-Europea Linguistics in Honor O Hans Henrich Hock on the Occasion of His Seventy-fifth Birthday. Ann Arbor: Beech Stave Press: 96–98. ISBN 978-0-9895142-0-0. OCLC 852488593 – via Maldives National University.

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