# Why is a cycloid path the fastest way to roll a ball downward? [duplicate]

Possible Duplicate:
Path to obtain the shortest traveling time

I've been told that if one would want to make a ramp to get a ball from point A to a lower point B (at a certain horizontal distance from A), the best shape to make this ramp in - by which I mean the ramp that makes the ball reach point B the fastest - would be a cycloid path. Why is this?

To simply explain the curve consider what it does. It allows the ball to drop first to pick up speed and then transitions to more horizontal motion to span the distance from A to B.