Jamshīd al-Kāshī
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Ghiyāth al-Dīn Jamshīd ibn Masʾūd al-Kāshī (or Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.
Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, which lies in a desert to the southeast of the Central Iranian range. This region was controlled by Tamurlane, better known as Timur, who was more interested in invading other areas than taking care of what he had. Due to this, al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.
The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Persian princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Their son, Ulugh Beg, was enthusiastic about science as well, and made some noted contributions in mathematics and astronomy himself. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world’s greatest mathematicians.
When he came into power, Ulugh Beg constructed the world’s most prestigious university at the time. Students from all over the Middle East, and beyond, flocked to this academy in Samarkand, the capital of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many, many great mathematicians and scientists of the Muslim world. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king’s favourite student.
Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are rather unclear.
In French, the Law of cosines is named Théorème d'Al-Kashi (Theorem of Al-Kashi), after Kashi's efforts to unify existing works on the subject.
In discussing decimal fractions, Struik states that (p. 7):[1]
"The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphelet De Thiende, published at Leyden in 1585, together with a French translation, La Disme, by the Flemish mathematician Simon Stevin (1548-1620), then settled in the Northern Netherlands. It is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and sexagesimal fractions with great ease in his Key to arithmetic (Samarkand, early fifteenth century).[2]"
Further, in considering the Pascal triangle, Struik notes that (p. 21):[3]
"The Pascal triangle appears for the first time (so far as we know at present) in a book of 1261 written by Yang Hui, one of the mathematicians of the Sung dynasty in China.[4] The properties of binomial coefficients were discussed by the Persian mathematician Jamshid Al-Kāshī in his Key to arithmetic of c. 1425.[5] Both in China and Persia the knowledge of these properties may be much older. This knowledge was shared by some of the Renaissance mathematicians, and we see Pascal's triangle on the title page of Peter Apian's German arithmetic of 1527. After this we find the triangle and the properties of binomial coefficients in several other authors.[6]"
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[edit] Notes
- ^ D.J. Struik, A Source Book in Mathematics 1200-1800 (Princeton University Press, New Jersey, 1986). ISBN 0-691-02397-2
- ^ P. Luckey, Die Rechenkunst bei Ğamšīd b. Mas'ūd al-Kāšī (Steiner, Wiesbaden, 1951).
- ^ D.J. Struik, op. cit.
- ^ J. Needham, Science and civilisation in China, III (Cambridge University Press, New York, 1959), 135.
- ^ Russian translation by B.A. Rozenfel'd (Gos. Izdat, Moscow, 1956); see also Selection I.3, footnote 1.
- ^ Smith, History of mathematics, II, 508-512. See also our Selection II.9 (Girard).
[edit] See also
[edit] References
- O'Connor, John J. & Robertson, Edmund F., “Ghiyath al-Din Jamshid Mas'ud al-Kashi”, MacTutor History of Mathematics archive
[edit] External links
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