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