Definition:Tautochrone
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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 a 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, which means the same as tautochrone.
Also see
- Results about tautochrones can be found here.
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