Tautochrone Problem

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 it takes same time to descend to $B$ from wherever you release the bead between $A$ and $B$?

Also see

 * Cycloid has Tautochrone Property


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