Click flag. Drag the blue circles to adjust relative sizes. Notes played are proportional to a, b, and c. (There must be a better way to represent this theorem with music. Give it a shot). I hold "a" constant. Whatever the relative sizes, the sum of squares of sides a and b equals the square of side c. The sum of the two green squares on the left must have the same area as the large green square on the right. That's because the left half screen has the same four right triangles as seen on the right side of the screen, despite being in different positions.
Musical notes don't add much, as it is. I play 3 notes, one each for a, b, and c. (c squared is always so high relative to a squared that you can't hear both). Can you think of a better way to represent this theorem musically? I used lots of sprites with simple code, no sine or cosine: Separate sprites for each coordinate, and separate pens for each segment. Pens redraw constantly in case user is adjusting sizes. The square on the left side of the screen has the same 4 triangles as the square on the right side of the screen, but those triangles are in a different position. The idea of this visualization is old and fairly well-known (but I wish they shown us this when I was in school). The sum of squares theorem is often attributed to Pythagoras (hence called the "Pythagorean theorem"), although Bablylonians had hit upon the idea much earlier.
