## Foredrag d. 12. november 2019

**Prof. K. Ramasubramanian**

Department of Humanitites and Social Sciences

IIT Bombay

## A short history of the evolution of the sine function in Indian mathematics

Starting from the simplest model for conceiving the planetary motion, the sine function pervades all of physical, engineering, mathematical, medical and biological sciences. So much so, today it would be almost impossible to conceive of any discipline of science, without this sine function.

Briefly touching upon how the sine function was conceived in India, we shall highlight the various techniques that got invented over centuries to determine its value for different arguments. Aryabhata by the end of the 5th century had proposed an interesting geometric approach and an analytic one involving an interesting recursive relation. For those who are mathematically inclined, it may be mentioned that this relation essentially happens to be the discrete analogue of what is today referred to as the harmonic equation. At this stage, we may also point out how distinct this conception is from the way it has been characterized by the Greek civilization.

Yet another interesting recursive relation, which is very different in its structure and nature form the one given by Aryabhata, has been proposed by Kerala astronomers, in connection with their study of the properties of cyclic quadrilaterals. During the talk, shall attempt to take the audience through this fascinating journey that the Indian mathematicians seem to have taken in trying to evaluate the sine function in multiple ways!