A cycloid hanging downwards.
Brachistochrone is a term from Greek meaning "shortest time." The
special property of a brachistochrone is the fact that a bead sliding
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