Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi ( ar, أبو الحسن أحمد بن ابراهيم الإقليدسي) was a

Muslim Muslims ( ar, المسلمون, , ) are people who adhere to Islam, a monotheistic religion belonging to the Abrahamic tradition. They consider the Quran, the foundational religious text of Islam, to be the verbatim word of the God of Abrah ...

Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...

mathematician, who was active in

Damascus )), is an adjective which means "spacious". , motto = , image_flag = Flag of Damascus.svg , image_seal = Emblem of Damascus.svg , seal_type = Seal , map_caption = , ...

and

Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon ...

. He wrote the earliest surviving book on the positional use of the

Arabic numerals Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such a ...

, ''Kitab al-Fusul fi al-Hisab al-Hindi (The Arithmetics of India)'' around 952.The Arithmetics of Al-Uqlisidi, The story of Hindu-Arabic Arithmetic, translated and annotated by A.S.Saidan, D.Reidel Publishing Company,Boston, 1978 It is especially notable for its treatment of

decimal fraction 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 num ...

s, and that it showed how to carry out

calculations A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to t ...

without deletions. While the Persian mathematician

Jamshīd al-Kāshī Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) ( fa, غیاث الدین جمشید کاشانی ''Ghiyās-ud-dīn Jamshīd Kāshānī'') (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer ...

claimed to have discovered decimal fractions himself in the 15th century, J. Lennart Berggren notes that he was mistaken, as decimal fractions were first used five centuries before him by al-Uqlidisi as early as the 10th century. A. S. Saidan who studied al-Uqlidisi's mathematical treatise in detail wrote:

The most remarkable idea in this work is that of
decimal fraction 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 num ...
. Al-Uqlidisi uses decimal fractions as such, appreciates the importance of a
decimal sign A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The c ...
, and suggests a good one. Not
al-Kashi Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) ( fa, غیاث الدین جمشید کاشانی ''Ghiyās-ud-dīn Jamshīd Kāshānī'') (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer an ...
(d. 1436/7) who treated decimal fractions in his "Miftah al-Hisab", but al-Uqlidisi, who lived five centuries earlier, is the first Muslim mathematician so far known to write about decimal fractions.

Notes

References

* 10th-century Arabs 10th-century mathematicians Medieval Syrian mathematicians People from Damascus 10th-century Syrian people {{asia-mathematician-stub