The Origin of Pythagorean theorem

The Pythagorean theorem takes its name from the ancient Greek mathematician Pythagoras (569 B.C.?-500 B.C.?), who was perhaps the first to offer a proof of the theorem. But people had noticed the special relationship between the sides of a right triangle long before Pythagoras.

The Pythagorean theorem states that the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypoteneuse, or, in mathematical terms, for the triangle shown at right, a² + b² = c². Integers that satisfy the conditions a² + b² = c² are called "Pythagorean triples." 

Ancient clay tablets from Babylonia indicate that the Babylonians in the second millennium B.C., 1000 years before Pythagoras, had rules for generatingPythagorean triples, understood the relationship between the sides of a right triangle, and, in solving for the hypoteneuse of an isosceles right triangle, came up with an approximation of accurate to five decimal places. [They needed to do so because the lengths would represent some multiple of the formula: 1² + 1² = ()².]

We do not know for sure how Pythagoras himself proved the theorem that bears his name because he refused to allow his teachings to be recorded in writing. But probably, like most ancient proofs of the Pythagorean theorem, it was geometrical in nature. That is, such proofs are demonstrations that the combined areas of squares with sides of length aand b will equal the area of a square with sides of length c, where a, b, andc represent the lengths of the two sides and hypoteneuse of a right triangle.