Brachistochrone Problem

Classic Problem
The Brachistochrone problem was raised by to the readers of  in June 1696.

He published the solution in the same journal in May 1697.

Statement of Problem
Let a point $A$ be joined by a wire to a lower point $B$.

Let the wire be allowed to be bent into whatever shape is required.

Let a bead be released at $A$ to slide down without friction to $B$.

What is the shape of the wire so that the bead takes least time to descend from $A$ to $B$?

Also see

 * Brachistochrone is Cycloid


 * Definition:Brachistochrone
 * Definition:Tautochrone
 * Definition:Cycloid