Tautochrone

A cycloid hanging downwards.

Note: Tautochrone is a term from Greek meaning "the same time." The special property of a tautochrone is the fact that a bead sliding down a tautochrone-shaped frictionless wire will take the same amount of time to reach the bottom no matter how high or low the release point. In fact, since a tautochrone is also a brachistochrone, the bead will take the shortest possible time to reach the bottom out of all possible shapes of the wire.

Movie clip

Tautochrone--sliding beads on a cycloid (257K)