Pythagoras' Theorem Steampunk Mathematical Machine. Pythagoras' Theorem relates the lengths of the sides of a right-angled triangle and says that the square of the length of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides. The squares of the sides of the triangle are shown as coloured glass windows with brass frames. This image is a still taken from an animation which shows the hypotenuse rotating about its left point and so describing a series of right angled triangles. Steep perspective suggesting that the viewer is looking up at a giant semaphore.