Madhava

Madhava (1350-1425) was born in town of Irinjalakkuda, near Cochin, Kerala was at the time known as Sangamagrama has major mathematician of the Kerala school who is considered the father of mathematical analysis for having taken the decisive step from the finite procedures of ancient mathematics to treat to their limit-passage to infinity, which is the kernel of modern classical analysis.He is the first to have developed infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity". His discoveries opened the doors to what has today come to be known as mathematical analysis.

One of the greatest mathematician-astronomers of the Middle Ages, Madhava contributed to infinite series, calculus, trigonometry, geometry and algebra.

The following presents a summary of results that have been attributed to Madhava by various scholars.

Infinite series
He discovered the infinite series for the trigonometric functions of sine, cosine, tangent and arctangent, and many methods for calculating the circumference of a circle.

Trigonometry
Madhava also gave a most accurate table of sines, defined in terms of the values of the half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle.

Algebra
Madhava also carried out investigations into other series for arclengths and the associated approximations to rational fractions of ð, found methods of polynomial expansion, discovered tests of convergence of infinite series, and the analysis of infinite continued fractions.He also discovered the solutions of transcendental equations by iteration, and found the approximation of transcendental numbers by continued fractions.

Calculus, Geometry

Madhava has been called "the greatest mathematician-astronomer of medieval India".

Courtesy : Internet