# World’s Super Scientists – Bhaskara II

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Scientist Bhaskara II was born in a place near Bijapur (district, Karnataka state, South India) into the Deshastha Brahmin family and became head of the astronomical observatory at Ujjain.

In many ways, Scientist Bhaskara represents the peak of mathematical and astronomical knowledge in the 12th century A.D.

Lilavati written on the name of his daughter, the Persian translation of which states : Bhaskara II studied Lilavati’s horoscope and predicted that her husband would die soon after the marriage ; it turned out to be true.

Scientist Bhaskara II Contribution to Mathematics

• a proof of the Pythagorean theorem a2 + b2 = c2
• a cyclic chakravala method for solving indeterminate quadratic equations in the form ax2+bx+c = y; ax2+b=y2
• he conceived the concept of differential calculus.

Bhaskara’s arithmetic text Lilavati covers : arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon (shanku-chhAyA, see Aryabhatta), methods to solve indeterminate equations, and combinations.

Lilavati is divided into 13 chapters.

Mathematician Bhaskara’s method of solving indeterminate equations (Kuttaka), integer solutions (first and second order) was an improvement of the methods found in the work of Aryabhatta and subsequent mathematicians.

Scientist Bhaskara II Bijaganita (“Algebra”) was a work in 12 chapters. a cyclic chakravala method for solving indeterminate quadratic equations of the form ax2 + bx + c = y

Mathematician Bhaskara’s method for finding the solutions of the problem

Nx2 + 1 = y2 (the so-called “Pell’s equation”) is of considerable importance. Trigonometry

The Siddhanta Shiromani (written in 1150 AD)

• sin (a + b) = sin(a) cos(b) + cos(a) sin(b)
• sin (a – b) = sin(a) cos(b) – cos(a) sin(b)

Siddhanta Shiromani

Contains chapters on differential calculus, and integral calculus.

Early interpretation of Rolle’s theorem in the works of Bhaskara II

• If f(a) = f(b) = 0 then f'(x) = 0 for some x with a < x < b.

In the Surya Siddhant he makes a reference to ‘gravity’ which he discovered 500 years before Newton.

In computing the instantaneous motion of a planet, the time interval between successive positions of the planets wasno greater than a truth, or a 1/33750  of a second, an infinitesimal unit of time [Cf. Francis Crick].

Studies on astronomy in Scientist Bhaskara’s works were based on the heliocentric (with the sun as the centre) solar system of gravitation propounded earlier by Aryabhatta (499 AD), where the planets follow an elliptical orbit around the Sun.

One contribution is his accurate calculation of the sidereal (related to the stars that are far away, not the sun or planets) year, the time taken for the Earth to orbit the Sun, 365.2588 days. The modern accepted measurement is 365.2596 days.

Scientist Bhaskara II mathematical astronomy text Siddhanta Shiromani :

first part     :  mathematical astronomy – 12chapters

second part :  on the sphere – 13 chapters Influence

Scientist Bhaskara II achievements catapulted him to fame, name and immortality.Bhaskara’s works influenced later developments in the Middle East and Europe. This was known by the end of the 12th century.

The Mughal Emperor Akbar commissioned a famous Persian translation of the Lilavati in 1587.

Mathru Devo Bhava

Pithru Devo Bhava

Acharya Devo Bhava

Atidhi Devo Bhava

Rogi Devo Bhava

-Dr. O.A.. Sarma

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