An Overview of Mathematical Contributions of Ghiyath al-Din Jamshid Al-Kashi [Kashani]

Document Type: Special Issue: International Conference on Architecture and Mathematics

Author

University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722 USA

Abstract

In this paper, we study Ghiyath al-Din Jamshid al-Kashi's (1380-1429 A.D.) main mathematical achievements. We discuss his al-Risala al-muhitiyya ("The Treatise on the Circumference"), Risala al-watar wa'l-jaib ("The Treatise on the Chord and Sine"), and Miftah al-hisab ("The Key of Arithmetic"). In particular, we look at al-Kashi's fundamental theorem, his calculation of pi, and his calculation of sin1°.

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[1] M. K. Azarian, A study of Ris¯ala al-watar wa’l Jaib (“The treatise on the
chord and sine”), Forum Geom. 15 (2015) 229 - 242.

[2] M. K. Azarian, Al-Ris¯ala al-Muh¯ıt¯ıyya: A summary, Missouri J. Math. Sci.
22(2) (2010) 64 - 85.
[3] M. K. Azarian, The introduction of al-Ris¯ala al-Muh¯ıt¯ıyya: An english translation,
Int. J. Pure Appl. Math. 57(6) (2009) 903 - 914.
[4] M. K. Azarian, Al-K¯ash¯ı’s fundamental theorem, Int. J. Pure Appl. Math.
14(4) (2004) 499 - 509.
[5] M. K. Azarian, Meftah al-hesab [Mift¯ah al-his¯ab]: A summary, Missouri J.
Math. Sci. 12(2) (2000) 75 - 95.
[6] M. K. Azarian, A summary of mathematical works of Ghiy¯ath ud-D¯ın
Jamsh¯ıd K¯ash¯an¯ı, J. Recreat. Math. 29(1) (1998) 32 - 42.
[7] D. H. Bailey, J. M. Borwein, P. B. Borwein and S. Plouffe, The quest for Pi,
Math. Intelligencer 19(1) (1997) 50 - 57.
[8] Abu’l-Q¯asim Qurb¯an¯ı, K¯ash¯an¯ı n¯ameh [A monograph on Ghiy¯ath al-D¯ın
Jamsh¯ıd Mas’¯ud al-K¯ash¯ı], Tehran University Press, Tehran, Iran, 1971.
[9] P. Trueb, Digit statistics of the first 22.4 trillion decimal digits of Pi,
arXiv:1612.00489.