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 Tantrasangraha 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.
An interesting piece of Nilakantha's work is the derivation of Leibniz-Gregory series:
Nilakantha's derivation of the above series is all the more interesting because it used the geometrical definition of π as the ratio of circumference and diameter of a circle.
In his Tantrasangraha, Nilakantha revised Aryabhata's model for the planets Mercury and Venus. His equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.
In his Aryabhatiyabhasya, a commentary on Aryabhata's Aryabhatiya, Nilakantha developed a computational system for a partially heliocentric planetary model in which Mercury, Venus, Mars, Jupiter and Saturn orbit the Sun, which in turn orbits the Earth, similar to the Tychonic system later proposed by Tycho Brahe in the late 16th century. Nilakantha's system, however, was mathematically more efficient than the Tychonic system, due to correctly taking into account the equation of the centre and latitudinal motion of Mercury and Venus. Most astronomers of the Kerala school who followed him accepted this planetary model.
* Indian mathematicians
1. ^ a b George G. Joseph (2000). The Crest of the Peacock: Non-European Roots of Mathematics, p. 408. Princeton University Press.
2. ^ K. Ramasubramanian, M. D. Srinivas, M. S. Sriram (1994). "Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 AD) and the implied heliocentric picture of planetary motion", Current Science 66, p. 784-790.