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| | Nice to meet you, my name is Ling and I completely dig that name. What she loves performing is taking part in croquet and she is trying to make it a profession. He presently life in Arizona and his parents live close by. His day job is a cashier and his salary has been really fulfilling.<br><br>Also visit my website; [http://Ysongs.com/profile.php?u=KaDimarco extended auto warranty] |
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| | birth_name =
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| | birth_date = c.1380 CE
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| | death_date = c.1460 CE
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| | resting_place_coordinates = <!-- {{coord|LAT|LONG|display=inline,title}} -->
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| | residence = Alathiyur, [[Tirur]] in [[Kerala]]
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| | nationality = [[India]]n
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| | ethnicity = [[Nambudiri]]
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| | known_for = Introducing the Drgganita system of astronomical computations
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| | notable works = Drgganita, Goladipika, Grahanamandana
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| | occupation = Astronomer-mathematician
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| | religion = [[Hindu]]
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| '''Vatasseri Parameshvara Nambudiri ([[Malayalam]]: വടശ്ശേരി പരമേശ്വരന്)''' (ca.1380–1460)<ref name="Pingree">{{cite book|last=David Edwin Pingree|title=Census of the exact sciences in Sanskrit|publisher=American Philosophical Society|year=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'' 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"/>
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| == Biographical details ==
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| Parameshvara was a [[Hindu]] of Bhrgu[[gotra]] following the [[Ashvalayana]]sutra of the Rgveda. Parameshvara's family name (''Illam'') was Vatasseri (also called Vatasreni) 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]].
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| Parameshvara studied under teachers Rudra and Narayana, and also under [[Sangamagrama Madhava]] (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]].
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| == Work ==
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| Parameshvara wrote commentaries on many mathematical and astronomical works such as those by [[Bhaskara I]] and [[Aryabhata]]. He made a series of eclipse observations over a 55 year period, and constantly attempted to compare these with the theoretically computed positions of the planets. He revised planetary parameters based on his observations.
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| Parameshvara's most significant contribution is his [[Mean value theorem|mean value type formula]] for the inverse interpolation of the sine. He was the first mathematician to give the [[radius]] of [[circle]] with an inscribed quadrilateral, an expression that is normally 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:
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| :<math> R = \sqrt {\frac{(ab + cd) (ac + bd) (ad + bc)}{(a + b + c - d) (b + c + d - a) (c + d + a - b) (d + a + b - c)}}.</math>
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| ==Works by Parameshvara==
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| 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}}</ref> A complete list of all manuscripts attributed to Parameshvara is available in Pingree.<ref name="Pingree"/>
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| *''Bhatadipika'' - Commentary on [[Āryabhaṭīya]] of [[Āryabhaṭa I]]
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| *''Karmadipika'' - Commentary on ''Mahabhaskariya'' of Bhaskara I
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| *''Paramesvari'' - Commentary on ''Laghubhaskariya'' of Bhaskara I
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| *''Sidhantadipika'' - Commentary on ''Mahabhaskariyabhashya'' of [[Govindasvāmi]]
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| *''Vivarana'' - Commentary on [[Surya Siddhanta]] and [[Lilāvati]]
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| *''Drgganita'' - Description of the ''Drk'' system (composed in 1431 CE)
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| *''Goladipika'' - Spherical geometry and astronomy (composed in 1443 CE)
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| *''Grahanamandana'' - Computation of eclipses (Its epoch is 15 July 1411 CE.)
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| *''Grahanavyakhyadipika'' - On the rationale of the theory of eclipses
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| *''Vakyakarana'' - Methods for the derivation of several astronomical tables
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| *[[David Pingree]], Biography in Dictionary of Scientific Biography (New York 1970-1990).
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| *Bhaskara, Laghubhaskariyam : With Parameshvara's commentary (Poona, 1946).
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| *Bhaskara, Mahabhaskariyam: With Parameshvara's commentary called Karmadipika (Poona, 1945).
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| *Munjala, Laghumanasam : with commentary by Parameshvara (Poona, 1944).
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| *[[T.A. Sarasvati Amma]], Geometry in ancient and medieval India (Delhi, 1979).
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| *K Shankar Shukla, The Surya-siddhanta with the commentary of Parameshvara (Lucknow, 1957).
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| *[[Radha Charan Gupta]], Parameshvara's rule for the circumradius of a cyclic quadrilateral, Historia Math. 4 (1977), 67-74.
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| *[[Radha Charan Gupta]], A mean-value-type formula for inverse interpolation of the sine, Ganita 30 (1-2) (1979), 78—82.
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| *K Plofker, An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text, Historia Math. 23 (3) (1996), 246-256.
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| *K K Raja, Astronomy and mathematics in Kerala, Brahmavidya 27 (1963), 136-143.
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| *{{cite journal|last=K. Chandra Hari|year=2003|title=Eclipse observations of Parameshvara, the 14 - 15 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|accessdate=28 January 2010}}
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| ==External links==
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| * {{cite encyclopedia | editor = Thomas Hockey et al | last = Achar | first = Narahari | title=Parameśvara of Vāṭaśśeri [Parmeśvara I] | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | year = 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])
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| *http://www-history.mcs.st-andrews.ac.uk/Biographies/Paramesvara.html
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| {{Indian mathematics}}
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| <!---->
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME =Parameshvara
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION =mathematician, astronomer
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| | DATE OF BIRTH =1380-00-00
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| | PLACE OF BIRTH =
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| | DATE OF DEATH =1425-00-00
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| | PLACE OF DEATH =
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| }}
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| [[Category:1380 births]]
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| [[Category:1425 deaths]]
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| [[Category:Indian Hindus]]
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| [[Category:Medieval Indian mathematicians]]
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| [[Category:14th-century mathematicians]]
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| [[Category:15th-century mathematicians]]
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| [[Category:15th-century astronomers]]
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| [[Category:Medieval Indian astronomers]]
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| [[Category:Medieval Indian astrologers]]
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| [[Category:Kerala school]]
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| [[Category:14th-century Indian people]]
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| [[Category:15th-century Indian people]]
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Nice to meet you, my name is Ling and I completely dig that name. What she loves performing is taking part in croquet and she is trying to make it a profession. He presently life in Arizona and his parents live close by. His day job is a cashier and his salary has been really fulfilling.
Also visit my website; extended auto warranty