Parameshvara Nambudiri

Work

Parameshvara wrote commentaries on many mathematical and astronomical works such as those by Bhāskara I and Aryabhata. 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 his mean value type formula for the inverse interpolation of the sine.

He was the first mathematician to give a formula for the radius of the circle circumscribing a cyclic quadrilateral. The expression is sometimes 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:

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

Works by Parameshvara

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

• Bhatadipika – Commentary on Āryabhaṭīya of Āryabhaṭa I
• Karmadipika – Commentary on Mahabhaskariya of Bhaskara I
• Paramesvari – Commentary on Laghubhaskariya of Bhaskara I
• Sidhantadipika – Commentary on Mahabhaskariyabhashya of Govindasvāmi
• Vivarana – Commentary on Surya Siddhanta and Lilāvati
• Drgganita – Description of the Drig 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