Bhāskara II

Bhāskara II  (c. 1114–1185), also known as Bhāskarāchārya and as Bhāskara II to avoid confusion with Bhāskara I, was an Indian mathematician and astronomer. His main work Siddhānta-Śiromani, (Sanskrit for "Crown of Treatises") is divided into four parts called Līlāvatī, Bījagaṇita, Grahagaṇita and Golādhyāya which are also sometimes considered four independent works. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karaṇā Kautūhala.

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 cancelling out terms to get a² + b² = c².
• In Līlāvatī, solutions of quadratic, cubic and quartic indeterminate equations are explained.
• Solutions of indeterminate quadratic equations (of the type ax² + b = y²).
• The first general method for finding the solutions of the problem x² − ny² = 1 (so-called "Pell's equation") was given by Bhaskara II.
• Preliminary concept of mathematical analysis.
• Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.
• Calculated the derivatives of trigonometric functions and formulae.
• In Siddhanta-Śiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.