Ghiyath al-Din Jamshid Masud al-Kashi
Al-Kashi remains to this day known for his great mathematical output. He produced his treatise Risala al-Muhitiya (Treatise on the Circumference) in July 1424, a work in which he calculated 2 [pi] to nine sexagesimal places and translated this into sixteen decimal places. This was an achievement far beyond anything which had been obtained before, either by the ancient Greeks or by the Chinese (who achieved 6 decimal places in the 5th century). It would be almost 200 years before van Ceulen surpassed Al-Kashi’s accuracy with 20 decimal places. Al-Kashi’s most impressive mathematical work was, however, Miftah al-Hisab (The Key to Arithmetic) which he completed on 2 March 1427. The work is a major text intended to be used in teaching students in Samarkand, in particular al-Kashi aims to give therein the necessary mathematics for those studying astronomy, surveying, architecture, accounting and trading. The miftah al-Hisab is divided into five books preceded by an introduction: On the Arithemetic of integrers; On the arithmetic of fractions; On the computation of astronomers (on sexagesimal fractions); On the measurement of plane figures and bodies; and on the solution of problems by means of algebra (Linear and quadratic equations) and of the rule of two false assumptions etc.
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