Pythagoras' Proof

The Pythagorean theorem was known and used by the Babylonians, and the origin of the use of the 3-4-5 triangle to generate a right angle is lost in antiquity. Pythagoras is credited with the first recorded proof of the theorem that bears his name. Pythagoras' proof is by dissection. One of the things that I think is really cool about the theorem of Pythagoras is how it extends to three and more dimensions. Pythagoras' proof is for two dimensions of continuous (Euclidian) space.

Consider this figure of one square inscribed in another:

Write this equation for the area of the larger square:

(a + b)² = c² + 4(ab/2)

Condensing and expanding we have:

a² + 2ab + b² = c² + 2ab

Which reduces to:

c² = a² + b²

QED.

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