Brahmagupta, Bhaskara-I, Madhava Samgramagrama – Three pearls of Indian Astronomy and Mathematics
A collection of some of our greats, Brahmagupta who studied the works of Aryabhatta, Latadeva, Varahamihira and others. He wrote the Brahmasputa Siddhanta and Khanda Katkaya transmitted by the Arabs. I’ll show that later. Solutions of linear and quadratic equations and the rules for zero operations, positive and negative numbers. Trignometric tables and in Astronomy he said that Moon is closer to the Earth than the Sun. And he solved this equation which is a very famous equation in literature. More than in this time frame he had the complete solution to the set of equations which the westerners refer to as the Pell’s equation. And even greats like Oiler and others were clueless on how to solve this and eventually after about a 100 years of trying Europe was able to solve this 1000 years after Brahmagupta had already solved it.
Bhaskara-I who wrote these works. Zero, positional arithmetic, approximation for sine. There is a very famous approximation that Sin x can be represented by this kind of expression. Very, very famous. Even today we use this and he is the one who invented that. Bhaskara II lived in Bijapur, Bijapur northern Karnataka and he went to Ujjain and became the Head of Department of Astronomy over there. An instance of people moving across the country and working in different places. He wrote Siddhanta Shiromani and he appears to have also got the elements of differential calculus. He computed precession like I told you. This statement he made. “At the highest point the instantaneous speed is zero”. This is an assertion of the Calculus of variation, where at the highest point the rate of change is zero. That is a property I use even today for living in optimization and fields like that. So I owe it all to this very famous scientist. One of my most famous favorite scientists from ancient India – Bhaskara II.
Madhava of Sangamagrama (Trissur), all these expressions that you see, this infinite series are attribute to him. So he is the one who invented this and much, much more. Founder of Kerala school of Astronomy and Mathematics. Infinite series, Calculus, Trignometry. Iterative solution of nonlinear equations, something I do for a living even today, originated with him. We typically think Newton is the one who talked about iterative solution for nonlinear equations. But it turns out that he was the one who did these things. George Joseph Geevarghese, professor and he says that Madhava’s math was transmitted to Europe a century before Newton by the Church and these are some of the alumni of the school.
Featured Image: – http://www.famous-mathematicians.com/madhava/