Kamāl alDīn alFārisī
Kamal alDin alFārisī  

Born  1265 
Died  12 January 1318 
Region  Persian scholar 
School 
Persian science 
Main interests  Optics, Physics, Mathematics, Science 
Influences

Kamal alDin Hasan ibn Ali ibn Hasan alFarisi ^{[1]}^{[2]}^{[3]} or Abu Hasan Muhammad ibn Hasan (1267– 12 January 1319,^{[4]}^{[5]} long assumed to be 1320)^{[6]}) (Persian: كمالالدين فارسی) was a Persian^{[7]}^{[8]} Muslim scientist. He made two major contributions to science, one on optics, the other on number theory. Farisi was a pupil of the astronomer and mathematician Qutb alDin alShirazi, who in turn was a pupil of Nasir alDin Tusi.
According to Encyclopædia Iranica, Kamal alDin was the most prominent Persian author on optics.^{[9]}
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 alHaytham (Alhacen), and 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 alDin AlShirazi himself was writing a commentary on works of Avicenna at the time.
Farisi is known for giving the first mathematically satisfactory explanation of the rainbow, and an explication of the nature of colours that reformed the theory of Ibn alHaytham Alhazen.^{[10]} Farisi also "proposed a model where the ray of light from the sun was refracted twice by a water droplet, one or more reflections occurring between the two refractions." He verified this through extensive experimentation using a transparent sphere filled with water and a camera obscura.^{[11]}
His research in this regard was based on theoretical investigations in dioptrics conducted on the socalled Burning Sphere (alKura almuhriqa) in the tradition of Ibn Sahl (d. ca. 1000) and Ibn alHaytham (d. ca. 1041) after him. As he noted in his Kitab Tanqih alManazir (The Revision of the Optics), Farisi used a large clear vessel of glass in the shape of a sphere, which was filled with water, in order to have an experimental largescale model of a rain drop. He then placed this model within a camera obscura that has a controlled aperture for the introduction of light. He projected light unto the sphere and ultimately deducted through several trials and detailed observations of reflections and refractions of light that the colors of the rainbow are phenomena of the decomposition of light. His research had resonances with the studies of his contemporary Theodoric of Freiberg (without any contacts between them; even though they both relied on Ibn alHaytham's legacy), and later with the experiments of Descartes and Newton in dioptrics (for instance, Newton conducted a similar experiment at Trinity College, though using a prism rather than a sphere).^{[12]}^{[13]}^{[14]}^{[15]}
Number theory
Farisi made a number of important contributions to number theory. His most impressive work in number theory is on amicable numbers. In Tadhkira alahbab fi bayan altahabb ("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 Farisi's approach is based on the unique factorization of an integer into powers of prime numbers. While the Greek mathematician Euclid took the first step on the way to the existence of prime factorization, alFarisi took the final step^{[16]} and stated for the first time the fundamental theorem of arithmetic.^{[17]}
Works
1. Asas alqawa'id fi usul alfawa'id (The base of the rules in the principles of uses) which comprises an introduction and five chapters dealing with arithmetic, notarial and sales rules, the areas of surfaces and solids, and the last two essays are on algebra. The book is a commentary on the treatise of AlBaha'i uses in the arithmetic rules of AlKhawam alBaghdadi.
2. Tanqih alManazir (Arabic: تنقيح المناظر ; The Revision of Ibn alHaytham's Optics). He completed the writing of this book in Ramadan 708 H.E. (FebMar 1309 A.D.).^{[18]} The autograph manuscript of this work has newly discovered. Before the discovery, the completion date of the Tanqih had been controversial, placed from sometime before 1290 (M. Nazif)^{[19]} to after 1302, but before Quṭb alDīn Shīrāzī’s death in 710/1311 (Wiedemann).^{[20]}
3. Tadhkira alahbab fi bayan altahabb (Memorandum for friends on the proof of amicability)
4. AlBasa'ir fi 'ilm almanazir (Insights Into the Sciences of Optics), a text book for students of optics, presenting the conclusion of the Tanqih without the proofs or experiments. He completed the writing of this book in 708 H.E. (1309 A.D.).
See also
 List of Iranian scientists and scholars
Notes
 ↑ "Archived copy". Archived from the original on 20101127. Retrieved 20100421.
 ↑ Library of the Madrasa Ali Shahid Mutahhari, Tehran: MS 554
 ↑ Tanqih alManazir, autograph manuscript, Adilnor Collection, Sweden.
 ↑ Library of the Madrasa Ali Shahid Mutahhari, Tehran: MS 554
 ↑ Ahmad Fuad Basha, Ahammiyat alMakhtutat alIlmiyyah alSharihah (Kitab Tanqih alManazir Namuzajan)
 ↑ Sameen Ahmed Khan, "Arab Origins of the Discovery of the Refraction of Light", in Optics and Photonics News, October 2007, pp. 22–23
 ↑ Leaman, Oliver (2015). The biographical encyclopedia of Islamic philosophy. London: Bloomsbury Academic. p. 188. ISBN 9781472569455.
...of the Persian mathematician and astronomer, Kamal alDin alFarasi (d. 1320)...
 ↑ Hamilton Alexander Rosskeen Gibb (1991). The Encyclopaedia of Islam: MAHKMID, Volume 6. Brill. p. 377. ISBN 9789004081123.
Towards the end of the 13th century, the Persian Kamal alDm alFarisT...
 ↑ "OPTICS – Encyclopaedia Iranica". www.iranicaonline.org.
