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.
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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