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Trisectrix

Named curves

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

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

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)

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