Pythagoras Proof

Splashery stretches a drumhead over this Splash's outline, twelve inches across, and finds the ways it can ring. Its lowest is 271.4 Hz, 64 cents sharp of C4, the nearest tine on the comb. The next fifteen are its overtones, and each one draws its own figure: sand gathers on the lines that stay still.

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.

Made in Splashery. Its code is MIT.

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