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    Spiral

    Named curves

    Archimedean spiral | Archimedes' spiral | atom-spiral | Atzema spiral | circle involute | cochleoid | Cornu spiral | Doppler spiral | ellipse involute | Fermat spiral | Galilean spiral | hyperbolic spiral | lituus | logarithmic spiral | neoid | Nielsen spiral | Poinsot csch spiral | Poinsot sech spiral | tractrix spiral (total: 19)

    Example plots

    Example plots Archimedean spiral

    Example plots Archimedes' spiral

    Example plots Atom-spiral

    Alternate names

    arithmetic spiral

    atomic spiral

    Pritch-Atzema spiral

    cochlioid | oui-ja board curve | snail curve

    clothoid | Euler spiral | spiro

    Equations

    Archimedean spiral | x(t) = a t^(1/n) cos(t) y(t) = a t^(1/n) sin(t) Archimedes' spiral | x(t) = a t cos(t) y(t) = a t sin(t) atom-spiral | x(t) = (t cos(t))/(t - a) y(t) = (t sin(t))/(t - a) Atzema spiral | x(t) = a (-t sin(t) + sin(t)/t - 2 cos(t)) y(t) = a (-2 sin(t) + t cos(t) - cos(t)/t) circle involute | x(t) = a (t sin(t) + cos(t)) y(t) = a (sin(t) - t cos(t)) cochleoid | x(t) = a sinc(t) cos(t) y(t) = a sinc(t) sin(t) Cornu spiral | x(t) = a C(t) y(t) = a S(t) Doppler spiral | x(t) = a (k t + t cos(t)) y(t) = a t sin(t) ellipse involute | x(t) = a ((sqrt(2) b sin(t) E(t|1 - a^2/b^2))/sqrt((b^2 - a^2) cos(2 t) + a^2 + b^2) + cos(t)) y(t) = b (sin(t) - (sqrt(2) b cos(t) E(t|1 - a^2/b^2))/sqrt((b^2 - a^2) cos(2 t) + a^2 + b^2)) Fermat spiral | x(t) = a sqrt(t) cos(t) y(t) = a sqrt(t) sin(t) Galilean spiral | x(t) = cos(t) (b t^2 - a) y(t) = sin(t) (b t^2 - a) hyperbolic spiral | x(t) = (a cos(t))/t y(t) = (a sin(t))/t lituus | x(t) = (a cos(t))/sqrt(t) y(t) = (a sin(t))/sqrt(t) logarithmic spiral | x(t) = a e^(b t) cos(t) y(t) = a e^(b t) sin(t) neoid | x(t) = cos(t) (a t + b) y(t) = sin(t) (a t + b) Nielsen spiral | x(t) = a Ci(t) y(t) = a Si(t) Poinsot csch spiral | x(t) = a cos(t) csch(n t) y(t) = a sin(t) csch(n t) Poinsot sech spiral | x(t) = a cos(t) sech(n t) y(t) = a sin(t) sech(n t) tractrix spiral | x(t) = a cos(t) cos(t - tan(t)) y(t) = a cos(t) sin(t - tan(t))

    Fermat spiral | tan((x^2 + y^2)/a^2) = y/x hyperbolic spiral | y/x = tan(a/sqrt(x^2 + y^2))

    Archimedean spiral | r(θ) = a θ^(1/n) Archimedes' spiral | r(θ) = a θ atom-spiral | r(θ) = θ/(θ - a) cochleoid | r(θ) = a sinc(θ) Fermat spiral | r(θ) = a sqrt(θ) Galilean spiral | r(θ) = b θ^2 - a hyperbolic spiral | r(θ) = a/θ lituus | r(θ) = a/sqrt(θ) logarithmic spiral | r(θ) = a e^(b θ) neoid | r(θ) = a θ + b Poinsot csch spiral | r(θ) = a csch(θ n) Poinsot sech spiral | r(θ) = a sech(θ n)

    Common properties

    parametric | spiral

    Derived curves

    | evolute circle involute | circle ellipse involute | ellipse

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