Brachistochrone Curve and Tautochrone Curve
Brachistochrone Curve
Brachistochrone curve 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.
Brachistochrone Curve Picture
Tautochrone Curve
Tautochrone curve 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.
Tautochrone Curve Video
Relation between Cycloid Curve and Brachistochrone Curve, Tautochrone Curve
Cycloid is both the brachistochrone curve and tautochrone curve.