The Scientific, Mathematical And Astronomical Contributions Of Jamshīd Al-Kāshī: A Critical Analytical Study

Abstract

This research is a critical and analytical study of the astronomical and mathematical works and contributions of Ghiyāth al-Dīn Jamshīd al-Kāshī, a great scientist of the Muslim world in medieval history. Al-Kāshī’s works described here in this research include “al-Rīsalah al-Mūhītiyah” (The Treatise on the Circumference), in which he approximated π to 16 decimal places, and “Rīsalat al-Witr wal-Jaib” (Treatise on the Chord and the Sine) where he approximated sin 1 gradually up to 16 decimal places, both of which have been regarded as great feats. Among al-Kāshī’s greatest works is “Miftah al-Hisab” (Key to Arithmetic). In one part of “Miftah al-Hisab”, al-Kāshī extracted integer roots with a high degree of accuracy. Although al-Kāshī cannot be regarded as the first to use decimal fractions in his arithmetic computations, he brilliantly used a methodical way to deal with them, which is comparable with modern mathematical practices. Furthermore, al-Kāshī expanded (a + b)ⁿ in a way that was very similar to Newton's expansion, and he used a trigonometric table similar to Pascal triangle to get the expansion’s coefficients.