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    Lemniscate

    Plot

    Plot

    Alternate names

    hyperbolic lemniscate | lemniscate of Bernoulli | lemniscus | pendant ribbon curve

    Equations

    x(t) = (a cos(t))/(sin^2(t) + 1) y(t) = (a sin(t) cos(t))/(sin^2(t) + 1)

    a^2 x^2 - a^2 y^2 - x^4 - 2 x^2 y^2 - y^4 = 0

    r(θ) = a sqrt(cos(2 θ))

    Properties

    algebraic | cissoid | closed | parametric | quartic

    Basic properties

    A = a^2

    s = (a Γ(1/4)^2)/sqrt(2 π)

    d = 4

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