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| {{Short description|Indian mathematician and astronomer (1444–1544)}} | {{Short description|Indian mathematician and astronomer (1444–1544)}} | ||
| {{More citations needed|date=April 2024}} | |||
| {{Use dmy dates|date=August 2019}} | {{Use dmy dates|date=August 2019}} | ||
| {{Use Indian English|date=August 2019}} | {{Use Indian English|date=August 2019}} | ||
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| | birth_name = | | birth_name = | ||
| | birth_date = 14 June 1444 | | birth_date = 14 June 1444 | ||
| | birth_place = ], ] | | birth_place = ], ] | ||
| | death_date = |
| death_date = 1544{{citation needed|date=February 2020}} | ||
| | death_place = | | death_place = | ||
| | resting_place_coordinates = <!-- {{coord|LAT|LONG|display=inline,title}} --> | | resting_place_coordinates = <!-- {{coord|LAT|LONG|display=inline,title}} --> | ||
| | nationality = |
| nationality = | ||
| | citizenship = | | citizenship = | ||
| | other_names = Kelallur Comatiri | | other_names = Kelallur Comatiri | ||
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| '''Keļallur |
'''Keļallur Nīlakaṇṭha Somayāji''' (14 June 1444 – 1544), also referred to as '''Keļallur Comatiri''',<ref>{{cite journal|last=K.D. Swaminathan|date=1972|title=Jyotisa in Kerala|journal=Indian Journal of History of Science|volume=8|issue=1 & 2|pages=28–36|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b62_28.pdf|access-date=3 February 2010}}</ref> was a major ] and ] of the ]. One of his most influential works was the comprehensive astronomical treatise '']'' completed in 1501. He had also composed an elaborate commentary on ] called the ''Aryabhatiya Bhasya''. In this Bhasya, Nilakantha had discussed ] expansions of ] and problems of ] and ]. ''Grahapariksakrama'' is a manual on making observations in astronomy based on instruments of the time. | ||
| ==Early life== | ==Early life== | ||
| Nilakantha was born into a Brahmin family which came from ] in ].<ref>{{Cite web|title=Nilakantha - Biography|url=https://mathshistory.st-andrews.ac.uk/Biographies/Nilakantha/|access-date=2022-01-11|website=Maths History|language=en}}</ref> | Nilakantha was born into a ] family which came from ] in ].<ref>{{Cite web|title=Nilakantha - Biography|url=https://mathshistory.st-andrews.ac.uk/Biographies/Nilakantha/|access-date=2022-01-11|website=Maths History|language=en}}</ref> | ||
| ==Biographical details== | ==Biographical details== | ||
| Line 39: | Line 40: | ||
| 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.<ref name="text">{{cite web|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf|title=Tantrasamgraha with English translation|last=] (editor)|others=Translated by V.S. Narasimhan|publisher=Indian National Academy of Science|pages=48|language=sa, en|access-date=17 January 2010|url-status=dead|archive-url=https://web.archive.org/web/20120309014402/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf|archive-date=9 March 2012}}</ref><ref>''Tantrasamgraha'', ed. ], trans. V. S. Narasimhan in the Indian Journal of History of Science, issue starting Vol. 33, No. 1 of March 1998</ref> | 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.<ref name="text">{{cite web|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf|title=Tantrasamgraha with English translation|last=] (editor)|others=Translated by V.S. Narasimhan|publisher=Indian National Academy of Science|pages=48|language=sa, en|access-date=17 January 2010|url-status=dead|archive-url=https://web.archive.org/web/20120309014402/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_2/20005a5d_s1.pdf|archive-date=9 March 2012}}</ref><ref>''Tantrasamgraha'', ed. ], trans. V. S. Narasimhan in the Indian Journal of History of Science, issue starting Vol. 33, No. 1 of March 1998</ref> | ||
| In one of his works titled '']-star'' and also in his own commentary on ''Siddhanta-darpana'', Nilakantha Somayaji |
In one of his works titled '']-star'' and also in his own commentary on ''Siddhanta-darpana'', Nilakantha Somayaji stated that he was born on ] 1,660,181 which works out to 14 June 1444 CE. A contemporary reference to Nilakantha Somayaji in a ] work on ] implies that Somayaji lived to a ripe old age even to become a centenarian. ], a pupil of Nilakantha Somayaji, in his commentary on ] titled ''Tantrasamgraha-vyakhya'', points out that the first and last verses of ] contain chronograms specifying the Kali-days of the commencement (1,680,548) and of completion (1,680,553) of Somayaji's magnum opus ]. Both these days occur in 1500 CE. | ||
