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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.
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.
There are infinitely many triplets, and in general, they do not have a name. If all three are integers, then they are known as Pythagorean triplets.
You could show the pythogorean theorem. Use triangles and squares and prove it. You could also show its many uses...hope it helped
A triangular based pyramid has 4 vertices.