Parameshvara

Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He was also an astrologer. Parameshvara was a proponent of observational astronomy in medieval India and he himself had made a series of eclipse 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 of Aryabhata. The computational scheme based on the revised set of parameters has come to be known as the Drgganita or Drig system. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.

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 , 350 years later. With the sides of the cyclic quadrilateral being a, b, c, and d, the radius R of the circumscribed circle is:

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