Indian Mathematics and Geometry

Aryabhata is considered the father of Indian mathematics due to his significant contributions to the field, including the development of the decimal system and the concept of zero.

Aryabhata developed the concept of the sine function, which is a fundamental trigonometric function used in various mathematical and scientific applications.

The Pythagorean theorem is a fundamental theorem in geometry that establishes the relationship between the sides of a right triangle.

Brahmagupta developed the concept of the Fibonacci sequence, a series of numbers in which each number is the sum of the two preceding ones.

The Sulba Sutras are a collection of ancient Indian mathematical texts that contain a detailed exposition of the Pythagorean theorem.

Bhaskara II developed the concept of the Pascal's triangle, a triangular array of binomial coefficients.

The Brahmasphuta Siddhanta is an Indian mathematical text that contains a systematic treatment of algebra, including the solution of quadratic equations and indeterminate equations.

Aryabhata developed the concept of the zero, which revolutionized mathematics and paved the way for the development of the decimal system.

Lilavati is an Indian mathematical text that contains a collection of mathematical problems and their solutions, covering various topics such as arithmetic, algebra, and geometry.

Brahmagupta developed the concept of the negative numbers, which expanded the scope of mathematical operations and allowed for the representation of quantities less than zero.

The Brahmasphuta Siddhanta contains a detailed exposition of the concept of infinity, including the idea of transfinite numbers and the concept of the infinite series.

Bhaskara II developed the concept of the calculus, including the ideas of differentiation and integration, centuries before their formal development in Europe.

The Aryabhatiya contains a systematic treatment of trigonometry, including the development of trigonometric functions and the derivation of trigonometric identities.

Brahmagupta developed the concept of the irrational numbers, which are numbers that cannot be expressed as a ratio of two integers.

The Brahmasphuta Siddhanta contains a detailed exposition of the concept of the golden ratio, a special number approximately equal to 1.618.