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1 Biographical details
2 Nilakantha Somayaji as a polymath
3 Mathematics
4 Astronomy
5 Works of Nilakantha Somayaji
6 See also
7 References
8 Further reading

Biographical details

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. So fortunately a few accurate particulars about Nilakantha Somayaji are known.[2][3]

In one of his works titled Siddhanta-darpana and also in his own commentary on Siddhanta-darpana, Nilakantha Somayaji has stated that he was born on Kali-day 1,660,181 which works out to 14 th 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 Rgveda. 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 near modern Tirur in 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.[4] 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

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.[2]

Mathematics

An interesting piece of Nilakantha's work is the derivation of Leibniz-Gregory series:

$\frac {\pi}{4} = 1 - \frac {1}{3} + \frac {1}{5} - \frac {1}{7} + \frac {1}{9} - \frac {1}{11} \cdots$

and

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

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.

Astronomy

In his Aryabhatiyabhasya, a commentary on Aryabhata's Aryabhatiya (499), Nilakantha revised Aryabhata's model and 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.[5][6] Nilakantha's planetary system also incorporated elliptic orbits[7] and the Earth's rotation on its axis.[8]

In his Tantrasangraha (1500), Nilakantha further revised Aryabhata's model for the interior planets Mercury and Venus. His equation of the centre for these planets was more accurate at predicting their heliocentric orbits than the later Tychonic and Copernican models, and remained the most accurate until the 17th century when Johannes Kepler reformed the computation for the interior planets in much the same way Nilakantha did.[9][5] Most astronomers of the Kerala school who followed him accepted his planetary model.[5][6]

Works of Nilakantha Somayaji

Further information: Tantrasamgraha and Jyotirmimamsa

The following is a brief description of the works by Nilakantha Somayaji dealing with astronomy and mathematics.[2][10]

Tantrasamgraha
Golasara : Description of basic astronomical elements and procedures
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.
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.
Aryabhatiya-bhashya : Elaborate commentary on Aryabhatiya.
Sidhhantadarpana-vyakhya : Commentary on his own Siddhantadarapana.
Chandrachhayaganita-vyakhya : Commentary on his own Chandrachhayaganita.
Sundaraja-prasnottara : Nilakantha's answers to questions posed by Sundaraja, a Tamil Nadu based astronomer.
Grahanadi-grantha : Rationale of the necessity of correcting old astronomical constants by observations.
Grahapariksakrama : Description of the principles and methods for verifying astronomical computations by regular observations.
Jyotirmimamsa : Analysis of astronomy

References

^ K.D. Swaminathan (1972). "Jyotisa in Kerala". Indian Journal of History of Science 8 (1 & 2): 28 - 36. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b62_28.pdf. Retrieved 03 February 2010.
^ ^a ^b ^c K.V. Sarma (editor); V.S. Narasimhan (translator). "Tantrasamgraha with English translation" (in Sanskrit and English). Indian National Academy of Science. pp. 48. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf. Retrieved 17 January 2010.
^ Tantrasamgraha, ed. K.V. Sarma, trans. V. S. Narasimhan in the Indian Journal of History of Science, issue starting Vol. 33, No. 1 of March 1998
^ P. Vinod Bhattathiripad; K.D. Nambudripad (3 May 2007). "Yaagam (Yajnam)". Namboothiri Websites Trust. http://www.namboothiri.com/articles/yajnam.htm. Retrieved 4 February 2010.
^ ^a ^b ^c George G. Joseph (2000). The Crest of the Peacock: Non-European Roots of Mathematics, p. 408. Princeton University Press.
^ ^a ^b 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.
^ B S Shylaja and J N Planetarium (April 2003), "500 years of Tantrasangraha—A landmark in the history of astronomy", Resonance (Springer) 8 (4): 66-68 [68], doi:10.1007/BF02883537, ISSN 0973-712X
^ Amartya Kumar Dutta (May 2006), "Āryabhata and axial rotation of earth", Resonance (Springer) 11 (5): 58-72 [70-1], doi:10.1007/BF02839373, ISSN 0973-712X
^ =Ramasubramanian, K., "Model of planetary motion in the works of Kerala astronomers", Bulletin of the Astronomical Society of India 26: 11-31 [23-4], http://adsabs.harvard.edu/full/1998BASI...26...11R, retrieved 2010-03-05
^ A.K. Bag (1980). "Indian literature on mathematics during 1400 - 1800 AD". Indian Journal of History of Science 15 (1): 79 - 93. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af2_79.pdf. Retrieved 30 January 2010.

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