Vatasseri Paramesvara
Born c.1380 CE

Died c.1460 CE

Residence Alattur, near Tirur in Kerala
Nationality Indian
Ethnicity Namputiri
Occupation Astronomer-mathematician
Notable works Drgganita, Goladipika, Grahanamandana
Known for Introducing the Drgganita system of astronomical computations
Religion Hindu

Vatasseri Paramesvara (Malayalam: വടശ്ശേരി പരമേശ്വരന്‍) (ca.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. Paramesvara 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, Paramesvara 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 system. Paramesvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Paramesvara.[1]

Biographical details

Paramesvara was a Namputiri Brahmin of Bhrgugotra following the Ashvalayanasutra of the Rgveda. Paramesvara's family name (Illam) was Vatasseri (also called Vatasreni) and his family resided in in the village of Alattur (Sanskritised as Asvatthagrama) in Kerala. Alattur is situated on the northern bank of the river Nila (river Bharathappuzha) at its mouth in Kerala.

Paramesvara 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. Paramesvara 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 Aryabhatta. 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.

Paramesvara's most significant contribution 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:

where

and

.

Works by Paramesvara

The following works of Paramesvara are well-known.[2] A complete list of all manuscripts attributed to Paramesvara is available in Pingree.[1]

• Bhatadipika - Commentary on Aryabhatiya of Aryabhata I
• Karmadipika - Commentary on Mahabhaskariya of Bhaskara I
• Paramesvari - Commentary on Laghubhaskariya of Bhaskara I
• Sidhantadipika - Commentary on Mahabhaskariyabhashya of Govindasvami
• Vivarana - Commentary on Suryasidhanta and Lilavati
• Drgganita - Description of the Drk 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

Further reading

• D Pingree, Biography in Dictionary of Scientific Biography (New York 1970-1990).
• Bhaskara, Laghubhaskariyam : With Paramesvara's commentary (Poona, 1946).
• Bhaskara, Mahabhaskariyam: With Paramesvara's commentary called Karmadipika (Poona, 1945).
• Munjala, Laghumanasam : with commentary by Paramesvara (Poona, 1944).
• T A Sarasvati Amma, Geometry in ancient and medieval India (Delhi, 1979).
• K Shankar Shukla, The Surya-siddhanta with the commentary of Paramesvara (Lucknow, 1957).
• R C Gupta, Paramesvara's rule for the circumradius of a cyclic quadrilateral, Historia Math. 4 (1977), 67-74.
• R C Gupta, A mean-value-type formula for inverse interpolation of the sine, Ganita 30 (1-2) (1979), 78--82.
• K Plofker, An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text, Historia Math. 23 (3) (1996), 246-256.
• K K Raja, Astronomy and mathematics in Kerala, Brahmavidya 27 (1963), 136-143.
• K. Chandra Hari (2003). "Eclipse observations of Paramesvara, the 14 - 15 century astronomer of Kerala". Indian Journal of History of Science 38 (1): 43 - 57. http://www.new.dli.ernet.in/rawdataupload/upload/insa/INSA_1/20008275_43.pdf. Retrieved 28 January 2010. 

External links

• http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Paramesvara.html

Indian mathematics
Mathematicians


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Influenced