Spherical Trigonometry and the Astronomy of the Medieval Kerala School

Abstract

Geocentric astronomy in the Graeco-Islamic tradition is practically synonymous with spherical trigonometry: the chief physical structures underying its measurement systems are great circles on the sphere.¹ Although the methods of plane trigonometry inspired by the Greek chord function became the cornerstone of classical Indian mathematical astronomy, the corresponding techniques for exact solution of triangles on the sphere’s surface seem never to have been fully developed within this tradition. Numerous rules nevertheless appear in Sanskrit texts for finding the great-circle arcs representing various astronomical quantities; these were presumably derived not primarily by spherics per se but from plane triangles inside the sphere or from analemmatic projections, and were supplemented by approximate formulas assuming small spherical triangles to be plane.²