Al-Farisi
Encyclopedia
Kamal al-Din Hasan ibn Ali ibn Hasan Farisi or Abu Hasan Muhammad ibn Hasan (1267– 12 January 1319, long assumed to be 1320)) was a prominent Persian born in Tabriz
, Iran
. He made two major contributions to science, one on optics
, the other on number theory
. 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.
of Ibn al-Haytham (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 al-Din Al-Shirazi 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 al-Haytham Alhazen. 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
.
His research in this regard was based on theoretical investigations in dioptrics conducted on the so-called Burning Sphere (al-Kura al-muhriqa) in the tradition of Ibn Sahl
(d. ca. 1000) and Ibn al-Haytham (d. ca. 1041) after him. As he noted in his Kitab Tanqih al-Manazir (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 large-scale 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 al-Haytham'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).
s. 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 Farisi's approach is based on the unique factorization of an integer
into powers of prime number
s.
2. Tanqih al-Manazir (Arabic: تنقيح المناظر ; The Revision of Ibn al-Haytham's Optics). He completed the writing of this book in Ramadan 708 H.E. (Feb-Mar 1309 A.D.). The autograph manuscript of this work has newly discovered. Before the discover, the completion date of the Tanqih had been controversial, placed from sometime before 1290 (M. Nazif) to after 1302, but before Quṭb al-Dīn Shīrāzī’s death in 710/1311 (Wiedemann).
3. Tadhkira al-ahbab fi bayan al-tahabb (Memorandum for friends on the proof of amicability)
4. Al-Basa'ir fi 'ilm al-manazir (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.).
Tabriz
Tabriz is the fourth largest city and one of the historical capitals of Iran and the capital of East Azerbaijan Province. Situated at an altitude of 1,350 meters at the junction of the Quri River and Aji River, it was the second largest city in Iran until the late 1960s, one of its former...
, Iran
Iran
Iran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...
. He made two major contributions to science, one on optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, the other on number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. Farisi was a pupil of the great astronomer
Islamic astronomy
Islamic astronomy or Arabic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age , and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and...
and mathematician Qutb al-Din al-Shirazi
Qutb al-Din al-Shirazi
Qotb al-Din Shirazi or Qutb al-Din al-Shirazi was a 13th century Persian Muslim polymath and Persian poet who made contributions astronomy, mathematics, medicine, physics, music theory, philosophy and Sufism.- Biography :...
, who in turn was a pupil of Nasir al-Din Tusi.
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 OpticsBook of Optics
The Book of Optics ; ; Latin: De Aspectibus or Opticae Thesaurus: Alhazeni Arabis; Italian: Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Muslim scholar Alhazen .-See also:* Science in medieval Islam...
of Ibn al-Haytham (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 al-Din Al-Shirazi himself was writing a commentary on works of Avicenna
Avicenna
Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā , commonly known as Ibn Sīnā or by his Latinized name Avicenna, was a Persian polymath, who wrote almost 450 treatises on a wide range of subjects, of which around 240 have survived...
at the time.
Farisi is known for giving the first mathematically satisfactory explanation of the rainbow
Rainbow
A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on to droplets of moisture in the Earth's atmosphere. It takes the form of a multicoloured arc...
, and an explication of the nature of colours that reformed the theory of Ibn al-Haytham Alhazen. 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
Camera obscura
The camera obscura is an optical device that projects an image of its surroundings on a screen. It is used in drawing and for entertainment, and was one of the inventions that led to photography. The device consists of a box or room with a hole in one side...
.
His research in this regard was based on theoretical investigations in dioptrics conducted on the so-called Burning Sphere (al-Kura al-muhriqa) in the tradition of Ibn Sahl
Ibn Sahl
This article is about the physicist. For the physician, see Ali ibn Sahl Rabban al-Tabari. For the poet, see Ibn Sahl of Sevilla.Ibn Sahl was a Muslim Persian mathematician, physicist and optics engineer of the Islamic Golden Age associated with the Abbasid court of Baghdad...
(d. ca. 1000) and Ibn al-Haytham (d. ca. 1041) after him. As he noted in his Kitab Tanqih al-Manazir (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 large-scale model of a rain drop. He then placed this model within a camera obscura
Camera obscura
The camera obscura is an optical device that projects an image of its surroundings on a screen. It is used in drawing and for entertainment, and was one of the inventions that led to photography. The device consists of a box or room with a hole in one side...
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
Theodoric of Freiberg
Theodoric of Freiberg was a German member of the Dominican order and a theologian and physicist...
(without any contacts between them; even though they both relied on Ibn al-Haytham's legacy), and later with the experiments of Descartes and Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
in dioptrics (for instance, Newton conducted a similar experiment at Trinity College, though using a prism rather than a sphere).
Number theory
Farisi made a number of important contributions to number theory. His most impressive work in number theory is on amicable numberAmicable number
Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. A pair of amicable numbers constitutes an aliquot sequence of period 2...
s. 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
Factorization
In mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original...
and combinatorial
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
methods. In fact Farisi's approach is based on the unique factorization of an integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
into powers of prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s.
His works
1. Asas al-qawa'id fi usul al-fawa'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 Al-Baha'i uses in the arithmetic rules of Al-Khawam al-Baghdadi.2. Tanqih al-Manazir (Arabic: تنقيح المناظر ; The Revision of Ibn al-Haytham's Optics). He completed the writing of this book in Ramadan 708 H.E. (Feb-Mar 1309 A.D.). The autograph manuscript of this work has newly discovered. Before the discover, the completion date of the Tanqih had been controversial, placed from sometime before 1290 (M. Nazif) to after 1302, but before Quṭb al-Dīn Shīrāzī’s death in 710/1311 (Wiedemann).
3. Tadhkira al-ahbab fi bayan al-tahabb (Memorandum for friends on the proof of amicability)
4. Al-Basa'ir fi 'ilm al-manazir (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.).
Further reading
- 'A G Agargün and C R Fletcher, al-Farisi and the fundamental theorem of arithmetic, Historia Math. 21 (2) (1994), 162–173.'
- M. Naẓīf, al-Ḥasan b. al-Hayṯam, 2 vols., Cairo, 1942–43.
- H G Topdemir, Kamal al-Din Explanation of the Rainbow, Humanity & Social Sciences Journal 2 (1): 75–85, 2007. ISSN 1818–4960. IDOSI Publications, 2007.
- '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).'
- '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.'
- Moustafa Mawaldi, l' Algèbre de Kamal al-Din al-Farisi, présentée par Moustafa Mawaldi sous la direction de Monsieur le Professeur Roshdi Rashed. 1989, Université de la Sorbonne Nouvelle, Paris.
- E. Wiedemann, “Eine Zeichnung des Auges, ”Zentralblatt für Augenheilkunde 34, 1910a.
- Tanqīḥ al-manāẓer, MS Istanbul, Topkapı Kütüphanesi, Ahmet III 3340 (copied at Nīšāpūr, 15 Šaʿbān 716/1316)
- ed. as Ketāb Tanqīḥ al-manāẓer le-ḏawī al-abṣār wa’l-baṣāʾer, 2 vols, Hyderabad (Deccan), 1347–48/1928–30 (this edition did not use the Topkapı manuscript and contains errors in both text and diagrams).