Vatasseri Parameshvara Nambudiri (c. 1380–1460)[1] was a majorIndianmathematician andastronomer of theKerala school of astronomy and mathematics founded byMadhava of Sangamagrama. He was also anastrologer. Parameshvara was a proponent ofobservational astronomy inmedieval India and he himself had made a series ofeclipse 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 ofAryabhata. The computational scheme based on the revised set of parameters has come to be known as theDrgganita orDrig system. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.^[1]

Parameshvara was aHindu of Bhrgugotra following theAshvalayanasutra of theRigveda. Parameshvara's family name (Illam) was Vatasseri and his family resided in the village of Alathiyur (Sanskritised asAsvatthagrama) inTirur,Kerala. Alathiyur is situated on the northern bank of the riverNila (riverBharathappuzha) at its mouth in Kerala. He was a grandson of a disciple ofGovinda Bhattathiri (1237–1295 CE), a legendary figure in the astrological traditions ofKerala.

Parameshvara studied under teachers Rudra and Narayana, and also underMadhava of Sangamagrama (c. 1350 – c. 1425) the founder of theKerala school of astronomy and mathematics.Damodara, another prominent member of theKerala school, was his son and also his pupil. Parameshvara was also a teacher ofNilakantha Somayaji (1444–1544) the author of the celebratedTantrasamgraha.

Parameshvara wrote commentaries on many mathematical and astronomical works such as those byBhāskara I andAryabhata. 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 hismean value type formula for the inverse interpolation of the sine.^[2]

He was the first mathematician to give a formula for theradius of thecircle circumscribing a cyclic quadrilateral.^[3] The expression is sometimes attributed toLhuilier [1782], 350 years later. With the sides of thecyclic quadrilateral beinga, b, c, andd, the radiusR of the circumscribed circle is:

${\displaystyle R=\sqrt{\frac{(ab+cd)(ac+bd)(ad+bc)}{(-a+b+c+d)(a-b+c+d)(a+b-c+d)(a+b+c-d)}}.}$

The following works of Parameshvara are well-known.^[4] A complete list of all manuscripts attributed to Parameshvara is available in Pingree.^[1]

• Bhatadipika – Commentary onĀryabhaṭīya ofĀryabhaṭa I
• Karmadipika – Commentary onMahabhaskariya of Bhaskara I
• Paramesvari – Commentary onLaghubhaskariya of Bhaskara I
• Sidhantadipika – Commentary onMahabhaskariyabhashya ofGovindasvāmi
• Vivarana – Commentary onSurya Siddhanta andLilāvati
• Drgganita – Description of theDrig 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

• List of astronomers and mathematicians of the Kerala school

• 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).
• 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 byHelaine 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.
• K. Chandra Hari (2003)."Eclipse observations of Parameshvara, the 14th–15th-century astronomer of Kerala"(PDF).Indian Journal of History of Science.38 (1):43–57. Archived fromthe original(PDF) on 16 March 2012. Retrieved28 January 2010.

Wikiquote has quotations related toParameshvara Nambudiri.

• Achar, Narahari (2007)."Parameśvara of Vāṭaśśeri [Parmeśvara I]". In Thomas Hockey; et al. (eds.).The Biographical Encyclopedia of Astronomers. New York: Springer. p. 870.ISBN 978-0-387-31022-0. (PDF version)
• O'Connor, John J.;Robertson, Edmund F.,"Parameshvara Nambudiri",MacTutor History of Mathematics Archive,University of St Andrews

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