Nilakantha Somayaji – An Indian Mathematician and Astronomer

Kelallur Nilakantha Somayaji was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. His most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501.

Nilakantha 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. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry.

Nilakantha was born into a Namputiri Brahmin family (14 June 1444) which came from South Malabar in Kerala. The Nambudiri is the main caste of Kerala. It is an orthodox caste whose members consider themselves descendants of the ancient Vedic religion. Nilakantha studied astronomy and Vedanta, one of the six orthodox systems of Indian Hindu philosophy.

Nilakantha studied astronomy and Vedanta, one of the six orthodox systems of Indian Hindu philosophy, under the teacher Ravi. He was also taught by Damodra who was the son of Paramesvara. Paramesvara was a famous Indian astronomer and Damodra followed his father’s teachings.

Tantrasamgraha 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. Description of chapters below
Chapter 1: deal with the motions and longitudes of the planets.
Chapter 2: deal with the motions and longitudes of the planets.
Chapter 3: Treatise on shadow deal;
Various problems related with the sun’s position on the celestial sphere;

The relationships of its ex-pressions in the three systems of coordinates namely ecliptic, equatorial and horizontal coordinates.

Chapter 4: on the lunar eclipse and On the solar eclipse
Chapter 5: treat various aspects of the eclipses of the sun and the moon
Chapter 6: vyatipata and deals with the complete deviation of the longitudes of the sun and the moon
Chapter 7: visibility computation discusses the rising and setting of the moon and planets
Chapter 8: elevation of the lunar cusps examines the size of the part of the moon which is illuminated by the sun and gives a graphical representation of it.

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. The Tantrasamgraha is not the only work of Nilakantha of which we have the text. He also wrote Golasara which is written in fifty-six Sanskrit verses and shows how mathematical computations are used to calculate astronomical data.

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