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

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°.

Keywords

• ghiyath al-dın jamshıd al-kashı
• jamshıd kashanı
• al-risala al-muhıtıyya
• miftah al-hisab
• risala al-watar wa’l-jaib
• al-kashı’s fundamental theorem
• euclid’s elements
• lambert identity
• ptolemy’s theorem
• pythagorean theorem
• pascal triangle
• ruffini-horner’s method