contributions made by Bhaskara
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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 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. (See Calculus section below.)
In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.
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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 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. (See Calculus section below.)
In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.
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