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    Limaçon

    Example plots

    Example plots

    Alternate names

    limaçon of Pascal | Pascal's snail | snail curve

    Equations

    x(t) = cos(t) (a cos(t) + b) y(t) = sin(t) (a cos(t) + b)

    a^2 x^2 - 2 a x^3 - 2 a x y^2 - b^2 x^2 - b^2 y^2 + x^4 + 2 x^2 y^2 + y^4 = 0

    r(θ) = a cos(θ) + b

    Properties

    algebraic | closed | loopy | oval | parametric | polar | quartic

    Basic properties

    A = 3/2 b sqrt(a^2 - b^2) + π (a^2/2 + b^2) - (a^2/2 + b^2) cos^(-1)(b/a)

    A^* = 1/2 π (a^2 + 2 b^2)

    s = 4 (a + b) E((4 a b)/(a + b)^2)

    d = 4

    Derived curves

    evolute | limaçon evolute

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