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- Clifford_torus abstract "In geometric topology, the Clifford torus is a special kind of torus sitting inside the unit 3-sphere S3 in R4, the Euclidean space of four dimensions. Or equivalently, it can be seen as a torus sitting inside C2 since C2 is topologically equivalent to R4. It is specifically the torus in S3 that is geometrically the cartesian product of two circles, each of radius sqrt(1/2).The Clifford torus is an example of a square torus, because it is isometric to a square with opposite sides identified. It is further known as a Euclidean 2-torus (the \"2\" is its topological dimension); figures drawn on it obey Euclidean geometry as if it were flat, whereas the surface of a common \"doughnut\"-shaped torus is positively curved on the outer rim and negatively curved on the inner. Although having a different geometry than the standard embedding of a torus in three-dimensional Euclidean space, the square torus can also be embedded into three-dimensional space, by the Nash embedding theorem; one possible embedding modifies the standard torus by a fractal set of ripples running in two perpendicular directions along the surface.".
- Clifford_torus thumbnail Clifford-torus.gif?width=300.
- Clifford_torus wikiPageID "7950934".
- Clifford_torus wikiPageLength "9940".
- Clifford_torus wikiPageOutDegree "29".
- Clifford_torus wikiPageRevisionID "705888018".
- Clifford_torus wikiPageWikiLink Category:Geometric_topology.
- Clifford_torus wikiPageWikiLink Doughnut.
- Clifford_torus wikiPageWikiLink Duocylinder.
- Clifford_torus wikiPageWikiLink Embedding.
- Clifford_torus wikiPageWikiLink Euclidean_geometry.
- Clifford_torus wikiPageWikiLink Euclidean_space.
- Clifford_torus wikiPageWikiLink Fractal.
- Clifford_torus wikiPageWikiLink Geometric_topology.
- Clifford_torus wikiPageWikiLink Group_action.
- Clifford_torus wikiPageWikiLink Heegaard_splitting.
- Clifford_torus wikiPageWikiLink Hopf_fibration.
- Clifford_torus wikiPageWikiLink Hsiangxe2x80x93Lawsons_conjecture.
- Clifford_torus wikiPageWikiLink Isometry.
- Clifford_torus wikiPageWikiLink Metric_tensor.
- Clifford_torus wikiPageWikiLink Minimal_surface.
- Clifford_torus wikiPageWikiLink Nash_embedding_theorem.
- Clifford_torus wikiPageWikiLink Orthogonal_group.
- Clifford_torus wikiPageWikiLink Orthogonal_transformation.
- Clifford_torus wikiPageWikiLink Simon_Brendle.
- Clifford_torus wikiPageWikiLink Solid_torus.
- Clifford_torus wikiPageWikiLink Square.
- Clifford_torus wikiPageWikiLink Stereographic_projection.
- Clifford_torus wikiPageWikiLink Submanifold.
- Clifford_torus wikiPageWikiLink Symplectic_geometry.
- Clifford_torus wikiPageWikiLink Symplectic_manifold.
- Clifford_torus wikiPageWikiLink Torus.
- Clifford_torus wikiPageWikiLink Unit_circle.
- Clifford_torus wikiPageWikiLink File:Clifford-torus.gif.
- Clifford_torus wikiPageWikiLink File:TorusAsSquare.svg.
- Clifford_torus wikiPageWikiLinkText "Clifford torus".
- Clifford_torus wikiPageWikiLinkText "Clifford".
- Clifford_torus wikiPageWikiLinkText "clifford torus".
- Clifford_torus subject Category:Geometric_topology.
- Clifford_torus hypernym Kind.
- Clifford_torus type Redirect.
- Clifford_torus comment "In geometric topology, the Clifford torus is a special kind of torus sitting inside the unit 3-sphere S3 in R4, the Euclidean space of four dimensions. Or equivalently, it can be seen as a torus sitting inside C2 since C2 is topologically equivalent to R4. It is specifically the torus in S3 that is geometrically the cartesian product of two circles, each of radius sqrt(1/2).The Clifford torus is an example of a square torus, because it is isometric to a square with opposite sides identified.".
- Clifford_torus label "Clifford torus".
- Clifford_torus sameAs Q5133090.
- Clifford_torus sameAs Toro_de_Clifford.
- Clifford_torus sameAs m.026l5xy.
- Clifford_torus sameAs Toru_di_Clifford.
- Clifford_torus sameAs Cliffordov_torus.
- Clifford_torus sameAs Q5133090.
- Clifford_torus wasDerivedFrom Clifford_torus?oldid=705888018.
- Clifford_torus depiction Clifford-torus.gif.
- Clifford_torus isPrimaryTopicOf Clifford_torus.
