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CISSOID OF ZAHRADNIK

Karl Zahradnik (1848 - ?): German 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).

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© Robert FERRÉOL 2017