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In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter...

A Darboux cyclide is an algebraic surface of degree at most 4 that contains multiple families of circles. Named after French mathematician Gaston Darboux...

spheres of a surface. It also allows for a natural treatment of Dupin cyclides and a conceptual solution of the problem of Apollonius. Lie sphere geometry...

Dupin cyclide (Figure 3). The envelope of Soddy's hexlets is a Dupin cyclide, an inversion of the torus. Thus Soddy's construction shows that a cyclide of...

particularly known for work in the field of mathematics, where the Dupin cyclide and Dupin indicatrix are named after him; and for his work in the field...

knot. Its directrix is a curve on a torus e) The 5. picture shows a Dupin cyclide (canal surface). Parallel surface Geometry and Algorithms for COMPUTER...

sheets (purple). A Dupin cyclide and its parallels are determined by a pair of focal conic sections. The diagram shows a ring cyclide together with its focal...

Clebsch cubic Monkey saddle (saddle-like surface for 3 legs.) Torus Dupin cyclide (inversion of a torus) Whitney umbrella Boy's surface Breather surface...

curve and the other sheet is a surface * For cones, cylinders, tori and cyclides both sheets form curves. * For the sphere the center of every osculating...

polyhedral approximation of a cyclide-offset....

Bispherical coordinates Flat-ring cyclide coordinates Flat-disk cyclide coordinates Bi-cyclide coordinates Cap-cyclide coordinates Newtonian potential Laplace...

There are many things named after him: Darboux basis Darboux chart Darboux cyclide Darboux cubic Darboux derivative Darboux equation Darboux frame Darboux...

(kuklikós) acyclic, anticyclone, anticyclonic, bicycle, cycle, cyclic, cyclide, cycloid, cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema,...

G ( 8 , 2 , 0 ) {\displaystyle {\mathcal {G}}(8,2,0)} Points, Darboux cyclides, quadrics surfaces Reflections, translations, rotations, dilations, others...

torus Angenent torus Annulus (geometry) Clifford torus Complex torus Dupin cyclide Elliptic curve Irrational winding of a torus Joint European Torus Klein...

Example 2, p. 32. Johnstone, John K. (1993), "A new intersection algorithm for cyclides and swept surfaces using circle decomposition" (PDF), Computer Aided Geometric...

Clebsch cubic Monkey saddle (saddle-like surface for 3 legs.) Torus Dupin cyclide (inversion of a torus) Whitney umbrella Right conoid (a ruled surface)...

More generally, the focal surface of a Dupin cyclide consists of a pair of focal conics. The Dupin cyclides are the only surfaces, whose focal surfaces...

circles. The inversion of a cylinder, cone, or torus results in a Dupin cyclide. A spheroid is a surface of revolution and contains a pencil of circles...

corresponding Steiner chain. The envelope of the hexlet spheres is a Dupin cyclide, the inversion of a torus. The six spheres are not only tangent to the...

analogues of Möbius transformations for oriented projective geometry Dupin cyclides, shapes obtained from cylinders and tori by inversion At the time of its...

particularly known for work in the field of mathematics, where the Dupin cyclide and Dupin indicatrix are named after him; and for his work in the field...

Frank Morley at Johns Hopkins University. Her thesis was titled "Dupin's cyclide as a self-dual surface". With her doctoral degree, Young was eventually...

for generating Dupin cyclides as canal surfaces in two ways. Focal conics can be seen as degenerate focal surfaces: Dupin cyclides are the only surfaces...

is finite, then it is said to be an arithmetic quartic surface. Dupin cyclides The Fermat quartic, given by x4 + y4 + z4 + w4 =0 (an example of a K3 surface)...

Comptes rendus de l'Académie des Sciences. She was known for her work on cyclides. Bortniker was born into a Jewish family on 20 May 1860 (according to the...

Parabolic conoid Plücker's conoid Whitney umbrella Châtelet surfaces Dupin cyclides, inversions of a cylinder, torus, or double cone in a sphere Gabriel's...

(kuklikós) acyclic, anticyclone, anticyclonic, bicycle, cycle, cyclic, cyclide, cycloid, cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema,...

designed the Orb Bag, a spherical, mirrored handbag modeled on a Dupin cyclide geometric form. In September 2024, Bentel collaborated with the retailer...

University of Ireland in 1885. 1880: On Cubic Transformations 1881: On Cyclides and Sphero-quartics, from Internet Archive 1882: The First Six Books of...

focal points of a family of planes (Semple & Roth 1949, p.85, 87) cyclide A cyclide is a quartic surface passing doubly through the absolute conic. (Semple...

curvature of curves and surfaces, including surfaces of revolution, Dupin cyclides, helicoids, and minimal surfaces including the Enneper surface, with commentary...

Tertiary Charles Dupin (1784–1873) – mathematician who discovered the Dupin cyclide and the Dupin indicatrix Stephan Endlicher (1804–1849) – botanist who formulated...