Pythagoras. It was proved by early Chinese mathematicians, fyi.
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The Persians discovered the theory long before Pythagoras, but Pythagoras made it well known and proved it many times. He got the idea from the Egyptian rope-stretchers, of which you can ask another question for them.
The value of "pi" was first calculated by Budhayana, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century long before the European mathematician.
Either Euclid or Pythagoras; Euclid being the "father of geometry," and Pythagoras having discovered possibly the most important geometrical relation. (The Pythagorean theorem)
There are infinitely many Pythagorean triples. To find a Pythagorean triple take two positive integers x, y with x > y. A Pythagorean triple is of the form x2 - y2, 2xy, x2 + y2.
You can use pythagorean theorem twice to find the diagonal of a cube