In mathematics, a brachistochrone curve (fromAncient Greekβράχιστος χρόνος (brakhistos khrónos), meaning "shortest time"), or curve of fastest descent, is the curve that would carry an idealized point-like body, starting at rest and moving along the curve, without friction, under constant gravity, to a given end point in the shortest time. For a given starting point, the brachistochrone curve is the same as the tautochrone curve.