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Summary Of: Torus

of the circle is called a torus in some contexts... A torus can be defined parametrically by... for a torus radially symmetric about the... of this torus are given by... A torus is the product of two circles... A torus is the product of two circles... A torus is the product of two circles... This topological torus is also often called the... to a topological torus as long as it does not intersect its own axis... The torus can also be described as a... of the torus is just the... If a torus is punctured and turned inside out then another torus results... torus can be represented as a two... The points on the torus corresponding to the ramification points are the... the conformal type of the torus is determined by the... The torus has a generalization to higher dimensions... Recalling that the torus is the product space of two circles... dimensional torus is the product of... The torus discussed above is the 2... dimensional torus is just the circle... dimensional torus is rather difficult to visualize... torus can be described as a quotient of... torus is obtained from the... torus in this sense is an example of an... Group multiplication on the torus is then defined by coordinate... which is a torus of the largest possible dimension... torus is a free abelian group of rank... torus is 0 for all... The flat torus is a specific embedding of the familiar... you cannot then bend this cylinder into a torus without stretching the paper... torus has a different meaning... torus resembles the surface of... An ordinary torus is a 1... torus is called a... torus a triple torus... torus is said to be an... torus is the 2... If a torus is divided into regions... This construction shows the torus divided into the maximum of seven regions... This construction shows the torus divided into the maximum of seven regions... This construction shows the torus divided into the maximum of seven regions... An algorithm that uses flat torus to visualize high dimensional data...

Encyclodia Page On: Torus

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| citations | footnotes | inline citations | A torus | | Torus (disambiguation) | geometry | surface of revolution | circle | coplanar | doughnuts | inner tubes | toroid | chord | Latin | cushion | Cartesian coordinates | axis | surface area | volume | A torus is the product of two circles. | | Topologically | surface | product | circles | Clifford torus | filled out | fiber bundle | Hopf bundle | relative topology | homeomorphic | stereographically projecting | quotient | Cartesian plane | unit square | fundamental polygon | Turning a torus inside-out (animated version) | | animated version | fundamental group | direct product | path | homology group | isomorphic | Hurewicz theorem | abelian | conformal structure | Weierstrass points | cross-ratio | action | lattice | hypercube | compact | manifold | abelian | Lie group | unit circle | complex numbers | compact Lie groups | maximal torus | subgroup | invertible | fundamental group | free abelian group | homology group | choose | Euler characteristic | cohomology ring | exterior algebra | module | Gaussian curvature | isometric | A triple torus | | surfaces | connected sum | sphere | double torus | orientable surface | genus | sphere | classification theorem | compact | connected | projective planes | real numbers | four color theorem | plane | This construction shows the torus divided into the maximum of seven regions, every one of which touches every other. | | Algebraic torus | Annulus | Clifford torus | Doughnut | Dupin cyclide | Elliptic curve | Loewner's torus inequality | Maximal torus | Period lattice | Sphere | Standard torus | Surface | Torus (nuclear physics) | Torus mandibularis | Torus palatinus | Umbilic Torus | Villarceau circles | Wikimedia Commons | cut-the-knot | Eric W. Weisstein | MathWorld | Categories | Surfaces | Articles with unsourced statements since December 2007 | All articles with unsourced statements |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Torus".