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Ke?allur N?laka??ha Somay?ji (14 June 1444 – 1544), also referred to as Ke?allur Comatiri , ^[1] was a major 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.

Early life [ edit ]

Nilakantha was born into a Brahmin family which came from South Malabar in Kerala . ^[2]

Biographical details [ edit ]

Nilakantha Somayaji was one of the very few authors of the scholarly traditions of India who had cared to record details about his own life and times. ^{[3] [4]}

In one of his works titled Siddhanta -star and also in his own commentary on Siddhanta-darpana , Nilakantha Somayaji stated that he was born on Kali-day 1,660,181 which works out to 14 June 1444 CE. A contemporary reference to Nilakantha Somayaji in a Malayalam work on astrology implies that Somayaji lived to a ripe old age even to become a centenarian. Sankara Variar , a pupil of Nilakantha Somayaji, in his commentary on Tantrasamgraha titled Tantrasamgraha-vyakhya , points out that the first and last verses of Tantrasamgraha contain chronograms specifying the Kali-days of the commencement (1,680,548) and of completion (1,680,553) of Somayaji's magnum opus Tantrasamgraha . Both these days occur in 1500 CE.

In Aryabhatiya -bhashya, Nilakantha Somayaji has stated that he was the son of Jatavedas and he had a brother named Sankara. Somayaji has further stated that he was a Bhatta belonging to the Gargya gotra and was a follower of Asvalayana-sutra of Rigveda . References in his own Laghuramayana indicate that Nilakantha Somayaji was a member of the Kelallur family (Sanskritised as Kerala-sad-grama) residing at Kundagrama, now known as Trikkandiyur in modern Tirur , Kerala . His wife was named Arya and he had two sons Rama and Dakshinamurti.

Nilakantha Somayaji studied vedanta and some aspects of astronomy under one Ravi. However, it was Damodara , son of Kerala-drgganita author Paramesvara , who initiated him into the science of astronomy and instructed him in the basic principles of mathematical computations. The great Malayalam poet Thunchaththu Ramanujan Ezhuthachan is said to have been a student of Nilakantha Somayaji.

The epithet Somayaji is a title assigned to or assumed by a Namputiri who has performed the vedic ritual of Somayajna . ^[5] So it could be surmised that Nilakantha Somayaji had also performed a Somayajna ritual and assumed the title of a Somayaji in later life. In colloquial Malayalam usage the word Somayaji has been corrupted to Comatiri.

Nilakantha Somayaji as a polymath [ edit ]

Nilakantha's writings substantiate his knowledge of several branches of Indian philosophy and culture. It is said that he could refer to a Mimamsa authority to establish his view-point in a debate and with equal felicity apply a grammatical dictum to the same purpose. In his writings he refers to a Mimamsa authority, quotes extensively from Pingala's chandas-sutra, scriptures, Dharmasastras, Bhagavata and Vishnupurana also. Sundararaja, a contemporary Tamil astronomer, refers to Nilakantha as sad-darshani-parangata, one who had mastered the six systems of Indian philosophy. ^[3]

Astronomy [ edit ]

In his Tantrasangraha , Nilakantha revised Aryabhata 's model for the planets Mercury and Venus . According to George G. Joseph his equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century. ^[6]

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. Most astronomers of the Kerala school who followed him accepted this planetary model. ^{[6] [7]}

Works [ edit ]

The following is a brief description of the works by Nilakantha Somayaji dealing with astronomy and mathematics. ^{[3] [8]}

1. Tantrasamgraha
2. Golasara  : Description of basic astronomical elements and procedures
3. Sidhhantadarpana  : A short work in 32 slokas enunciating the astronomical constants with reference to the Kalpa and specifying his views on astronomical concepts and topics.
4. Candrachayaganita  : A work in 32 verses on the methods for the calculation of time from the measurement of the shadow of the gnomon cast by the moon and vice versa.
5. Aryabhatiya-bhashya  : Elaborate commentary on Aryabhatiya.
6. Sidhhantadarpana-vyakhya  : Commentary on his own Siddhantadarapana.
7. Chandrachhayaganita-vyakhya  : Commentary on his own Chandrachhayaganita.
8. Sundaraja-prasnottara  : Nilakantha's answers to questions posed by Sundaraja, a Tamil Nadu-based astronomer.
9. Grahanadi-grantha  : Rationale of the necessity of correcting old astronomical constants by observations.
10. Grahapariksakrama  : Description of the principles and methods for verifying astronomical computations by regular observations.
11. Jyotirmimamsa  : Analysis of astronomy

See also [ edit ]

• Indian mathematicians
• Indian astronomy
• List of astronomers and mathematicians of the Kerala school

References [ edit ]

Further reading [ edit ]

• R.C. Gupta. "Second order interpolation in Indian mathematics up to the fifteenth century" (PDF) . Indian Journal of History of Science . 4 (1 & 2): 87?98. Archived from the original (PDF) on 9 March 2012.
• K. V. Sarma (2008) "Nilakantha Somayaji", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd edition) edited by Helaine Selin , Springer, ISBN   978-1-4020-4559-2 .
• Shailesh A Shirali (May 1997). "Nilakantha, Euler and pi" . Resonance : 28?43 . Retrieved 6 September 2016 .
• Ranjan Roy (December 1990). "The discovery of the series formula for π by Leibnitz, Gregory and Nilakantha" . Mathematics Magazine . 63 (5). Mathematical Association of America : 291?306. doi : 10.2307/2690896 . JSTOR   2690896 . Retrieved 6 September 2016 .

External links [ edit ]

Wikimedia Commons has media related to Nilakantha Somayaji .

• Official Website of Chenthala Vishnu Temple
• Tantrasamgraha Official Website
• Official Website of Kelallur Nilakantha Somayaji (archived)