Parameshvara: Encyclopedia II - Parameshvara - Work

Parameshvara - 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:

r2 = 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).

Adapted from the Wikipedia article "Work", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki