- Parameshvara
**Vatasseri Parameshvara (വടശ്ശേരി പരമേശ്വരന്)**(1360-1425) was a majorIndia nmathematician ofMadhava of Sangamagrama 'sKerala school, as well as anastronomer andastrologer . He presented a series form of thesine function that is equivalent to itsTaylor series expansion.**Birth**Paramesvara was born into a

Hindu family who were astrologers and astronomers. The family home was Vatasseri (also called Vatasreni) in the village of Alattur, Kerala. Paramesvara's coordinates with respect to Ujjain puts it at latitude 10 51' north. It is on the north bank of the river Nila, at its mouth.**Work**Parameshvara's teachers included Rudra, Madhava and

Narayana Pundit .Parameshvara wrote many commentaries on many mathematical and astronomical works, such as those byBhaskara I andAryabhatta .He made 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.

Paramesvara most significant contributions is his mean value type formula for inverse interpolation of sine. He is the first mathematician to give the

radius ofcircle with inscribedcyclic quadrilateral , an expression that is normally attributed toLhuilier (1782), 350 years later. With the sides of the cyclic quadrilateral being a, b, c and d, the radius r of the circumscribed circle calculates to::$r^2\; =\; frac\{x\}\{y\}$

where

:$x\; =\; (ab\; +\; cd)\; (ac\; +\; bd)\; (ad\; +\; bc)\; ,$

and

:$y\; =\; (a\; +\; b\; +\; c\; -\; d)\; (b\; +\; c\; +\; d\; -\; a)\; (c\; +\; d\; +\; a\; -\; b)\; (d\; +\; a\; +\; b\; -\; c)\; ,$.

**ee also***

Indian mathematicians

*Mathematical analysis

*Calculus

*History of calculus

*Neelakanta Somayaji

*Jyeshtadeva

*Achyuta Pisharati

*Melpathur Narayana Bhattathiri

*Achyuta Panikkar **External links***http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Paramesvara.html

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