View source for Parameshvara Nambudiri

{{Short description|Indian mathematician and astronomer (1380–1460)}}
{{for|the concept of God|Parameshwara (god)}}
{{Use dmy dates|date=August 2019}}
{{Use Indian English|date=August 2019}}
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| birth_date         = c. 1380
| birth_place        = [[Tirur]], [[Cochin Kingdom]]
| death_date         = c. {{Death date and age|1460|1380}}
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| known_for          = [[Mean value theorem]]<br/>[[Drig system]]<br/>[[cyclic quadrilateral#Parameshvara's circumradius formula|Circumradius formula]]
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| notable works      = Drgganita<br/>Goladipika<br/>Grahanamandana
| occupation         = Astronomer-mathematician
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'''Vatasseri Parameshvara Nambudiri''' ({{abbr|c.|circa}} 1380–1460)<ref name="Pingree">{{cite book|last=David Edwin Pingree|title=Census of the exact sciences in Sanskrit|publisher=[[American Philosophical Society]]|date=1981|series=A|volume=4|pages=187–192|isbn=978-0-87169-213-9}}</ref>  was a major [[India]]n [[mathematician]] and [[astronomer]] of the [[Kerala school of astronomy and mathematics]] founded by [[Madhava of Sangamagrama]]. He was also an [[astrologer]]. Parameshvara was a proponent of [[observational astronomy]] in [[medieval India]] and he himself had made a series of [[eclipse]] observations to verify the accuracy of the computational methods then in use. Based on his eclipse observations, Parameshvara proposed several corrections to the astronomical parameters which had been in use since the times of [[Aryabhata]]. The computational scheme based on the revised set of parameters has come to be known as the ''Drgganita'' or [[Drig system]]. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.<ref name="Pingree"/>

==Biographical details==

Parameshvara was a [[Hindu]] of Bhrgu[[gotra]] following the [[Ashvalayana]]sutra of the [[Rigveda]]. Parameshvara's family name (''Illam'') was Vatasseri and his family resided in the village of Alathiyur (Sanskritised as ''Asvatthagrama'') in [[Tirur]], [[Kerala]]. Alathiyur is situated on the northern bank of the river [[Nila River|Nila]] (river [[Bharathappuzha]]) at its mouth in Kerala. He was a grandson of a disciple of [[Govinda Bhattathiri]] (1237–1295 CE), a legendary figure in the astrological traditions of [[Kerala]].

Parameshvara studied under teachers Rudra and Narayana, and also under [[Madhava of Sangamagrama]] (c. 1350 – c. 1425) the founder of the [[Kerala school of astronomy and mathematics]]. [[Damodara]], another prominent member of the [[Kerala school of astronomy and mathematics|Kerala school]], was his son and also his pupil. Parameshvara was also a teacher of [[Nilakantha Somayaji]] (1444–1544) the author of the celebrated [[Tantrasamgraha]].

==Work==
Parameshvara wrote commentaries on many mathematical and astronomical works such as those by [[Bhāskara I]] and [[Aryabhata]]. He made a series of  eclipse observations over a 55-year period. Constantly attempted to compare these with the theoretically computed positions of the planets. He revised planetary parameters based on his observations.

One of Parameshvara's more significant contributions was his [[Mean value theorem|mean value type formula]] for the inverse interpolation of the sine.<ref>Radha Charan Gupta [1979] "A mean-value-type formula for inverse interpolation of the sine", ''Ganita'' 30 (1–2): 78—82.</ref>

He was the first mathematician to give a formula for the [[radius]] of the [[circle]] circumscribing a cyclic quadrilateral.<ref>Radha Charan Gupta [1977] "Parameshvara's rule for the circumradius of a cyclic quadrilateral", ''Historia Mathematica'' 4: 67–74</ref> The expression is sometimes attributed to [[Lhuilier]] [1782], 350 years later. With the sides of the [[cyclic quadrilateral]] being ''a, b, c,'' and ''d'', the radius ''R'' of the circumscribed circle is:
:<math> R = \sqrt {\frac{(ab + cd)(ac + bd)(ad + bc)}{(- a + b + c + d)(a - b + c + d)(a + b - c + d)(a + b + c - d)}}.</math>

