Nilakantha Somayaji

Keļallur Nīlakaṇṭha Somayāji (14 June 1444 – 1544), also referred to as Keļallur Comatiri, was a mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501. He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapariksakrama is a manual on making observations in astronomy based on instruments of the time. Quotes Why is it that the actual value is left out and this very near value stated? Let me say. It is impossible to state the actual value. Why? That unit which leaves no remainder when the diameter is measured will leave a remainder if used again for measuring circumference. Likewise, the unit which leaves no remainder in the measure of the circumference will leave a remainder in the diameter if measured by the same unit. Hence if both (the diameter and circumference) are measured by the same unit, a remainderless state is never attained. Even if this is carried out farther to a great extent only diminution of the remainder can be obtained but absence of remainder can never be obtained— this is the meaning. Mallayya, V. Madhukar. ‘The Indian Mathematical Tradition with Special Reference to Kerala: Methodology and Motivation’. In Ancient Indian Leaps into Mathematics, edited by B. S. Yadav and Man Mohan, pp. 153-170. Birkhäuser, 2011. Nilakantha, in his commentary on the Aryabhatiya, quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189 One has to realize that the five siddhantas [i.e. astronomical systems] had been correct at a particular time. Therefore, one should search for a siddhanta that does not show discord with actual observations (at the present time). Such accordance with observation has to be ascertained by (astronomical) observers during times of eclipses etc. When siddhantas show discord, that is, when an earlier siddhanta is in discord, observations should be made of revolutions etc. (which would give results in accord with actual observations) and a new siddhanta enunciated. Subarayappa, B. V. and Sarma, K. V. Indian Astronomy: A Source Book. Bombay: Nehru Centre, 1985. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189 One has to accept that [each of ] the five siddhantas had been authoritative at one time [though they might not be so now]. Therefore one has to look for a system which tallies with observation. The said tallying has to be verified by contemporary experimenters at the time of eclipses etc. Ramasubramanian and Sriram, Tantrasangraha of Nilakantha Somayaji, 2011:quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189 External links Category:1444 births Category:1544 deaths Category:Hindus from India Category:Astronomers from India Category:Kerala school of astronomy and mathematics Category:Mathematicians from India