 ↑ Nader ElBizri, 'Ibn alHaytham et le problème de la couleur', OriensOccidens: Cahiers du centre d'histoire des sciences et des philosophies arabes et médiévales, C.N.R.S. Vol. 7 (2009), pp. 201–226; see also: Nader ElBizri, Grosseteste’s Meteorological Optics: Explications of the Phenomenon of the Rainbow after Ibn alHaytham', in Robert Grosseteste and the Pursuit of Religious and Scientific Knowledge in the Middle Ages, eds. J. Cunningham and M. Hocknull (Dordrecht: Springer, 2016), pp. 2139 .
 ↑ O'Connor, J. J.; Robertson, E. F. (November 1999). "Kamal alDin Abu'l Hasan Muhammad AlFarisi". University of St. Andrews. Retrieved 20070607.
 ↑ Nader ElBizri, "Ibn alHaytham", in Medieval Science, Technology, and Medicine: An Encyclopedia, eds. Thomas F. Glick, Steven J. Livesey, and Faith Wallis (New York — London: Routledge, 2005), pp. 237–240.
 ↑ Nader ElBizri, "Optics", in Medieval Islamic Civilization: An Encyclopedia, ed. Josef W. Meri (New York – London: Routledge, 2005), Vol. II, pp. 578–580
 ↑ Nader ElBizri, "AlFarisi, Kamal alDin," in The Biographical Encyclopaedia of Islamic Philosophy, ed. Oliver Leaman (London — New York: Thoemmes Continuum, 2006), Vol. I, pp. 131–135
 ↑ Nader ElBizri, "Ibn alHaytham, alHasan", in The Biographical Encyclopaedia of Islamic Philosophy, ed. Oliver Leaman (London — New York: Thoemmes Continuum, 2006), Vol. I, pp. 248–255.
 ↑ A Historical Survey of the Fundamental Theorem of Arithmetic "One could say that Euclid takes the first step on the way of to the existence of prime factorization, and alFarisi takes the final step by actually proving the existence of a finite prime factorisation in his first proposition"
 ↑ Encyclopedia of the History of Arabic Science  Roshdi Rashed "The famous physicist and mathematician Kamal alDin alFarisi compiled a paper in which he set out deliberately to prove the theorem of Ibn Qurra in an algebraic way. This forced him to an understanding of the first arithmetical functions and to a full preparation which led him to state for the first time the fundamental theorem of arithmetic."
 ↑ Tanqih alManazir, Farisi's Autograph manuscript, dated Ramadan 708 H.E./1309 A.D., Adilnor Collection.
 ↑ M. Naẓīf, alḤasan b. alHayṯam, 2 vols., Cairo, 1942–43.
 ↑ E. Wiedemann, “Eine Zeichnung des Auges, ”Zentralblatt für Augenheilkunde 34, 1910a
Further reading
 A.G. Agargün and C.R. Fletcher, "alFarisi and the Fundamental Theorem of Arithmetic", Historia Mathematica, 21 (1994), 162–173.
 M. Naẓīf, alḤasan b. alHayṯam, 2 vols., Cairo, 1942–43.
 H.G. Topdemir, "Kamal alDin Explanation of the Rainbow", Humanity & Social Sciences Journal, 2 (2007), 75–85. ISSN 18184960. IDOSI Publications, 2007.
 Roshdi Rashed, The Development of Arabic Mathematics: Between Arithmetic and Algebra (London, 1994).
 Roshdi Rashed, Entre arithmétique et algèbre: Recherches sur l'histoire des mathématiques arabes (Paris, 1984).
 Roshdi Rashed, "Materials for the Study of the History of Amicable Numbers and Combinatorial Analysis (Arabic)", J. Hist. Arabic Sci., 6 (1982), 278–209.
 Roshdi Rashed, "Nombres amiables, parties aliquotes et nombres figurés aux XIIIème et XIVème siècles", Archive for History of Exact Sciences, 28 (1983), 107–147.
 Roshdi Rashed, "Le modèle de la sphère transparente et l'explication de l'arcenciel : Ibn alHaytham – alFarisi", Revue d'histoire des sciences, 22 (1970), 109–140.
 Moustafa Mawaldi, l' Algèbre de Kamal alDin alFarisi, présentée par Moustafa Mawaldi sous la direction de Monsieur le Professeur Roshdi Rashed. 1989, Université de la Sorbonne Nouvelle, Paris.
 Nader ElBizri, 'Ibn alHaytham et le problème de la couleur', OriensOccidens: Cahiers du centre d'histoire des sciences et des philosophies arabes et médiévales, C.N.R.S. 7 (2009), 201–226.
 Nader ElBizri, 'Grosseteste’s Meteorological Optics: Explications of the Phenomenon of the Rainbow after Ibn alHaytham', in Robert Grosseteste and the Pursuit of Religious and Scientific Knowledge in the Middle Ages, eds. J. Cunningham and M. Hocknull (Dordrecht: Springer, 2016), 2139
 E. Wiedemann, "Eine Zeichnung des Auges, Zentralblatt für Augenheilkunde, 34 (1910).
 Tanqīḥ almanāẓer, MS Istanbul, Topkapı Kütüphanesi, Ahmet III 3340 (copied at Nīšāpūr, 15 Šaʿbān 716/1316)
 ed. as Ketāb Tanqīḥ almanāẓer leḏawī alabṣār wa’lbaṣāʾer, 2 vols, Hyderabad (Deccan), 1347–48/1928–30 (this edition did not use the Topkapı manuscript and contains errors in both text and diagrams).