Algorithms in Indian Astronomy

Abstract

Indian Astronomy is rich in algorithms. The algorithms presented in the Indian astronomical texts have varying degrees of complexities starting from the simple trairāśika rule, to the treatment of parallax in a solar eclipse or the computation of the elevation of lunar cusps. In the present article we will discuss a few algorithms that are representative of the ingenuity and continuity of the Indian astronomical tradition. We start with the interpolation formula presented by Brahmagupta (c.665 AD) and then proceed to describe a select few algorithms from Tantrasaṅgraha of Nīlakaṇṭha composed in 1500 AD. Here we present the algorithm for the calculation of time from shadow measurements and the exact algorithm for the computation of lagna and the time for the duration of an eclipse. We also comment on the iterative process known as aviśeṣakarma which aims at circumventing the problem of interdependencies among several variables.