# MATHEMATICS IN MEDIEVAL INDIA: THE KERALA SCHOOL

__MATHEMATICS IN
MEDIEVAL INDIA: THE KERALA SCHOOL __

The south Indian state of Kerala located at the tip of the Indian peninsula is well known as a tourist destination. But it has more to offer than scenic beauty and exotic history. Its contribution to mathematics and astronomy is slowly being recognized amongst scholars around the world. Its greatest contribution to this field were between the fourteenth and seventeenth centuries .

Many of their contributions, preceded discoveries in European mathematics by almost 200 years

The most prominent mathematicians of the Kerala School and their works were:

Nilakantha's *Tantra
Samgraha*,

Jyesthadeva's *Yuktibhasa*,

Putumana Somayaji's *Karana Paddhati*

Sankara Varman' s *Sadratnamala* . * *

The Kerala schools contributions include:

The Gregory and Leibniz series for the inverse tangent,

The Leibniz power series for p,

Newton power series for the sine and cosine,

Rational approximations of trigonometric functions

**Madhavan
of Sangamagrama **(c. 1340-1425)

He
is credited to be the founder of the Kerala school. Though his work *Karana
Paddhati* was supposed to have been written between 1375 and 1475, it is
only through the works of later scholars we get to know him

Madhava's discoveries include

The Taylor series for the sine, cosine, tangent and arctangent functions;

The second-order and the third-order Taylor series approximations of the sine and cosine functions

The power
series of π, now known as the Madhava-Leibniz
series; Madhava correctly computed the value
of π to 9 decimal places^{}and 13 decimal
places, and produced sine and cosine tables to 9 decimal places of accuracy.^{}

### Narayanan Pandit

(1340-1400), His major works, are
arithmetical treatise called *Ganita Kaumudi* and an algebraic treatise
called *Bijganita Vatamsa*. His other work or *Karma-Paddhati *is a commentary of Bhaskara II’s
Lilavathi. Narayanan’s major works contain a variety of mathematical
developments and they are

A rule to calculate approximate values of square roots,

Investigations into the second order indeterminate equation *nq*^{2}
+ 1 = *p*^{2}

Solutions of indeterminate higher-order equations

Mathematical operations with zero

Geometrical rules and a discussion of
magic squares and similar figures.^{}

^{}

### Nilakanthan
Somayaji (1444-1555) was an
astronomer, but his *Aryabhatiya Bhasya* and *Tantra Samgraha*
contain work on infinite-series expansions, problems of algebra and spherical
geometry.

Nilakantha's most notable work
however was *Tantra Samgraha*. He
also wrote a commentary of ARYABHATIYA named *Aryabhatiya-bhashya*, His
most significant contribution has been the derivation and proof of the
Madhava-Gregory series for the arctangent trigonometric function where he used
inductive mathematical proofs. He also gave sophisticated explanations of the
irrationality of π, the correct formulation for the equation of the center of
the planets, and a heliocentric model of the solar system.

Jyesthadeva (c. 1500)

Jyesthadeva wrote, in the regional
language Malayalam and not Sanskrit. His
work *YUKTIBHASA *contained detailed derivations of many theorems
and formulae used in those times. . It contained most of the developments of
earlier Kerala School mathematicians, particularly from Madhava Jyesthadevan
also gave the earliest statement of Wallis theorem

The contributions of above mathematicians were two centuries before the invention of calculus in Europe. However, they did not formulate a systematic theory of differentiation and integration

Links

http://www-history.mcs.st-and.ac.uk/history/Biographies/Madhava.html

http://www-history.mcs.st-and.ac.uk/history/Biographies/Narayana.html

http://www-history.mcs.st-and.ac.uk/history/Biographies/Nilakantha.html

http://www-history.mcs.st-and.ac.uk/history/Biographies/Jyesthadeva.html

http://yuktibhasa.bestguide1.com/

http://www.nationmaster.com/encyclopedia/Yuktibhasa

http://india_resource.tripod.com/mathematics.htm

http://www.experiencefestival.com/history_of_calculus_-_controversy_newton_leibnitz_or_madhava

http://www-groups.dcs.st-andrews.ac.uk/~history/References/Madhava.html

http://www.jstor.org/pss/3620374

http://www.experiencefestival.com/indian_mathematician