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    Trisectrix

    Named curves

    Archimedes' spiral | cycloid of Ceva | quadratrix of Hippias | limaçon trisectrix | Maclaurin trisectrix | conchoid of Nicomedes | Tschirnhausen cubic (total: 7)

    Example plots

    Example plots Archimedes' spiral

    Example plots Cycloid of Ceva

    Example plots Quadratrix of Hippias

    Alternate names

    cycloidum anomalarum

    quadratix of Dinostratus

    cochloid

    Catalan trisectrix | l'Hôpital cubic

    Equations

    Archimedes' spiral | x(t) = a t cos(t) y(t) = a t sin(t) cycloid of Ceva | x(t) = a cos(t) (2 cos(2 t) + 1) y(t) = a sin(t) (2 cos(2 t) + 1) quadratrix of Hippias | x(t) = (2 a cos(t))/(π sinc(t)) y(t) = (2 a sin(t))/(π sinc(t)) limaçon trisectrix | x(t) = a cos(t) (2 cos(t) + 1) y(t) = a sin(t) (2 cos(t) + 1) Maclaurin trisectrix | x(t) = (a (t^2 - 3))/(t^2 + 1) y(t) = (a t (t^2 - 3))/(t^2 + 1) conchoid of Nicomedes | x(t) = cos(t) (a sec(t) + b) y(t) = sin(t) (a sec(t) + b) Tschirnhausen cubic | x(t) = a (1 - 3 t^2) y(t) = a t (3 - t^2)

    cycloid of Ceva | a^2 (y^2 - 3 x^2)^2 = (x^2 + y^2)^3 limaçon trisectrix | a^2 (3 x^2 - y^2) + (x^2 + y^2)^2 = 4 a x (x^2 + y^2) Maclaurin trisectrix | 3 a x^2 - a y^2 + x^3 + x y^2 = 0 conchoid of Nicomedes | b^2 x^2 = (x - a)^2 (x^2 + y^2) Tschirnhausen cubic | (a - x) (8 a + x)^2 = 27 a y^2

    Archimedes' spiral | r(θ) = a θ cycloid of Ceva | r(θ) = a (2 cos(2 θ) + 1) quadratrix of Hippias | r(θ) = (2 a)/(π sinc(θ)) limaçon trisectrix | r(θ) = a (2 cos(θ) + 1) Maclaurin trisectrix | r(θ) = a (-2 cos(2 θ) - 1) sec(θ) conchoid of Nicomedes | r(θ) = a sec(θ) + b Tschirnhausen cubic | r(θ) = a sec^3(θ/3)

    Common properties

    parametric | trisectrix

    Basic properties

    cycloid of Ceva | A = 3 π a^2 limaçon trisectrix | A = ((3 sqrt(3))/2 + 2 π) a^2

    cycloid of Ceva | s = a (-3 K(13/16) + 16 E(13/16) + 3 Π(1/4|13/16)) limaçon trisectrix | s = 12 a E(8/9)

    cycloid of Ceva | d = 6 limaçon trisectrix | d = 4 Maclaurin trisectrix | d = 3 conchoid of Nicomedes | d = 4 Tschirnhausen cubic | d = 3

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