Parameśvara

Parameśvara (1380-1460 CE) was a major Indian mathematician and astronomer of the Kerala school of astronomy and mathematics founded by Mādhava of Saṅgamagrāma. Parameśvara was born into a Namputiri Brahmana family who were astrologers and astronomers. He played an important part in the remarkable developments in Mathematics which took place in Kerala in the late 14th and early part of the 15th century. Āryabhaṭa gave a rule for determining the height of a pole from the lengths of its shadows in the Āryabhaṭīya. Parameśvara gave several illustrative examples of the method in his commentary on the Āryabhaṭīya.

Parameśvara is known to have been a pupil of Narayana Pandit, and also Madhava of Sangamagramma, who is thought to have been a significant influence.

Parameśvara proposed several corrections to the astronomical parameters which had been in use since the times of Āryabhaṭa based on his eclipse observations. The computational scheme based on the revised set of parameters is known as Dṛk system. Dṛggaṇita is the text composed based on this system.

The expression for the radius of the circle in which a cyclic quadrilateral is inscribed, given in terms of the sides of the quadrilateral, is usually attributed to Lhuilier in 1782. However Paramesvara described the rule 350 years earlier. If the sides of the cyclic quadrilateral are a, b, c and d then the radius r of the circumscribed circle was given by Parameśvara as:

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)

His works are mentioned below.


 * Bhaṭadīpikā – Commentary on Āryabhaṭīya of Āryabhaṭa I
 * Karmadīpikā – Commentary on Mahābhāskarīya of Bhāskara I
 * Paramesvarī – Commentary on Laghubhāskarīya of Bhāskara I
 * Sidhantadīpikā – Commentary on Mahābhāskarīyabhāshya of Govindasvāmi
 * Vivarana – Commentary on Surya Siddhānta and Līlāvatī
 * Dṛggaṇita – Description of the Dṛk system (composed in 1431 CE)
 * Goladīpikā – Spherical geometry and astronomy (composed in 1443 CE)
 * Grahaṇamaṇḍana – Computation of eclipses (Its epoch is 15 July 1411 CE.)
 * Grahaṇavyakhyādīpikā – On the rationale of the theory of eclipses
 * Vākyakaraṇa – Methods for the derivation of several astronomical tables