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.

Linguistic Note

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

Sources

• 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{V}$: "Greatness and Misery of Man"
• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 6$: The Brachistochrone. Fermat and the Bernoullis: Problem $2$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.17$: Huygens ($\text {1629}$ – $\text {1695}$)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): isochrone (tautochrone)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): tautochrone
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): isochrone (tautochrone)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): tautochrone
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): tautochrone