The Pythagorean theorem relates the sides of a right triangle: the square of the hypotenuse equals the sum of squares of the other two sides.
Babylonian tablets predating Pythagoras show the relationship was known empirically. Euclid gave the first rigorous proof in his Elements around 300 BCE.
Why it matters
Every distance on a flat map, every diagonal brace in a roof, and every GPS triangulation uses this identity. It is the bridge between algebra and geometry.
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