Kamalkara- The Famous Indian Mathematician About him Major works Contribution to the field of Mathemetics Facts about him

2. About Him
Kamalakara ,an Indian
astronomer and mathematician, came from a
learned family of scholars from Golagrama, a
village on the northern bank of the river Godavari.
His father was Nrsimha who was born in 1586.
Two of Kamalakara's three brothers were also
astronomer and mathematicians.
Divakara was born in 1606,was the eldest of the
brothers.
Ranganatha was the youngest of the three
brothers.
Kamalakara learnt astronomy from his elder

3. About Him [Cont…]
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 :-
“Hecombined traditionalIndianastronomywith
AristotelianphysicsandPtolemaicastronomyas
presented bysamicscientists(especiallyUlughBeg).
Followinghisfamily'straditionhewrotea
commentary, Manorama,onGanesa'sGrahalaghava
and,likehisfather,Nrsimha,anothercommentary on

4. Major Works
Kamalakara's major work,
"Siddhantatattvaviveka", was compiled
in Varanasi at about 1658 and has been
published by Sudhaka Dwivedi in the Varanasi
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, etc.
His other works include Sesavasana and
sauravasan. He was bitter opposed to

5. Major Works [Contd…]
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
The Siddhanta-tattva-viveka is a Sanskrit
text and in it Kamalakara makes frequent

6. Major Works [Contd...]
It is wrongly believed by some moderners
that Kamalakara 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 :
“uttaanapada-putro-asau medhibhooto dhruvo divi | sa hi bhraman
bhtaamayate nityam chandraadityau grahaih saha||”
The above text means that-'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'.
Kamalakara's contribution was to
rejuvenate this forgotten idea.

7. Contributions
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).

8. Contributions [Contd…]
According to David 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.
Kamalakara also gives a table
for finding the right ascension

9. Some Facts
He was a critic of Bhaskara and his
Siddhantasiromani and an arch-rival of
Munisvara, a close follower of Bhaskara.
His rivalry erupted into a bitter critiques
of the astronomical front.
He also wrote two other works related to
Siddhanta-Tattvaviveka, one a regular
commentary on the work, called
Tattvavivekodharana, and other a
supplement to that work called as
Sesavasana, in which he supplied
elucidations and new material for a proper
understanding of his new work.
He held the Suryasiddhanta in great