Bhaskaracharya

Bhaskara (also known as Bhaskaracharya), (1114 - 1185), was an Indian mathematician and astronomer. He was born in Bijapur in modern Karnataka.

Bhaskara and his works represents a significant contribution to mathematical and astronomical knowledge in 12th century. He has been called the greatest mathematician of medieval India. His main work SIDDHANTHA SHIROMANI, (Sanskrit of "Crown of Treaties") is divided into  four parts called LILAVATI, BIJAGANITA, GRAHAGANITA and GOLADHYAYA, which are also sometimes considered four independent works. These four section deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treaties named KARANA KAUTUHALA.

Bhaskara's work on calculus predates Newton and Leibniz by over half a millennium. Hes is particularly known in the discovery of the principles of differential calculus and its application to astronomical prob;ems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.



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 quadratic and cubic indeterminate equation are explained.

• Solutions of indeterminate quadratic equations (of the type ax + b = y).

• Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules he gives are (in effect) the same as those given by the Renaissance European mathematicians of the 17th century

• A cyclic Chakravala method for solving indeterminate equations of the form ax + bx + c = y. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the chakravala method.

• The first general method for finding the solutions of the problem x − ny = 1 (so-called “Pell’s equation “)was given by Bhaskara II.

• Solutions of Diophantine Equations of the second order, such as 61x + 1 = y. This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat , but its solution was unknown in Europe until the time of Euler in the 18th century.

• Solved quadratic equations with more than one unknown, and found negative and irrational i solutions.

• Preliminary concept of mathematical analysis.

• Preliminary concept of infinitesimal Calculus, along with notable contributions towards integral calculus .
• Conceived differential calculus, after discovering the derivative and differential coefficient.

• Stated Roll’s theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.

• Calculated the derivatives of trigonometric functions and formulae.

• In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.