Kamalakara (1616 – 1700) was an Indian
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
and
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, came from a learned family of scholars from Golagrāma, a village situated in
Maharashtra
Maharashtra (; , abbr. MH or Maha) is a states and union territories of India, state in the western India, western peninsular region of India occupying a substantial portion of the Deccan Plateau. Maharashtra is the List of states and union te ...
State near Partha-puri (Pathari) on the northern bank of the river Godāvarī.
His father was Nrsimha who was born in 1586. 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.
Major works
Kamalākara's major work, "Siddhāntatattvaviveka", was compiled in
Varanasi
Varanasi (; ; also Banaras or Benares (; ), and Kashi.) is a city on the Ganges river in northern India that has a central place in the traditions of pilgrimage, death, and mourning in the Hindu world.
*
*
*
* The city has a syncretic t ...
at about 1658 and has been published by
Sudhakar Dwivedi
Sudhakara Dvivedi (1855–1910) was an Indian scholar in Sanskrit and mathematics.
Biography
Sudhakara Dvivedi was born in 1855 in Khajuri, a village near Varanasi. In childhood he studied mathematics under Pandit Devakrsna.
In 1883 he was appo ...
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
Munishvara
Munishvara or Munīśvara Viśvarūpa (born 1603) was an Indian mathematician who wrote several commentaries including one on astronomy ''Siddhanta Sarvabhauma'' (1646) which included descriptions of astronomical instruments such as the ''pratoda ...
, 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 Brahmananda Purana and Matsya Purana by sage Veda Vyaasa: ''"uttAnapAda-putro-asau meDhibhooto dhruvo divi , sa hi bhraman bhtaamayate nityam chandraadityau grahaiH saha , , "''. The meaning of this expression is "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.
Contribution
* He combined traditional Indian
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
with Aristotelian
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
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
David Pingree
David Edwin Pingree (January 2, 1933, New Haven, Connecticut – November 11, 2005, Providence, Rhode Island) was an American historian of mathematics in the ancient world. He was a University Professor and Professor of History of Mathematics ...
, he presents the only Sanskrit treatise on geometrical optics.
D Pingree, Biography in ''Dictionary of Scientific Biography'' (New York 1970–1990)
/ref>
* 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
Articles
* A K Bag, "Indian literature on mathematics during 1400–1800 A.D.", ''Indian J. Hist. Sci.'' 15 (1) (1980), 79–93.
* Radha Charan Gupta
Radha Charan Gupta (born 1935 in GursaraiJhansi, in present-day Uttar Pradesh) is an Indian historian of mathematics.
Early life of Radha Charan Gupta
Gupta graduated from the University of Lucknow, where he made his bachelor's degree in 1955 ...
, "Kamalakara's mathematics and construction of Kundas", ''Ganita Bharati'' 20 (1-4) (1998), 8–24.
* Radha Charan Gupta, "Addition and subtraction theorems for the sine and the cosine in medieval India", ''Indian J. History Sci.'' 9 (2) (1974), 164–177.
* Radha Charan Gupta, "Sines and cosines of multiple arcs as given by Kamalakara", ''Indian J. History Sci.'' 9 (2) (1974), 143–150.
* Radha Charan Gupta, "Sines of sub-multiple arcs as found in the Siddhanta-tattva-viveka", ''Ranchi Univ. Math. J.'' 5 (1974), 21–27.
* David Pingree
David Edwin Pingree (January 2, 1933, New Haven, Connecticut – November 11, 2005, Providence, Rhode Island) was an American historian of mathematics in the ancient world. He was a University Professor and Professor of History of Mathematics ...
, "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
* Golagrama, village in India associated with astronomers and mathematicians
* Dadhigrama, village in India associated with astronomers and mathematicians
* Jambusagaranagara, region in India associated with astronomers and mathematicians
Citations
References
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PDF version
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External links
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{{Authority control
1616 births
1700 deaths
17th-century Indian astronomers
17th-century Indian mathematicians
Scientists from Maharashtra
Scholars from Maharashtra
People from Maharashtra