next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

CISSOID OF ZAHRADNIK

Karel Zahradnik (1848 - 1916): Czech mathematician. |

Cartesian equation of the cissoid of the conic
and the line x = d: .
Polar equation: . |

The cissoids of Zahradnik are the cissoids of a conic and a line, the pole being a point on the conic.

They are exactly the rational cubics whose singular point is not at infinity and that have at least one asymptote (at finite distance).

When the conic is a circle, we get precisely the rational circular cubics.

Examples listed in this work, in the non-circular case:

- Descartes'
folium and the Tschirnhausen
cubic (case of an ellipse)

- the mixed
cubic (case of a parabola)

- the equilateral
trefoil (case of a hyperbola).

next curve | previous curve | 2D curves | 3D curves | surfaces | fractals | polyhedra |

© Robert FERRÉOL 2017