Brachistochrone

A cycloid hanging downwards.

Note: Brachistochrone is a term from Greek meaning "shortest time." The special property of a brachistochrone is the fact that a bead sliding down a brachistochrone-shaped frictionless wire will take a shorter time to reach the bottom than with a wire curved into any other shape. In addition, since a brachistochrone is also a tautochrone, the bead will take the same amount of time to reach the bottom no matter how high or low the release point.