your moment of science-nerdiness

I first saw this video of Michael Stevens and Adam Savage a couple years back, and it fascinated me, partly because it deals with a physical law called the principle of least time:

The shape in question is called a brachistochrone, which is simply part of a cycloid (def. 6).  As you see in the above video, this shape allows a roller that rolls along its length to traverse the distance in the least amount of time.  This may seem counterintuitive at first:  you'd think that the fastest path would be a perfectly straight slope.  As it turns out, though, a straight slope forces the roller to waste time accelerating because it can't take advantage of gravity during the initial moments of the roll.  The brachistochrone, by contrast, dips more radically at the beginning, thus prompting quicker acceleration.  At the same time, the brachistochrone isn't so curved that it describes a too-lengthy pathway from A to B.  It's the perfect balance of several factors—length, acceleration, etc.—that allow a roller to go from A to B in the least amount of time.  Crazy stuff, but utterly fascinating.