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CAYLEY'S SECTIC

Curve studied by Maclaurin in 1718 and Cayley in 1867.
Arthur Cayley (1821-1895): British mathematician. |

Polar equation: .
Rational Cartesian parametrization: ( t
=
tan q ).
Cartesian equation: . Tricircular. rational. sextic. Curvilinear abscissa: . Radius of curvature: . Pedal equation: . Length: . |

Cayley's sextic is the pedal of the cardioid with respect to its cuspidal point (here, the cardioid is ).

It also is the inverse of the Tschirnhausen cubic with respect to its focus.

Its evolute is the nephroid centred on (*a*/2, 0) and passing through *O*.

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© Robert FERRÉOL, Jacques MANDONNET 2017