# 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 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.