Bhaskarachārya was an Indian mathematician and astronomer who extended Brahmagupta's work on number systems. He was born near Bijjada Bida

Bhaskara (1114 – 1185) (also known as Bhaskara II and Bhaskarachārya
Bhaskaracharya's work in Algebra, Arithmetic and Geometry catapulted him to fame and immortality. His renowned mathematical works called Lilavati" and Bijaganita are considered to be unparalleled and a memorial to his profound intelligence. I. In his treatise Siddhant Shiromani he writes on planetary positions, eclipses, cosmography, mathematical techniques and astronomical equipment. In the Surya Siddhant he makes a note on the force of gravity:
"Objects fall on earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon, and sun are held in orbit due to this attraction."
Bhaskaracharya was the first to discover gravity, 500 years before Sir Isaac Newton. He was the champion among mathematicians of ancient and medieval India . His works fired the imagination of Persian and European scholars, who through research on his works earned fame and popularity.
Some of Bhaskara's contributions to mathematics include the following:
A proof of the Pythagorean Theorem by calculating the same area in two different ways and then canceling out terms to get a + b = c.
In Lilavati, solutions of quadric , cubic and quartic indeterminate equation are explained.
Solutions of indeterminate quad
ratic equations (of the type ax + b = y)
Arithmetic Edit
Bhaskara's arithmetic text Leelavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, methods to solve indeterminate equations, and combinations.
Lilavati is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and measurement. More specifically the contents include:
Definitions.
Properties of zero (including division, and rules of operations with zero).
Further extensive numerical work, including use of negative numbers and surds.
Estimation of π.
Arithmetical terms, methods of multiplication, and squaring.
Inverse rule of three, and rules of 3, 5, 7, 9, and 11.
Problems involving interest and interest computation.
Indeterminate equations (Kuṭṭaka), integer solutions (first and second order). His contributions to this topic are particularly important,[citation needed] since the rules he gives are (in effect) the same as those given by the renaissance European mathematicians of the 17th century, yet his work was of the 12th century. Bhaskara's method of solving was an improvement of the methods found in the work of Arya
Definitions.
Properties of zero (including division, and rules of operations with zero).
Further extensive numerical work, including use of negative numbers and surds.
Estimation of π.
Arithmetical terms, methods of multiplication, and squaring.
Inverse rule of three, and rules of 3, 5, 7, 9, and 11.
Problems involving interest and interest computation.
Indeterminate equations (Kuṭṭaka), integer solutions (first and second order). His contributions to this topic are particularly important,[citation needed] since the rules he gives are (in effect) the same as those given by the renaissance European mathematicians of the 17th century, yet his work was of the 12th century. Bhaskara's method of solving was an improvement of the methods found in the work of Aryabhata and subsequent mathematicians.
His work is outstanding for its systemisation, improved methods and the new topics that he has introduced. Furthermore, the Lilavati contained excellent recreative problems and it is thought that Bhaskara's intention may have
Algebra Edit
His Bijaganita ("Algebra") was a work in twelve chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root).[15] His work Bijaganita is effectively a treatise on algebra and contains the following topics:
Positive and negative numbers.
Zero.
The 'unknown' (includes determining unknown quantities).
Determining unknown quantities.
Indeterminate quadratic equations (of the type ax2 + b = y2).
Solutions of indeterminate equations of the second, third and fourth degree.
Quadratic equations.
Quadratic equations with more than one unknown.
Operations with products of several unknowns.
Bhaskara derived a cyclic, chakravala method for solving indeterminate quadratic equations of the form ax2 + bx + c = y.[15] Bhaskara's method for finding the solutions of the problem Nx2 + 1 = y2 (the so-called "Pell's equation") is of considerable importance.[13]
Trigonometry Edit
The Siddhānta Shiromani (written in 1150) demonstrates Bhaskara's knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also discovered spherical trigonometry, along with other interesting trigonometrical results. In particular Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhaskara, discoveries first found in his works include computation of sines of angles of 18 and 36 degrees, and the now well known formulae for {\displaystyle \sin \left(a+b\right)} and {\displaystyle \sin \left(a-b\right)}.
Calculus Edit
Evidence suggests Bhaskara was acquainted with some ideas of differential calculus.
There is evidence of an early form of Rolle's theorem in his work
If {\displaystyle f\left(a\right)=f\left(b\right)=0} then {\displaystyle f'\left(x\right)=0} for some {\displaystyle \ x} with {\displaystyle \ a<x<b}
He gave the result that if {\displaystyle x\approx y} then {\displaystyle \sin(y)-\sin(x)\approx (y-x)\cos(y)}, thereby finding the derivative of sine, although he never developed the notion of derivatives.[17]
Arithmetic Edit
Bhaskara's arithmetic text Leelavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, methods to solve indeterminate equations, and combinations.
Definitions.
Properties of zero (including division, and rules of operations with zero).
Further extensive numerical work, including use of negative numbers and surds.
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