| In ]-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 ] and was a follower of ] of ]. 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 ], ]. His wife was named Arya and he had two sons Rama and Dakshinamurti. | In ]-bhashya, Nilakantha Somayaji has stated that he was the son of Jatavedas and he had a brother named '''Sankara'''.<ref name=Sarma>{{cite book |last1=K. V. Sarma |title=A History of the Kerala School of Hindu Astronomy |date=1972 |publisher=Vishveshvaranand Institute of Sanskrit and Indological Studies, Panjab University, Hoshiarpur |url=https://archive.org/details/KeralaSchoolOfAstronomy/page/n71/mode/2up?view=theater|access-date=15 July 2024| page=58}}</ref> Somayaji has further stated that he was a Bhatta belonging to the Gargya ] and was a follower of ] of ]. 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 ] in modern ], ]. His wife was named Arya and he had two sons Rama and Dakshinamurti. | ||
| Nilakantha Somayaji studied ] and some aspects of astronomy under one Ravi. However, it was ], son of Kerala-drgganita author ], who initiated him into the science of astronomy and instructed him in the basic principles of mathematical computations. The great ] poet ] is said to have been a student of Nilakantha Somayaji. | Nilakantha Somayaji studied ] and some aspects of astronomy under one Ravi. However, it was ], son of Kerala-drgganita author ], who initiated him into the science of astronomy and instructed him in the basic principles of mathematical computations. The great ] poet ] is said to have been a student of Nilakantha Somayaji. | ||
| The epithet ''Somayaji'' is a title assigned to or assumed by a ] who has performed the vedic ritual of '']''.<ref>{{cite web|url=http://www.namboothiri.com/articles/yajnam.htm|title=Yaagam (Yajnam)|last=P. Vinod Bhattathiripad|author2=K.D. Nambudripad |date=3 May 2007|publisher=Namboothiri Websites Trust|access-date=4 February 2010}}</ref> 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. | The epithet ''Somayaji'' is a title assigned to or assumed by a ] who has performed the vedic ritual of '']''.<ref>{{cite web|url=http://www.namboothiri.com/articles/yajnam.htm|title=Yaagam (Yajnam)|last=P. Vinod Bhattathiripad|author2=K.D. Nambudripad |date=3 May 2007|publisher=Namboothiri Websites Trust|access-date=4 February 2010}}</ref> 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. | ||
| Somayāji’s "Āryabhaṭīyabhāṣya" is the most extensive commentary on Āryabhaṭīya. He takes all pains to expose the rationale and the objective behind the statements and observations made by Āryabhaṭa.<ref>''Nilakantha's critique on Aryabhata's verses on squaring and square rooting'', N. K. Sundareswaran, '''', Vol 39, No. 2, 2017</ref> | |||
| ==Nilakantha Somayaji as a polymath == | ==Nilakantha Somayaji as a polymath == | ||
| Line 52: | Line 55: | ||
| ==Astronomy== | ==Astronomy== | ||
| In his '']'', Nilakantha revised ]'s model for the planets ] and ]. |
In his '']'', Nilakantha revised ]'s model for the planets ] and ]. According to ] his equation of the ] for these planets remained the most accurate until the time of ] in the 17th century.<ref name=Joseph>George G. Joseph (2000). ''The Crest of the Peacock: Non-European Roots of Mathematics'', p. 408. ].</ref> | ||
| In his ''Aryabhatiyabhasya'', a commentary on Aryabhata's '']'', Nilakantha developed a computational system for a partially ] planetary model in which Mercury, Venus, ], ] and ] orbit the ], which in turn orbits the ], similar to the ] later proposed by ] in the late 16th century. Most astronomers of the Kerala school who followed him accepted this planetary model.<ref name=Joseph/><ref>K. Ramasubramanian, M. D. Srinivas, M. S. Sriram (1994). "", '']'' '''66''', p. 784-790.</ref> | In his ''Aryabhatiyabhasya'', a commentary on Aryabhata's '']'', Nilakantha developed a computational system for a partially ] planetary model in which Mercury, Venus, ], ] and ] orbit the ], which in turn orbits the ], similar to the ] later proposed by ] in the late 16th century. Most astronomers of the Kerala school who followed him accepted this planetary model.<ref name=Joseph/><ref>K. Ramasubramanian, M. D. Srinivas, M. S. Sriram (1994). "", '']'' '''66''', p. 784-790.</ref> | ||
| Somayaji time and again advocates the necessity of periodical modification of computation system based on observations and experimentations. One of his works, ''Jyotirmimamsa'', is written exclusively for this purpose. His critical and analytical approach is reflected in all works.<ref name="N K Sundareswaran">{{cite book |title=Kerala School of Mathematics:Trajectories and Impact |date=2014 |publisher=University of Calicut |isbn=9788193116807 |edition=2014 |ref=The critical and rational approach of Kelallur Nilakantha Somayaji}}</ref> | |||
| ==Works == | ==Works == | ||
| Line 81: | Line 85: | ||
| {{reflist}} | {{reflist}} | ||
| <ref name="N K Sundareswaran">{{cite book |title=The Contribution of Kelallur Nilakantha Somayaji to Astronomy |title-link=N. K. Sundareswaran |date=2009 |publisher=University of Calicut |year=2009 |isbn=9788177481495 |edition=2009 |location=Calicut |language=English}}</ref>==Further reading== | |||
| ==Further reading== | |||
