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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

Also known as

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

Linguistic Note

The word tautochrone derives from the Greek tauto- meaning same, and chrono meaning time.