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  2. Möbius strip - Wikipedia

    en.wikipedia.org/wiki/Möbius_strip

    For strips too short to apply this method directly, one can first "accordion fold" the strip in its wide direction back and forth using an even number of folds. With two folds, for example, a 1 × 1 {\displaystyle 1\times 1} strip would become a 1 × 1 3 {\displaystyle 1\times {\tfrac {1}{3}}} folded strip whose cross section is in the shape of ...

  3. Tietze's graph - Wikipedia

    en.wikipedia.org/wiki/Tietze's_graph

    In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz Friedrich Tietze, who showed in 1910 that the Möbius strip can be subdivided into six regions that all touch each other – three along the boundary of the strip and three along its center line – and therefore that graphs that are embedded ...

  4. Non-orientable wormhole - Wikipedia

    en.wikipedia.org/wiki/Non-orientable_wormhole

    As with a Möbius strip, once the two distinct connections have been made, we can no longer identify which connection is "normal" and which is "reversed" – the lack of a global definition for charge becomes a feature of the global geometry. This behaviour is analogous to the way that a small piece of a Möbius strip allows a local distinction ...

  5. Orientability - Wikipedia

    en.wikipedia.org/wiki/Orientability

    A torus is an orientable surface The Möbius strip is a non-orientable surface. Note how the disk flips with every loop. The Roman surface is non-orientable.. In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". [1]

  6. Vector bundle - Wikipedia

    en.wikipedia.org/wiki/Vector_bundle

    The Möbius strip can be constructed by a non-trivial gluing of two trivial bundles on open subsets U and V of the circle S 1. When glued trivially (with g UV =1) one obtains the trivial bundle, but with the non-trivial gluing of g UV =1 on one overlap and g UV =-1 on the second overlap, one obtains the non-trivial bundle E, the Möbius strip

  7. Three utilities problem - Wikipedia

    en.wikipedia.org/wiki/Three_utilities_problem

    Proof without words: One house is temporarily deleted. The lines connecting the remaining houses with the utilities divide the plane into three regions. Whichever region the deleted house is placed into, the similarly shaded utility is outside the region. By the Jordan curve theorem, a line connecting them must intersect one of the existing lines.

  8. I-bundle - Wikipedia

    en.wikipedia.org/wiki/I-bundle

    An annulus is an orientable I-bundle. This example is embedded in 3-space with an even number of twists This image represents the twisted I-bundle over the 2-torus, which is also fibered as a Möbius strip times the circle.

  9. Klein bottle - Wikipedia

    en.wikipedia.org/wiki/Klein_bottle

    A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.