What is the nilakantha somayaji's invention in mathematics?
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The Tantrasamgraha is his major astronomy treatise written in 1501. It consists of 432 Sanskrit verses divided into 8 chapters, and it covers various aspects of Indian astronomy. It is based on the epicyclic and eccentric models of planetary motion.
Nilakantha derived the series expansion
tan-1x = x - x3/3 + x5/5 - x7/7 + ...
by obtaining an approximate expression for an arc of the circumference of a circle and then considering the limit. An interesting feature of his work was his introduction of several additional series for π/4 that converged more rapidly than
π/4 = 1 - 1/3 + 1/5 - 1/7+ ... .
Nilakantha derived the series expansion
tan-1x = x - x3/3 + x5/5 - x7/7 + ...
by obtaining an approximate expression for an arc of the circumference of a circle and then considering the limit. An interesting feature of his work was his introduction of several additional series for π/4 that converged more rapidly than
π/4 = 1 - 1/3 + 1/5 - 1/7+ ... .
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