Brachistochrone Curve

A Brachistochrone curve (Gr. βράχιστος, brachistos - the shortest, χρόνος, chronos - time), or curve of fastest descent, is the curve between two points that is covered in the least time by a point-like body that starts at the first point with zero speed and is constrained to move along the curve to the second point, under the action of constant gravity and assuming no friction.