Cycloid as Brachistochrone


An inverted cycloid is the brachistochrone, that is the curve between two points in a vertical plane, along which a bead needs the shortest time to travel. Click on start to watch a race between a bead on an inverted cycloidal ramp and one on a linear ramp.

Animation



 
Source: http://www.f.waseda.jp/takezawa/mathenglish/geometry/cyclo/cyc/cyc.htm