Pythagorean 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 side opposite the right angle) equals the sum of the squares of the other two sides. This animation shows the hypotenuse rotating about its left point and so describing a smoothly changing right angled triangle. Each side of the triangle is extended to form its square. In this way, the areas change dynamically to give a feel of what is happening. The whole is rendered as an imaginary steampunk style engine in which brass framed windows of stained glass change size, driven by cog wheels.