The brachistochrone problem was one of the earliest problems posed in the calculus of variations. |
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The brachistochrone is a cycloid, but that cycloid is not the only curve satisfying the equation. |
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Here one can see a graph of the brachistochrone for the given endpoint. |
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An inverted cycloid is the brachistochrone, that is the curve between two points in a vertical plane, along which a bead needs the shortest time to travel. |
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