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- Dupin_cyclide abstract "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 by (and named after) Charles Dupin in his 1803 dissertation under Gaspard Monge. The key property of a Dupin cyclide is that it is a channel surface (envelope of a one-parameter family of spheres) in two different ways. This property means that Dupin cyclides are natural objects in Lie sphere geometry.Dupin cyclides are often simply known as cyclides, but the latter term is also used to refer to a more general class of quartic surfaces which are important in the theory of separation of variables for the Laplace equation in three dimensions.Dupin cyclides were investigated not only by Dupin, but also by A. Cayley und J.C. Maxwell.Today, Dupin cylides are used in computer-aided design (CAD), because cyclide patches have rational representations and are suitable for blending canal surfaces (cylinder, cones, tori, and others).".
- Dupin_cyclide thumbnail Cyclide.png?width=300.
- Dupin_cyclide wikiPageExternalLink index.html.
- Dupin_cyclide wikiPageExternalLink cyclidededupin.shtml.
- Dupin_cyclide wikiPageExternalLink H71.pdf?sequence=1.
- Dupin_cyclide wikiPageExternalLink bk-arrangements-eurocg08.pdf.
- Dupin_cyclide wikiPageID "705128".
- Dupin_cyclide wikiPageLength "15241".
- Dupin_cyclide wikiPageOutDegree "59".
- Dupin_cyclide wikiPageRevisionID "695621254".
- Dupin_cyclide wikiPageWikiLink Abelian_group.
- Dupin_cyclide wikiPageWikiLink Arthur_Cayley.
- Dupin_cyclide wikiPageWikiLink Category:Surfaces.
- Dupin_cyclide wikiPageWikiLink Channel_surface.
- Dupin_cyclide wikiPageWikiLink Charles_Dupin.
- Dupin_cyclide wikiPageWikiLink Computer-aided_design.
- Dupin_cyclide wikiPageWikiLink Cone.
- Dupin_cyclide wikiPageWikiLink Curvature_sphere.
- Dupin_cyclide wikiPageWikiLink Cylinder_(geometry).
- Dupin_cyclide wikiPageWikiLink Directrix.
- Dupin_cyclide wikiPageWikiLink Envelope_(mathematics).
- Dupin_cyclide wikiPageWikiLink Euclidean_vector.
- Dupin_cyclide wikiPageWikiLink Focal_surface.
- Dupin_cyclide wikiPageWikiLink Gaspard_Monge.
- Dupin_cyclide wikiPageWikiLink Great_circle.
- Dupin_cyclide wikiPageWikiLink Implicit_surface.
- Dupin_cyclide wikiPageWikiLink Inversive_geometry.
- Dupin_cyclide wikiPageWikiLink Involution_(mathematics).
- Dupin_cyclide wikiPageWikiLink James_Clerk_Maxwell.
- Dupin_cyclide wikiPageWikiLink Laplaces_equation.
- Dupin_cyclide wikiPageWikiLink Lie_sphere_geometry.
- Dupin_cyclide wikiPageWikiLink MacTutor_History_of_Mathematics_archive.
- Dupin_cyclide wikiPageWikiLink Mathematics.
- Dupin_cyclide wikiPageWikiLink Multiplicative_inverse.
- Dupin_cyclide wikiPageWikiLink Möbius_transformation.
- Dupin_cyclide wikiPageWikiLink Point_at_infinity.
- Dupin_cyclide wikiPageWikiLink Principal_curvature.
- Dupin_cyclide wikiPageWikiLink Quadric.
- Dupin_cyclide wikiPageWikiLink Quartic_surface.
- Dupin_cyclide wikiPageWikiLink Soddys_hexlet.
- Dupin_cyclide wikiPageWikiLink Subgroup.
- Dupin_cyclide wikiPageWikiLink Tangent.
- Dupin_cyclide wikiPageWikiLink Torus.
- Dupin_cyclide wikiPageWikiLink File:Cyclide.png.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-0.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-1.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-11.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-2.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-3.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-4.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-iv-keg1.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-iv-tor1.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-iv-zyl1.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-iv-zyl2.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-p-0.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-p-1.svg.
- Dupin_cyclide wikiPageWikiLink File:Zyklide-p-2.svg.
- Dupin_cyclide wikiPageWikiLinkText "Dupin cyclide".
- Dupin_cyclide wikiPageWikiLinkText "cyclides".
- Dupin_cyclide wikiPageUsesTemplate Template:Citation.
- Dupin_cyclide wikiPageUsesTemplate Template:Cite_web.
- Dupin_cyclide wikiPageUsesTemplate Template:Commons_category.
- Dupin_cyclide wikiPageUsesTemplate Template:External_links.
- Dupin_cyclide wikiPageUsesTemplate Template:Mathworld.
- Dupin_cyclide wikiPageUsesTemplate Template:Reflist.
- Dupin_cyclide subject Category:Surfaces.
- Dupin_cyclide type Surface.
- Dupin_cyclide comment "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 by (and named after) Charles Dupin in his 1803 dissertation under Gaspard Monge. The key property of a Dupin cyclide is that it is a channel surface (envelope of a one-parameter family of spheres) in two different ways.".
- Dupin_cyclide label "Dupin cyclide".
- Dupin_cyclide sameAs Q4907706.
- Dupin_cyclide sameAs Dupinsche_Zyklide.
- Dupin_cyclide sameAs Ciklido.
- Dupin_cyclide sameAs m.034895.
- Dupin_cyclide sameAs Dupinova_ciklida.
- Dupin_cyclide sameAs Q4907706.
- Dupin_cyclide wasDerivedFrom Dupin_cyclide?oldid=695621254.
- Dupin_cyclide depiction Cyclide.png.
- Dupin_cyclide isPrimaryTopicOf Dupin_cyclide.