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In mathematics, a Möbius strip, Möbius band, or Möbius loop [a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE .
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]
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
In 1977, two mathematicians created a conjecture that proposed the minimum size a paper strip needed to be in order to form an embedded strip. Although they proposed an aspect ration of 1.73 (or ...
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 ...
[21] [5] Similarly, if the three utilities puzzle is presented on a sheet of a transparent material, it may be solved after twisting and gluing the sheet to form a Möbius strip. [ 22 ] Another way of changing the rules of the puzzle that would make it solvable, suggested by Henry Dudeney , is to allow utility lines to pass through other houses ...
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 ...
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.