An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere

While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.