A cycloid hanging downwards.
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