==Works by Parameshvara==
The following works of Parameshvara are well-known.<ref>{{cite journal|last=A.K. Bag|date=May 1980|title=Indian literature on mathematics during 1400–1800 AD|journal=[[Indian Journal of History of Science]]|volume=15|issue=1|pages=79–93|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af2_79.pdf|url-status=dead|archive-url=https://web.archive.org/web/20120309124530/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20005af2_79.pdf|archive-date=2012-03-09}}</ref> A complete list of all manuscripts attributed to Parameshvara is available in Pingree.<ref name="Pingree"/>

*''Bhatadipika'' – Commentary on [[Āryabhaṭīya]] of [[Āryabhaṭa I]]
*''Karmadipika'' – Commentary on ''Mahabhaskariya'' of Bhaskara I
*''Paramesvari''&nbsp;– Commentary on ''Laghubhaskariya'' of Bhaskara I
*''Sidhantadipika'' – Commentary on ''Mahabhaskariyabhashya'' of [[Govindasvāmi]]
*''Vivarana'' – Commentary on [[Surya Siddhanta]] and [[Lilāvati]]
*''Drgganita'' – Description of the [[Drig system]] (composed in 1431 CE)
*''Goladipika'' – Spherical geometry and astronomy (composed in 1443 CE)
*''Grahanamandana'' – Computation of eclipses (Its epoch is 15 July 1411 CE.)
*''Grahanavyakhyadipika'' – On the rationale of the theory of eclipses
*''Vakyakarana'' – Methods for the derivation of several astronomical tables

==See also==
*[[List of astronomers and mathematicians of the Kerala school]]

==References==
{{Reflist}}

==Further reading==
*[[David Pingree]], Biography in Dictionary of Scientific Biography (New York 1970–1990).
*Bhaskara, Laghubhaskariyam : With Parameshvara's commentary (Poona, 1946).
*Bhaskara, Mahabhaskariyam: With Parameshvara's commentary called Karmadipika (Poona, 1945).
*[[Muñjāla|Munjala]], Laghumanasam : with commentary by Parameshvara (Poona, 1944).
* [[T.A. Sarasvati Amma]] (1979) ''Geometry in ancient and medieval India'', (Delhi).
* K. Shankar Shukla (1957) ''The Surya-siddhanta with the commentary of Parameshvara'' (Lucknow).
* [[K. V. Sarma]] (2008), "Paramesvara", [[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}}.
* [[Kim Plofker]] (1996) "An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text", ''Historia Mathematica'' 23 (3): 246–256.
* K. K. Raja (1963) "Astronomy and mathematics in Kerala", ''Brahmavidya'' 27; 136–143.
* {{cite journal|last=K. Chandra Hari|date=2003|title=Eclipse observations of Parameshvara, the 14th–15th-century astronomer of Kerala|journal=Indian Journal of History of Science|volume=38|issue=1|pages=43–57|url=http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20008275_43.pdf|access-date=28 January 2010|url-status=dead|archive-url=https://web.archive.org/web/20120316082647/http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20008275_43.pdf|archive-date=16 March 2012}}

==External links==
* {{cite encyclopedia | editor = Thomas Hockey |display-editors=etal | last = Achar | first = Narahari | title=Parameśvara of Vāṭaśśeri &#91;Parmeśvara I&#93; | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | date = 2007 | location = New York | page = 870 | url=http://islamsci.mcgill.ca/RASI/BEA/Paramesvara_of_Vatesseri_BEA.htm | isbn=978-0-387-31022-0}} ([http://islamsci.mcgill.ca/RASI/BEA/Paramesvara_of_Vatesseri_BEA.pdf PDF version])
* {{MacTutor|Parameshvara}}

{{Kerala School}}
{{Indian mathematics}}
{{Scientific Research in Kerala |state=collapsed}}

{{Authority control}}

[[Category:1380s births]]
[[Category:1425 deaths]]
[[Category:Indian Hindus]]
[[Category:14th-century Indian mathematicians]]
[[Category:15th-century Indian astronomers]]
[[Category:Medieval Indian astrologers]]
[[Category:Kerala school of astronomy and mathematics]]
[[Category:15th-century Indian mathematicians]]
[[Category:14th-century astrologers]]
[[Category:15th-century astrologers]]
[[Category:Scientists from Kerala]]
[[Category:People from Malappuram district]]
[[Category:Scholars from Kerala]]