MathematicsGeneralQuality 83 · Exceptional

The Pythagorean Theorem and Why It Works

@author · 2026-06-20 · v1

7 min read

In a right triangle,

a^2 + b^2 = c^2

. Rearranging four copies of the triangle into a large square proves it visually: the inner square has side

c

, and the four triangles plus the inner square fill a square of side

a+b

, so

c^2 = (a+b)^2 - 2(\frac{1}{2}ab) = a^2 + b^2

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