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Kamalakara (1616-1700), an Indian astronomer and mathematician, came from a learned family of scholars from Golagrāma, a village on the northern bank of the river Godāvarī. His father was Nrsimha who was born in 1586.[1] Two of Kamalakara's three brothers were also astronomer and mathematicians: Divakara, who was the eldest of the brothers born in 1606, and Ranganatha who was youngest. Kamalākara learnt astronomy from his elder brother Divākara, who compiled five works on astronomy. His family later moved to Vārāṇasī.[2]

Major works

Kamalākara's major work, Siddhāntatattvaviveka, was compiled in Vārāṇasī at about 1658 and has been published by Sudhākara Dvivedi in the Vārāṇasī series. This work consists of 13 chapters in 3,024 verses. It deals with the topics of: units of time measurement; mean motions of the planets; true longitudes of the planets; the three problems of diurnal rotation; diameters and distances of the planets; the earth's shadow; the moon's crescent; risings and settings; syzygies; lunar eclipses, solar eclipses; planetary transits across the sun's disk; the patas of the moon and sun; the "great problems"; along a conclusion. His other works include Śeṣavāsanā and Sauravāsanā.Kamalākara was bitterly opposed to Munīśvara, the author of Siddhāntasārvabhauma.

It is wrongly believed by some moderners that Kamalākara discovered the idea that the pole star we see at present is not exactly at the pole. But this ideas was first expressed in Brahmaanda Purana and Matsya Purana by sage Veda Vyaasa :

"uttAnapAda-putro-asau meDhibhooto dhruvo divi | sa hi bhraman bhtaamayate nityam chandraadityau grahaiH saha||"

'Uttanapada's son Dhruva is fixed like a pole in the Heaven, but it is moving itself and is making all the planets together with Sun and Moon move'.

Kamalākara's contribution was to rejuvenate this forgotten idea.

He combined traditional Indian astronomy with Aristotelian physics and Ptolemaic astronomy as presented by Islamic scientists.
In the third chapter of the Siddhanta-tattva-viveka Kamalakara used the addition and subtraction theorems for the sine and the cosine to give trigonometric formulae for the sines and cosines of double, triple, quadruple and quintuple angles. In particular he gives formulae for sin(A/2) and sin(A/4) in terms of sin(A) and iterative formulae for sin(A/3) and sin(A/5).
According to D. Pingree, he presents the only Sanskrit treatise on geometrical optics.D Pingree, Biography in Dictionary of Scientific Biography (New York 1970-1990)
He has assumed a value of 60 units for the radius of the Earth and gives values for sines at 1° intervals.
Kamalākara also gives a table for finding the right ascension of a planet from its longitude


A K Bag, Indian literature on mathematics during 1400-1800 A.D., Indian J. Hist. Sci. 15 (1) (1980), 79-93.
R C Gupta, Kamalakara's mathematics and construction of Kundas, Ganita Bharati 20 (1-4) (1998), 8-24.
R C Gupta, Addition and subtraction theorems for the sine and the cosine in medieval India, Indian J. History Sci. 9 (2) (1974), 164-177.
R C Gupta, Sines and cosines of multiple arcs as given by Kamalakara, Indian J. History Sci. 9 (2) (1974), 143-150.
R C Gupta, Sines of sub-multiple arcs as found in the Siddhanta-tattva-viveka, Ranchi Univ. Math. J. 5 (1974), 21-27.
D Pingree, Islamic astronomy in Sanskrit, J. Hist. Arabic Sci. 2 (2) (1978), 315-330; 425.
A N Singh, Hindu trigonometry, Proc. Benares Math. Soc. 1 (1939), 77-92.

See also



^ "Biography of Kamalakara".
^ Achar 2007.


Achar, Narahari (2007). "Kamalākara". In Thomas Hockey et al. The Biographical Encyclopedia of Astronomers. New York: Springer. p. 609. ISBN 9780387310220. (PDF version)
G G Joseph (1991). "Mathematics in India". The crest of the peacock. London.
Dvivedi, Sudhakar (1935). The Siddhantatattvaviveka of Kamalakara. Benares.

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