Methods and Techniques Used by Indian Mathematicians

Indian mathematicians used various methods to solve quadratic equations, including completing the square, factorization, and using the quadratic formula.

The Sulba Sutras provide instructions for constructing triangles, squares, and circles, among other geometric shapes.

Aryabhata, a renowned mathematician and astronomer, is credited with introducing the concept of zero and the decimal system to the world.

Brahmagupta provided a recursive definition for the Fibonacci sequence in his work, making him the first mathematician to describe it.

Brahmagupta was the first mathematician to systematically develop and use negative numbers in calculations.

Bhaskara II made significant contributions to trigonometry, including developing formulas for sine, cosine, and tangent.

The Kerala School of Mathematics made significant contributions to calculus, including developing methods for finding derivatives and integrals.

Madhava of Sangamagrama developed a series expansion for the arctangent function, which is considered a precursor to modern calculus.

Brahmagupta developed a formula for calculating the area of a triangle using half of its base and height, known as Brahmagupta's formula.

Srinivasa Ramanujan made significant contributions to number theory, including developing new methods for studying prime numbers and modular forms.

Brahmagupta developed a method for solving indeterminate linear equations, known as Brahmagupta's method.

Pingala made significant contributions to combinatorics, including developing a method for counting the number of ways to arrange objects in a specific order.

Bhaskara II developed a geometric method for solving quadratic equations, known as the chakravala method.

Varahamihira made significant contributions to astronomy, including developing methods for calculating the positions of celestial bodies.

Bhaskara II developed a method for solving cubic equations, known as the Cardano-Tartaglia method.