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As well as being the solution to the brachistochrone problem, the cycloid has another property. Suppose that a cycloid is positioned as in the diagram for the brachistochrone problem. If a particle starts from rest at any point of the cycloid and travels along the curve under the force of gravity, the time it takes to reach the lowest point is independent of its starting point. So the cycloid is also called the tautochrone (from the Greek for ‘same time’).

Subjects: Mathematics.

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