A proof that's so simple, it's almost as if the gods themselves had a hand in it.

Proof 3: The Pythagorean Theorem

Let a and b be the legs of a right triangle. Let c be the hypotenuse. Then, the sum of the squares of the legs is equal to the square of the hypotenuse. Or, in other words:

This is, of course, a fundamental theorem. But don't just take my word for it! You can easily verify it with some simple algebra:

Let a = 3 and b = 4. Then, the square of the hypotenuse is c² = 25. And indeed, 3² + 4² = 9 + 16 = 25. Ah, the gods are smiling upon us!

But, what about counterexamples, you ask? Oh, don't be so quick to jump the gun. We'll get to that later.

Next up: Proof 2, because 1 was clearly not enough.