Definition:Tautochrone

Definition
Let $A$ and $B$ be points in space that are neither on the same horizontal line nor on the same vertical line.

A tautochrone is the curve into which a wire is to be shaped so that a bead sliding down it (without friction) takes the same time to reach the lowest point independently of where on that wire it is released from rest.

Also see

 * Cycloid has Tautochrone Property

Also known as
The word isochrone can sometimes be seen, and means the same as tautochrone.