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CYCLIDE

From the Greek Kuklos: circle, wheel and eidos: appearance. |

2 equal a_i : dupin berger 20.7.3 |

The cyclides are the envelopes of spheres (C) the centers of which describe a curve or a surface (G_{0})
(the *deferent*) and such that a fixed point *O* has a constant power *p* with respect to these spheres (this notion is therefore analogous to that of cyclic curve in the plane).

They are therefore circled surfaces.

The cyclides with a parabola or a paraboloid as a deferent are the spherical cubic surfaces and the cyclides with a conic or a quadric of another kind are the bispherical quartic surfaces, also called "Darboux cyclides".

General equation: .
When the deferent is a conic, the cyclide is called "Dupin cyclide".

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© Robert FERRÉOL 2017