Pythagoras Proof

Tap to rearrange. Hands-on: slide the triangles yourself to turn a² + b² into c².

In a right triangle, the two short sides a and b and the long side c always fit a rule: a² + b² = c². So a square drawn on the long side has the same area as the squares on the two short sides put together. It is named after Pythagoras, a Greek thinker of about 2,500 years ago, though people in Babylon knew it even earlier.

This is a rearrangement proof. Four copies of the triangle fill a big square, leaving two empty squares, a² and b². Tap it and the triangles slide into the corners, and the empty space becomes one tilted square, c², so a² + b² must equal c². Then they slide back.

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