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    Cycloid

    Plot

    Plot

    Alternate names

    brachistochrone curve | Helen of Geometers | tautochrone curve

    Equations

    x(t) = a (t - sin(t)) y(t) = a (1 - cos(t))

    abs(x/a - 2 π floor(x/(2 π a) + 1/2)) = cos^(-1)(1 - y/a) - sqrt((2 y)/a - y^2/a^2)

    Properties

    parametric | roulette

    Basic properties

    A = 3 π a^2

    Derived curves

    evolute | cycloid involute | cycloid

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