The Great Brachistochrone Race
The Great Brachistochrone Race
Construct a smooth slide so that a particle can descend from one point to another positioned below it (but not directly below). The classic brachistochrone problem: what form should the slide take to minimize the time of descent?
Naively, one might think the answer is a straight line, but in fact, a straight slide is slower than many other curves; instead, the slide should be made in the shape of an arc of a cycloid.
Move the lower point around. When you've selected the point, animate the descent to show that the cycloid always wins the race against the straight line.