# Tautochrone Problem

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Let a marble roll down a curved slope. In a tautochrone (curve of equal descent), the marble reaches the bottom in the same amount of time no matter where it starts. In a brachistochrone (curve of fastest descent), the marble reaches the bottom in the fastest time. Jakob Bernoulli solved the tautochrone problem in a paper marking the first usage (1690) of an integral. The cycloid is the solution to *both* problems. His brother Johann posed the brachistochrone problem in 1696. Newton, Leibniz, L'Hôpital, and Jakob Bernoulli sent in solutions.

Contributed by: Ed Pegg Jr (March 2011)

Based on a program by: Eric W. Weisstein

Open content licensed under CC BY-NC-SA

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"Tautochrone Problem"

http://demonstrations.wolfram.com/TautochroneProblem/

Wolfram Demonstrations Project

Published: March 7 2011