# Parameshvara

Parameshvara
Bornc. 1380 CE
Diedc. 1460 CE
ResidenceAlathiyur, Tirur in Kerala
NationalityIndian
OccupationAstronomer-mathematician
Known forDrig system
Notable work
Drgganita
Grahanamandana

Vatasseri Parameshvara Nambudiri (c. 1380–1460)[1] 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.[1]

## Biographical details

Parameshvara was a Hindu of Bhrgugotra following the Ashvalayanasutra of the Rgveda. Parameshvara's family name (Illam) was Vatasseri (also called Vatasreni) and his family resided in the village of Alathiyur (Sanskritised as Asvatthagrama) in Tirur, Kerala. Alathiyur is situated on the northern bank of the river Nila (river Bharathappuzha) at its mouth in Kerala. He was a grandson of a disciple of Govinda Bhattathiri (1237–1295 CE), a legendary figure in the astrological traditions of Kerala.

Parameshvara studied under teachers Rudra and Narayana, and also under Sangamagrama Madhava (c. 1350 – c. 1425) the founder of the Kerala school of astronomy and mathematics. Damodara, another prominent member of the Kerala school, was his son and also his pupil. Parameshvara was also a teacher of Nilakantha Somayaji (1444–1544) the author of the celebrated Tantrasamgraha.

## Work

Parameshvara wrote commentaries on many mathematical and astronomical works such as those by Bhaskara I and Aryabhata. He made a series of 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.

One of Parameshvara's more significant contributions was his mean value type formula for the inverse interpolation of the sine.[2]

He was the first mathematician to give the radius of circle with an inscribed quadrilateral.[3] 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:

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

## Works by Parameshvara

The following works of Parameshvara are well-known.[4] A complete list of all manuscripts attributed to Parameshvara is available in Pingree.[1]

• Bhatadipika – Commentary on Āryabhaṭīya of Āryabhaṭa I
• 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

## References

1. ^ a b c David Edwin Pingree (1981). Census of the exact sciences in Sanskrit. A. 4. American Philosophical Society. pp. 187–192. ISBN 978-0-87169-213-9.
2. ^ Radha Charan Gupta (1979) "A mean-value-type formula for inverse interpolation of the sine", Ganita 30 (1–2): 78—82.
3. ^ Radha Charan Gupta (1977) "Parameshvara's rule for the circumradius of a cyclic quadrilateral", Historia Mathematica 4: 67–74
4. ^ A.K. Bag (May 1980). "Indian literature on mathematics during 1400–1800 AD" (PDF). Indian Journal of History of Science. 15 (1): 79–93. Archived from the original (PDF) on 2012-03-09.