Which brings us to Pythagoras, the ancient Ionian… or some geometer from India… or China . . or Mesopotamia. No matter: the equation a2 + b2 = c2 applies anytime, anywhere you want to know how many steps a shortcut will save you. Whatever the answer, the square root of C2 will always be less than if you take the long way around the corner AB. Every time.
This elegant formula has stood the test of time, an intellectual delight to some of the finest minds of the past three or four millennia, useful to kings, surely, for assessing taxes or building ziggurats or pyramids, to sailors on voyages of exploration, to generals constructing a catapult.
And with all that, there is also a kind of moral dimension. The formula provides a mathematical value to our choice of routes, a comparison between alternatives, between the energy and effort spent in taking one direction rather than another. To getting home sooner rather than later.
Seeking The Hypotenuse 