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In the history of mathematics, Arabic mathematics or Islamic mathematics refers to the mathematics developed by the Islamic civilisation between 622 and 1600. While most scientist in this period where Muslim and Arabic was the dominant language contributions where made by people of many religions (Christian, Jewish, Zoroastrian) and ethnicities (Persian, Turkish, Tajik).

Islamic science and mathematics flourished under the Islamic Caliphate (also known as the Arab Empire or Islamic Empire) established across the Middle East, Central Asia, North Africa, Sicily, the Iberian Peninsula, and in parts of France and Pakistan (known as India at the time) in the 8th century. Although most Islamic texts on mathematics were written in Arabic, they were not all written by Arabs, since — much like the status of Greek in the Hellenistic world — Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time. Many of the most important Islamic mathematicians were Persians.

Recent research paints a new picture of the debt that we owe to Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects, the mathematics studied today is far closer in style to that of Islamic mathematics than to that of Hellenistic mathematics.

Influences

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Hellenistic mathematics and Indian mathematics had an important role in the development of early Islamic mathematics, especially works such as Euclid's classic geometry, Aryabhata's trigonometry and Brahmagupta's arithmetic, and it is thought that they contributed to the era of Islamic scientific innovation that lasted until the 14th century. Many ancient Greek texts have survived only as Arabic translations by Islamic scholars. Perhaps the most important mathematical contribution from India was the decimal place-value Indo-Arabic numeral system, also known as the Hindu numerals. The Persian historian al-Biruni (c. 1050) in his book Tariq al-Hind states that the great king al-Ma'mun had an embassy from India and with them brought a book which was translated to Arabic as Sindhind. It is assumed that Sindhind is none other than Brahmagupta's Brahmasphuta-siddhanta.

HE WAS A BIG BUTT VERY BIG 1!!!!! :)

BIG BUTT

AND THEN A BIG HOLE IN THE BIG BUTT!!

Translations

Many Arabic texts on Islamic mathematics were translated into Latin and had an important role in the evolution of later European mathematics. A list of translations, from Greek and Sanskrit to Arabic, and from Arabic to Latin, is given below.

Greek to Arabic

The following mathematical Greek texts on Hellenistic mathematics were translated into Arabic, and subsequently into Latin:

• Euclid's Data, Optics, Phaenomena and On Divisions.
• Euclid's Elements by al-Hajjaj (c. 8th century)
• Revision of Euclid's Elements by Thabit ibn Qurra.
• Apollonius' Conics by Thabit ibn Qurra.
• Ptolemy's Almagest by Thabit ibn Qurra.
• Archimedes' Sphere and Cylinder and Measurement of the Circle by Thabit ibn Qurra.
• Archimedes' On triangles by Sinan ibn Thabit.
• Diophantus' Arithmetica by Abu'l-Wáfa.
• Menelaus of Alexandria's Sphaerica.
• Theodosius of Bithynia's Spherics.
• Diocles' treatise on mirrors.
• Pappus of Alexandria's work on mechanics.

Sanskrit to Arabic

The following mathematical Sanskrit texts on Indian mathematics were translated into Arabic, and subsequently into Latin:

• The Sindhind by Ibrahim al-Fazari, Muhammad al-Fazari and Yaqub ibn Tāriq (c. 8th century).
• Surya Siddhanta by al-Fazari.
• Brahmagupta's Brahma Sphuta Siddhanta by al-Fazari.
• Brahmagupta's Khandakhayaka.
• Aryabhata's Aryabhatiya.
• Aryabhata's Arya Siddhanta.
• Varahamihira's Pancha Siddhanta.
• Bhaskara I's Lagu Bhaskariya.
• Bhaskara II's Lilavati (to Persian rather than Arabic).

Arabic to Latin

The following mathematical Arabic texts on Islamic mathematics were translated into Latin:

• Introduction to Astronomy by Adelard of Bath (fl. 1116-1142).
• Al-Khwarizmi's arithmetical work Liber ysagogarum Alchorismi and Astronomical Tables by Adelard of Bath.
• Al-Khwarizmi's trigonometrical tables which deal with the sine and tangent by Adelard of Bath (1126).
• Al-Khwarizmi's Zij al-Sindhind in Spain (1126).
• Liber alghoarismi de practica arismetrice, an ellaboration of al-Khwarizmi's Arithmetic, by John of Seville and Domingo Gundisalvo (fl. 1135-1153).
• Secretum Secretorum by John of Seville and Domingo Gundisalvo.
• Costa Ben Luca's De differentia spiritus et animae by John of Seville and Domingo Gundisalvo.
• al-Battani's De motu stellarum, which contains important material on trigonometry, by Plato of Tivoli (fl. 1134-1145).
• Abraham bar Hiyya's Liber embadorum by Plato of Tivoli.
• Liber de compositione alchimiae (The Book of the Composition of Alchemy) by Robert of Chester (f. 1141-1150).
• Al-Khwarizmi's Kitab al-Jabr wa-l-Muqabala (Algebra), Kitab al-Adad al-Hindi (Algoritmi de numero Indorum), and revised astronomical tables by Robert of Chester.
• Al-Khwarizmi's Kitab-ul Jama wat Tafriq by Bon Compagni (1157).
• Al-Khwarizmi's Algebra by Gerard of Cremona (fl. 1150-1185).
• Jabir ibn Aflah's Elementa astronomica by Gerard of Cremona.
• The Banu Musa's (Muhammad bin Musa, Ahmad bin Musa and Hasan bin Musa) works on geometry by Gerard of Cremona.
• Abdur Rahman's commentary on Euclid's Elements by Gerard of Cremona.
• Muhammad ibn Muhammad Baqi's commentary on Euclid's Elements by Gerard of Cremona.
• Abul Abbas Nairizi's commentaries on Euclid and Ptolemy by Gerard of Cremona.
• The works of Thabit ibn Qurra by Gerard of Cremona.
• Abu Kamil's Algebra.
• Al-Biruni's Tariq Al Hind.
• Al-Fazari's The Sindhind.
• The works of Omar Khayyam.
• The works of Nasir al-Din Tusi.
• The works of Mu'ayyad al-Din al-'Urdi (c. 1250).
• The works of Ibn al-Shatir (1304–1375).
• The works of Nasir al-Din Tusi (to Byzantine Greek rather than Latin).

References

1. J. P. Hogendijk. Bibliography of Mathematics in Medieval Islamic Civilization. January 1999.

• Berggren, J. L. Episodes in the Mathematics of Medieval Islam. Springer-Verlag: 1986.
• Berggren, J. L. Mathematics in medieval Islam. Encyclopaedia Britannica.
• Burton, David M. The History of Mathematics: An Introduction. McGraw Hill: 1997.
• Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics, 2nd Edition. Penguin Books: 2000.
• Katz, Victor J. A History of Mathematics: An Introduction, 2nd Edition. Addison-Wesley: 1998.
• Rashed, Roshdi. The Development of Arabic Mathematics: Between Arithmetic and Algebra. Transl. by A. F. W. Armstrong. Kluwer Academic Publishers: 1994.
• John J. O'Connor and Edmund F. Robertson. Arabic mathematics : forgotten brilliance?. MacTutor History of Mathematics archive. St Andrews University. 1999.
• John J. O'Connor and Edmund F. Robertson. Arabic/Islamic mathematics. MacTutor History of Mathematics archive. St Andrews University. 2004.
• George Saliba, Whose Science is Arabic Science in Renaissance Europe?, Columbia University, 1999.
• History of Trigonometry
• http://www.usc.edu/dept/MSA/introduction/woi_knowledge.html#28

• Arabic mathematics
• Islam and science