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Dupin cyclide

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 are themselves examples of Dupin cyclides. They were discovered c. 1802 by (and named after) Charles Dupin, while he was still a student at the École polytechnique following Gaspard Monge's lectures. The…

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Overview

Definitions and properties

Parametric and implicit representation

Cyclide as channel surface

Dupin cyclides and geometric inversions

Separation of variables

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Map overview Semantic statistics

Dupin cyclide

Nodes56
Edges55
Triples118
Avg. degree1.96
Density0.035714
Components1

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Dupin cyclide

Top relations

related to References · 88
Dupin cyclide → American Journal, Applications, Applied Mathematics, Bachelier, Blaschke, Braunschweig, Cayley, Cecil, Chandru, Chelsea Publishing, Cohn-Vossen, Collections, Computer-Aided Design, Connor, Curves, Cyclide Blending, Cyclides, David, Differential Geometry, Domina Eberle
related to External links · 13
Dupin cyclide → Arrangements, Berberich, Cyclide, Dupin, Dupin Cyclides, Eric, Genus One, Kerber, MathCurve, MathWorldE, Surfaces, Tori, Weisstein
related to Definitions and properties · 6
Dupin cyclide → Dupin, In, Möbius, Since, There, This
is a · 4
Dupin cyclide → channel surface, circle, envelope of the one-parameter family of spheres tangent to three given spheres, image either of a right circular cylinder or a right circular double cone or a torus of revolution by an inversion
related to Separation of variables · 4
Dupin cyclide → Cartesian, Dupin, Thus, Whereas
related to Cyclide as channel surface · 3
Dupin cyclide → Dupin, The, There

Important terminology Word statistics

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Important terminology

cyclide displaystyle dupin cyclides one spheres surface inversion hyperbola circles surfaces ellipse see torus parametric gets diagram representation two cylinder

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dupin cyclideis achannel surface0.90text
Dupin cyclideis aenvelope of the one-parameter family of spheres tangent to three given spheres0.90text
Dupin cyclideis acircle0.90text
Dupin cyclideis aimage either of a right circular cylinder or a right circular double cone or a torus of revolution by an inversion0.90text
Dupin cycliderelated to Cyclide as channel surfaceThere0.60section
Dupin cycliderelated to Cyclide as channel surfaceDupin0.60section
Dupin cycliderelated to Cyclide as channel surfaceThe0.60section
Dupin cycliderelated to Definitions and propertiesThere0.60section
Dupin cycliderelated to Definitions and propertiesDupin0.60section
Dupin cycliderelated to Definitions and propertiesIn0.60section
Dupin cycliderelated to Definitions and propertiesThis0.60section
Dupin cycliderelated to Definitions and propertiesMöbius0.60section

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