A
tautochrone or
isochrone curve (from Greek prefixes meaning
same or
equal, and
time) is the curve for which the time taken by an object sliding without friction in uniform
gravity to its lowest point is independent of its starting point. The curve is a
cycloid, and the time is equal to
p times the
square root of the radius over the acceleration of gravity. The tautochrone curve is the same as the
brachistochrone curve for any given starting point.