Samgamagr\=ama M\=adhava: An Updated Biography

TL;DR

This paper provides an updated biography of Samgamagrama Madhava, highlighting recent scholarly insights into his contributions to mathematics and astronomy, including his algorithms and value of pi, with new geographical and contextual details.

Contribution

It compiles recent research findings on Madhava's work, updating his biography with new geographical, mathematical, and astronomical insights.

Findings

Updated geographical location of Madhava's work in Kerala

Details on Madhava's algorithms for sine and cosine calculations

Revised estimate of Madhava's value of pi

Abstract

This paper presents an updated biography of Samgamagr\=ama M\=adhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his contributions to mathematics and astronomy. One major updation is with regard to the geographical location in Kerala where M\=adhava flourished. Other updations include observations on M\=adhava's algorithm to compute the numerical values of the sine and cosine functions and on his value of the mathematical constant $\pi$.