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# Pendant-Mobius Heart

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Pendant-Mobius Heart
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Pendant-Mobius Heart
\$0.00
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Pendant-Mobius Heart _Designed by BRO1977 ( https://www.shapeways.com/model/2813146/pendant-mobius-heart.html?li=productGroup&materialId=83 ) _The Möbius strip or Möbius band , also Mobius or Moebius, is a surface with only one side and only one boundary component. 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. _A model can easily 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 geometry (i.e., of only one exact size and shape), such as the half-twisted paper strip depicted in the illustration to the right. 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. _A half-twist clockwise will give 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 "handedness" (right-handed or left-handed). 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 (see section Open Möbius band below) 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 (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution. _Giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the playing time). Möbius strips are common in the manufacture of fabric computer printer and typewriter ribbons, as they allow the ribbon to be twice as wide as the print head while using both halves evenly.