Question

How was the Pythagoras theorem discovered?

Answer 1

Hint: The Babylonians had used the theorem in the second millennium. The Indian texts from 600-800 BC speak about the theorem. Ancient Egyptians have used the relation in constructing pyramids.

Complete step by step solution:
The Pythagorean theorem states that the number of the squares on a right triangle's legs equals the square on the hypotenuse or, in familiar algebraic notation,
\[{a^2} + {b^2} = {c^2}\]. The theorem has long been identified with Pythagoras (570–500/490 BCE), a Greek mathematician and philosopher, but it is actually much older.
The Babylonians had rules for producing Pythagorean triples in the second millennium B.C., 1000 years before Pythagoras, according to some ancient clay tablets from Babylonia. This relationship between the sides of a right-angled triangle was clear to them. They might also solve the hypotenuse of an isosceles right-angled triangle, arriving at a close estimate of up to five decimal places of the final value.
Several problems involving finding the length of one of the sides of a right triangle when given the other two sides are given, along with their solutions, in the Nine Chapters on Mathematical Procedures, compiled in the 1st century CE in China. Liu Hui provided a proof of the Pythagorean theorem in his Commentary from the third century.
The Pythagorean theorem was known to Indian mathematicians in ancient times, and they used the Sulbasutras (800-600 B.C.) to explain the theorem in the sense of strict criteria for the orientation, form, and area of altars for religious purposes.

Note: Since no texts written by Pythagoras have been found, we can't be sure if he was the first to discover this relationship between the sides of right triangles. In reality, we have no evidence that the man ever existed. However, the theorem \[{a^2} + {b^2} = {c^2}\] was named after him. Around 200 years later, another Greek, Euclid, wrote about the theorem in his book "Elements."