# Parameshvara

Parameshvara

Vatasseri Parameshvara (വടശ്ശേരി പരമേശ്വരന്‍) (1360-1425) was a major Indian mathematician of Madhava of Sangamagrama's Kerala school, as well as an astronomer and astrologer. He presented a series form of the sine function that is equivalent to its Taylor 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 by Bhaskara I and Aryabhatta.

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 of circle with inscribed cyclic 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 calculates to:

:$r^2 = frac\left\{x\right\}\left\{y\right\}$

where

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

and

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

ee also

*Indian mathematicians
*Mathematical analysis
*Calculus
*History of calculus
*Neelakanta Somayaji
*Achyuta Pisharati
*Melpathur Narayana Bhattathiri
*Achyuta Panikkar

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

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