Tautochrone curve
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
Tautochrone problem; Tautochrone; Tautochrone Problem; Abel's mechanical problem; Abel's integral equation; Abel integral equation; Abel problem; Isochrone curve; Isochronous curve; Tautochrone curves; Isochrone curves
A tautochrone or isochrone curve (from Greek prefixes [meaning same or iso-] 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 on the curve. The curve is a [[cycloid, and the time is equal to π times the square root of the radius (of the circle which generates the cycloid) over the acceleration of gravity.