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.

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