Ghiyath al-Din Jamshid Mas’ud al-Kashani or Al-Kashi who was born in 1380 in Khasan and died in 22 June 1429 at Samarkand is an astronomer and one of the best mathematician in Islam. He spent her life in Mathematics and Astronomy

Details of **Jamshid al-Kashi**‘s life and works are better known than many others from this period although details of his life are sketchy. One of the reasons we is that he dated many of his works with the exact date on which they were completed, another reason is that a number of letters which he wrote to his father have survived and give fascinating information.

Al-Kashi was born in Kashan which lies in a desert at the eastern foot of the Central Iranian Range. At the time that al-Kashi was growing up Timur (often known as Tamburlaine) was conquering large regions. He had proclaimed himself sovereign and restorer of the Mongol empire at Samarkand in 1370 and, in 1383, Timur began his conquests in Persia with the capture of Herat. Timur died in 1405 and his empire was divided between his two sons, one of whom was Shah Rokh.

While Timur was undertaking his military campaigns, conditions were very difficult with widespread poverty. al-Kashi lived in poverty, like so many others at this time, and devoted himself to astronomy and mathematics while moving from town to town. Conditions improved markedly when Shah Rokh took over after his father’s death. He brought economic prosperity to the region and strongly supported artistic and intellectual life. With the changing atmosphere, al-Kashi’s life also improved markedly. The first event in al-Kashi’s life which we can date accurately is his observation of an eclipse of the moon which he made in Kashan on 2 June 1406.

During the period his work to Ulugh Beg, he produced *Treatise on the Circumference* and *Key to Arithmetic (1429)*. Al-Kashi distinguished himself by a very elegant method and the simplicity of his numerical estimates went far beyond all previous attempts (Dahlan, Amy; Dalmedico; Preiffer, Jeanne;, 2010). The way he proved the methods is also much more interesting and economical in calculation. His curiosity in numerical analysis and methods of approximation let him correctly computed 2π to 9 sexagimal digits that is equivalent to 16 decimal places of accuracy that was far more accurate than the estimates earlier given. Al-Kashi also worked with Qasi-Sada in the establishment of astronomical tables of extra ordinary precision-Zig, Ulugh Beg, which comprised sinus and tangents for arcs varying by a minutes.

His life is filmed in a serial movies entitled with “Ladder of the Sky”. You can watch it by click in

http://www.shiasource.com/drive/self/iranian-serials-and-films/ladder-of-the-sky/

and a completed bioghraphy also can be read in these link:

http://en.wikipedia.org/wiki/Jamsh%C4%ABd_al-K%C4%81sh%C4%AB

http://www.gap-system.org/~history/Printonly/Al-Kashi.html

# Bibliography

Dahlan, Amy; Dalmedico; Preiffer, Jeanne;. (2010). *History of Mathematics.* Mathematical Assosiation of America.

http://www.gap-system.org/~history/Printonly/Al-Kashi.html

http://en.wikipedia.org/wiki/Jamsh%C4%ABd_al-K%C4%81sh%C4%AB