|Born: about 1616 in Benares (now
Died: about 1700 in India Kamalakara was an
Indian astronomer and mathematician who came from a family of famous
astronomers. Kamalakara's father was Nrsimha who was born in 1586.
Two of Kamalakara's three brothers were also famous astronomer/
mathematicians, these being Divakara, who was the eldest of the
brothers born in 1606, and Ranganatha who was younger than
As was common throughout the classical period of
Indian mathematics, members of the family acted as teachers to other
family members. In particular Kamalakara was taught by his elder
brother Divakara while Divakara himself had been taught by their
uncle Siva. Pingree writes in :-
traditional Indian astronomy with Aristotelian physics and Ptolemaic
astronomy as presented by Islamic scientists (especially Ulugh Beg).
Following his family's tradition he wrote a commentary, Manorama, on
Ganesa's Grahalaghava and, like his father, Nrsimha, another
commentary on the Suryasiddhanta, called the Vasanabhasya ...
Kamalakara's most famous work, the Siddhanta-tattva-viveka, was
commented on by Kamalakara himself. The work was completed in 1658.
It is a work of fifteen chapters covering standard topics for Indian
astronomy texts at this time. 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"; and a final chapter which forms
The third chapter of the
Siddhanta-tattva-viveka contains some of the most interesting
mathematical results. In that chapter 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). See for example  and  for a discussion
of the details of Kamalakara's work in this area.
Siddhanta-tattva-viveka is a Sanskrit text and in it Kamalakara makes
frequent use of the place-value number system with Sanskrit numerals.
This and many other aspects of the work are discussed in .
Article by: J J O'Connor and E F Robertson