Geometry has two great treasures: one is the theorem of Pythagoras; the other is the division of a line into an extreme and an average proportion. We may compare the first to a measure of gold; the second we may call a precious jewel. Jonannes Kepler (1596)The Pythagorean theorem, as Kepler (1596) says, is one of the greatest treasures of Geometry, it states that "in every right triangle the measure of the hypotenuse squared is equal to the sum of...