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'Kamal al-Din Abu'l-Hasan Muhammad Al-Farisi' (1260-1320) () was a prominent Persian Muslim mathematician, physicist and scientist born in Tabriz, Iran. He made two major contributions to mathematics, one on optics, the other on number theory. Al-Farisi was a pupil of the great astronomer and mathematician Qutb al-Din al-Shirazi, who in turn was a pupil of Nasir al-Din Tusi.

Contents

Optics

Number theory

Notes

References

Optics

His work on optics was prompted by a question put to him concerning the refraction of light. Shirazi advised him to consult the ''Book of Optics'' of Ibn al-Haytham (Alhacen), and al-Farisi made such a deep study of this treatise that Shirazi suggested that he write what is essentially a revision of that major work, which came to be called the ''Tanqih''. Qutb al-Din Al-Shirazi himself was writing a commentary on works of Avicenna at the time.
Al-Farisi is known for giving the first mathematically satisfactory explanation of the rainbow.^[1]

Number theory

Al-Farisi made a number of important contributions to number theory. His most impressive work in number theory is on amicable numbers. In ''Tadhkira al-ahbab fi bayan al-tahabb'' ("Memorandum for friends on the proof of amicability") introduced a major new approach to a whole area of number theory, introducing ideas concerning factorization and combinatorial methods. In fact al-Farisi's approach is based on the unique factorization of an integer into powers of prime numbers.

Notes

1. Kamal al-Din Abu'l Hasan Muhammad Al-Farisi O'Connor, J. J.; Robertson, E. F.

References

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★ 'R Rashed, The development of Arabic mathematics : between arithmetic and algebra (London, 1994).'

★ 'R Rashed, Entre arithmétique et algèbre: Recherches sur l'histoire des mathématiques arabes (Paris, 1984).'

★ 'A G Agargün and C R Fletcher, al-Farisi and the fundamental theorem of arithmetic, Historia Math. 21 (2) (1994), 162-173.'

★ 'R Rashed, Materials for the study of the history of amicable numbers and combinatorial analysis (Arabic), J. Hist. Arabic Sci. 6 (1-2) (1982), 278-209.'

★ 'R Rashed, Nombres amiables, parties aliquotes et nombres figurés aux XIIIème et XIVème siècles, Arch. Hist. Exact Sci. 28 (2) (1983), 107-147.'

★ 'R Rashed, Le modèle de la sphère transparente et l'explication de l'arc-en-ciel : Ibn al-Haytham - al-Farisi, Revue d'histoire des sciences 22 (1970), 109-140.'