| *{{cite journal|last=R.C. Gupta|title=Second order interpolation in Indian mathematics up to the fifteenth century|journal=Indian Journal of History of Science|volume=4|issue=1 & 2|pages=87–98|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b65_86.pdf|url-status=dead|archive-url=https://web.archive.org/web/20120309121926/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b65_86.pdf|archive-date=2012-03-09}} | *{{cite journal|last=R.C. Gupta|title=Second order interpolation in Indian mathematics up to the fifteenth century|journal=Indian Journal of History of Science|volume=4|issue=1 & 2|pages=87–98|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b65_86.pdf|url-status=dead|archive-url=https://web.archive.org/web/20120309121926/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005b65_86.pdf|archive-date=2012-03-09}} | ||
| Line 92: | Line 96: | ||
| * | * | ||
| * | * | ||
| * | * (archived) | ||
| {{Kerala School}} | |||
| {{Indian mathematics}} | {{Indian mathematics}} | ||
Latest revision as of 12:36, 6 January 2025
Indian mathematician and astronomer (1444–1544) | This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Nilakantha Somayaji" – news · newspapers · books · scholar · JSTOR (April 2024) (Learn how and when to remove this message) |
| Nilakantha Somayaji | |
|---|---|
| Born | 14 June 1444 Tirur, Vijayanagara Empire |
| Died | 1544 |
| Other names | Kelallur Comatiri |
| Occupation | Astronomer-mathematician |
| Known for | Authorship of Tantrasamgraha |
| Notable work | Golasara, Candrachayaganita, Aryabhatiya-bhashya, Tantrasamgraha |
| Title | Somayaji |
| Spouse | Arya |
| Children | Rama, Dakshinamurti |
| Parent | Jatavedan (father) |
Keļallur Nīlakaṇṭha Somayāji (14 June 1444 – 1544), also referred to as Keļallur Comatiri, 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
Nilakantha was born into a Brahmin family which came from South Malabar in Kerala.
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.
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. 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.
Somayāji’s "Āryabhaṭīyabhāṣya" is the most extensive commentary on Āryabhaṭīya. He takes all pains to expose the rationale and the objective behind the statements and observations made by Āryabhaṭa.
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.
Astronomy
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.
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. Somayaji time and again advocates the necessity of periodical modification of computation system based on observations and experimentations. One of his works, Jyotirmimamsa, is written exclusively for this purpose. His critical and analytical approach is reflected in all works.
Works
Further information: Tantrasamgraha and JyotirmimamsaThe following is a brief description of the works by Nilakantha Somayaji dealing with astronomy and mathematics.
- 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
See also
References
- K.D. Swaminathan (1972). "Jyotisa in Kerala" (PDF). Indian Journal of History of Science. 8 (1 & 2): 28–36. Retrieved 3 February 2010.
- "Nilakantha - Biography". Maths History. Retrieved 11 January 2022.
- ^ K.V. Sarma (editor). "Tantrasamgraha with English translation" (PDF) (in Sanskrit and English). Translated by V.S. Narasimhan. Indian National Academy of Science. p. 48. Archived from the original (PDF) on 9 March 2012. Retrieved 17 January 2010.
{{cite web}}:|last=has generic name (help) - 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
- K. V. Sarma (1972). A History of the Kerala School of Hindu Astronomy. Vishveshvaranand Institute of Sanskrit and Indological Studies, Panjab University, Hoshiarpur. p. 58. Retrieved 15 July 2024.
- P. Vinod Bhattathiripad; K.D. Nambudripad (3 May 2007). "Yaagam (Yajnam)". Namboothiri Websites Trust. Retrieved 4 February 2010.
- Nilakantha's critique on Aryabhata's verses on squaring and square rooting, N. K. Sundareswaran, Ganita Bharati, Vol 39, No. 2, 2017
- ^ George G. Joseph (2000). The Crest of the Peacock: Non-European Roots of Mathematics, p. 408. Princeton University Press.
- 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.
- Kerala School of Mathematics:Trajectories and Impact (2014 ed.). University of Calicut. 2014. ISBN 9788193116807.
- A.K. Bag (1980). "Indian literature on mathematics during 1400 - 1800 AD" (PDF). Indian Journal of History of Science. 15 (1): 79–93. Archived from the original (PDF) on 9 March 2012. Retrieved 30 January 2010.
==Further reading==
- 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
- Official Website of Chenthala Vishnu Temple
- Tantrasamgraha Official Website
- Official Website of Kelallur Nilakantha Somayaji (archived)
- The Contribution of Kelallur Nilakantha Somayaji to Astronomy (2009 ed.). Calicut: University of Calicut. 2009. ISBN 9788177481495.
{{cite book}}: CS1 maint: date and year (link)