Baudhayana, an Indian mathematician, is credited with discovering the Pythagorean Theorem around 800 BCE, centuries before Pythagoras.

The Pythagorean Theorem is first mentioned in the Sulba Sutras, a collection of ancient Indian mathematical texts dating back to around 800-600 BCE.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

A Pythagorean triple is a set of three positive integers that satisfy the Pythagorean Theorem, i.e., a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides and c is the length of the hypotenuse.

(3, 4, 5) is the most famous Pythagorean triple because it is the smallest and most well-known.

The Pythagorean Theorem was used in ancient India for a variety of purposes, including constructing altars and temples, measuring land and property, and calculating the distance between two points.

The Pythagorean Theorem is one of the most important theorems in mathematics. It is the foundation of trigonometry and is used in many different branches of mathematics, including geometry, algebra, and calculus.

The Pythagorean Theorem can be proved using a variety of methods, including geometric proofs, algebraic proofs, and trigonometric proofs.

The Pythagorean Theorem has many applications in real life, including surveying, navigation, and architecture.

In Ancient India, the Pythagorean Theorem was known as Baudhayana's Theorem, named after the Indian mathematician Baudhayana who first discovered it.

In the Sulba Sutras, the Pythagorean Theorem was stated as 'The diagonal of a rectangle is equal to the sum of the squares of its sides.'

The Pythagorean Theorem was significant in ancient Indian architecture as it was used for various purposes, including constructing altars and temples with precise dimensions, designing buildings with strong and stable structures, and creating intricate patterns and designs.

Baudhayana provided a geometric proof for the Pythagorean Theorem in his Sulba Sutra, making him the first known mathematician to do so.

The Pythagorean Theorem had a profound influence on the development of mathematics in ancient India, leading to new mathematical concepts, advancements in geometry and trigonometry, and inspiring the study of mathematics as a formal discipline.

The Pythagorean Theorem continues to have a significant legacy in modern mathematics, serving as a fundamental theorem in geometry and trigonometry, finding applications in various branches of mathematics and science, and inspiring mathematicians and scientists to explore new mathematical concepts.