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    Cardioid

    Plot

    Plot

    Alternate name

    cardioide

    Equations

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

    (a x + x^2 + y^2)^2 = a^2 (x^2 + y^2)

    r(θ) = a (1 - cos(θ))

    Properties

    algebraic | closed | heart | parametric | polar | quartic | roulette

    Basic properties

    A = (3 π a^2)/2

    s = 8 a

    d = 4

    Derived curves

    evolute | cardioid involute | cardioid

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