Nilakantha Somayaji

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Nilakantha Somayaji (Malayalam: നീലകണ്ഠ സോമയാജി, नीलकण्ठ सोमयाजि) (1444-1544), from Kerala, was a major Indian mathematician and astronomer of the Kerala School of astronomy and mathematics and was a student of Damodara. Later, he lived in Tryambakeshwar. Among his many influential books, he wrote the comprehensive astronomical treatise Tantrasamgraha in 1501. He also wrote the Aryabhatiya Bhasya, which contains work on infinite series expansions, problems of algebra, spherical geometry, and many results of calculus. Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time.

[edit] Nilakantha's work

An interesting piece of Nilakantha's work is the derivation of Leibniz-Gregory series $\frac {\pi}{4} = 1 - \frac {1}{3} + \frac {1}{5} - \frac {1}{7} + \frac {1}{9} - \frac {1}{11} ..............$

And

$\pi = \sqrt{12} ( 1 - \frac {1}{3.3} + \frac {1}{5.3^2} - \frac {1}{7.3^3} + \frac {1}{9.3^4} ..........)$

Nilakantha's derivation the of above series is all the more interesting because it is derived using the geometrical definition of π as the ratio of circumference and diameter of a circle.