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- Möbius_strip abstract "The Möbius strip or Möbius band (/ˈmɜːrbiəs/ (non-rhotic) or US /ˈmoʊbiəs/; German: [ˈmøːbi̯ʊs]), Mobius or Moebius, is a surface with only one side and only one boundary. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.An example of a Möbius strip can be created by taking a paper strip and giving it a half-twist, and then joining the ends of the strip together to form a loop. However, the Möbius strip is not a surface of only one exact size and shape, such as the half-twisted paper strip depicted in the illustration. Rather, mathematicians refer to the closed Möbius band as any surface that is homeomorphic to this strip. Its boundary is a simple closed curve, i.e., homeomorphic to a circle. This allows for a very wide variety of geometric versions of the Möbius band as surfaces each having a definite size and shape. For example, any rectangle can be glued to itself (by identifying one edge with the opposite edge after a reversal of orientation) to make a Möbius band. Some of these can be smoothly modeled in Euclidean space, and others cannot.A half-twist clockwise gives a different embedding of the Möbius strip than a half-twist counterclockwise – that is, as an embedded object in Euclidean space the Möbius strip is a chiral object with right- or left-handedness. However, the underlying topological spaces within the Möbius strip are homeomorphic in each case. There are an infinite number of topologically different embeddings of the same topological space into three-dimensional space, as the Möbius strip can also be formed by twisting the strip an odd number of times greater than one, or by knotting and twisting the strip, before joining its ends. The complete open Möbius band is an example of a topological surface that is closely related to the standard Möbius strip but that is not homeomorphic to it.It is straightforward to find algebraic equations, the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface, having zero Gaussian curvature. A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.The Euler characteristic of the Möbius strip is zero.".
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- Möbius_strip wikiPageExternalLink illiview.html.
- Möbius_strip wikiPageExternalLink CD-The-Infinite-Road.htm.
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- Möbius_strip wikiPageWikiLink 0_(number).
- Möbius_strip wikiPageWikiLink 3-sphere.
- Möbius_strip wikiPageWikiLink Algebraic_variety.
- Möbius_strip wikiPageWikiLink August_Ferdinand_Möbius.
- Möbius_strip wikiPageWikiLink Boundary_(topology).
- Möbius_strip wikiPageWikiLink Brady_Haran.
- Möbius_strip wikiPageWikiLink Category:Recreational_mathematics.
- Möbius_strip wikiPageWikiLink Category:Surfaces.
- Möbius_strip wikiPageWikiLink Category:Topology.
- Möbius_strip wikiPageWikiLink Chemistry.
- Möbius_strip wikiPageWikiLink Chirality_(mathematics).
- Möbius_strip wikiPageWikiLink Circle.
- Möbius_strip wikiPageWikiLink Clockwise.
- Möbius_strip wikiPageWikiLink Closed_manifold.
- Möbius_strip wikiPageWikiLink Configuration_space.
- Möbius_strip wikiPageWikiLink Continuum_(set_theory).
- Möbius_strip wikiPageWikiLink Conveyor_belt.
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- Möbius_strip wikiPageWikiLink Diffeomorphism.
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- Möbius_strip wikiPageWikiLink Dyad_(music).
- Möbius_strip wikiPageWikiLink Embedding.
- Möbius_strip wikiPageWikiLink Euclidean_space.
- Möbius_strip wikiPageWikiLink Euler_characteristic.
- Möbius_strip wikiPageWikiLink Fiber_bundle.
- Möbius_strip wikiPageWikiLink Gaussian_curvature.
- Möbius_strip wikiPageWikiLink Geodesic.
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- Möbius_strip wikiPageWikiLink Homeomorphism.
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- Möbius_strip wikiPageWikiLink Klein_bottle.
- Möbius_strip wikiPageWikiLink Klein_four-group.
- Möbius_strip wikiPageWikiLink Lie_group.
- Möbius_strip wikiPageWikiLink List_of_cycles.
- Möbius_strip wikiPageWikiLink Loop_(knot).
- Möbius_strip wikiPageWikiLink Mathematician.
- Möbius_strip wikiPageWikiLink Mathematics.
- Möbius_strip wikiPageWikiLink Mathematics_of_paper_folding.
- Möbius_strip wikiPageWikiLink Molecular_knot.
- Möbius_strip wikiPageWikiLink Music_theory.
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- Möbius_strip wikiPageWikiLink Möbius_ladder.
- Möbius_strip wikiPageWikiLink Möbius_resistor.
- Möbius_strip wikiPageWikiLink Möbius_transformation.
- Möbius_strip wikiPageWikiLink Neighbourhood_(mathematics).
- Möbius_strip wikiPageWikiLink Nikola_Tesla.
- Möbius_strip wikiPageWikiLink Orbifold.
- Möbius_strip wikiPageWikiLink Orientability.
- Möbius_strip wikiPageWikiLink Overhand_knot.
- Möbius_strip wikiPageWikiLink Paradox.
- Möbius_strip wikiPageWikiLink Physics.
- Möbius_strip wikiPageWikiLink Poincaré_half-plane_model.
- Möbius_strip wikiPageWikiLink Quotient_space_(topology).
- Möbius_strip wikiPageWikiLink Real_projective_plane.
- Möbius_strip wikiPageWikiLink Rhoticity_in_English.
- Möbius_strip wikiPageWikiLink Riemannian_manifold.
- Möbius_strip wikiPageWikiLink Ruled_surface.
- Möbius_strip wikiPageWikiLink Square.
- Möbius_strip wikiPageWikiLink Stereographic_projection.
- Möbius_strip wikiPageWikiLink Strange_loop.
- Möbius_strip wikiPageWikiLink Sudan.
- Möbius_strip wikiPageWikiLink Superconductivity.
- Möbius_strip wikiPageWikiLink Surface.
- Möbius_strip wikiPageWikiLink Symmetric_group.
- Möbius_strip wikiPageWikiLink Topological_space.
- Möbius_strip wikiPageWikiLink Topology.
- Möbius_strip wikiPageWikiLink Toroidal_polyhedron.
- Möbius_strip wikiPageWikiLink Trefoil_knot.
- Möbius_strip wikiPageWikiLink Typewriter_ribbon.
- Möbius_strip wikiPageWikiLink Umbilic_torus.
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- Möbius_strip wikiPageWikiLink File:August_Ferdinand_Möbius.png.
- Möbius_strip wikiPageWikiLink File:MobiusJoshDif.jpg.
- Möbius_strip wikiPageWikiLink File:MobiusSnail2B.png.
- Möbius_strip wikiPageWikiLink File:Moebius_strip.svg.
- Möbius_strip wikiPageWikiLink File:Moebiusstripscarf.jpg.
- Möbius_strip wikiPageWikiLink File:MöbiusStripAsSquare.svg.
- Möbius_strip wikiPageWikiLink File:Möbius_strip.jpg.
- Möbius_strip wikiPageWikiLinkText "Mobius".
- Möbius_strip wikiPageWikiLinkText "Moebius strip".
- Möbius_strip wikiPageWikiLinkText "Moebius".