Mobius Strip

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An example of a Möbius strip can be created by taking a strip of paper and giving one end a half-twist, then joining the ends to form a loop; its boundary is a simple closed curve which can be traced by a single unknotted string. Any topological space homeomorphic to this example is also called a Möbius strip, allowing for a very wide variety of geometric realizations as surfaces with a definite size and shape. For example, any rectangle can be glued left-edge to right-edge with a reversal of orientation. Some, but not all, of these can be smoothly modeled as surfaces in Euclidean space. A closely related, but not homeomorphic, surface is the complete open Möbius band, a boundaryless surface in which the width of the strip is extended infinitely to become a Euclidean line.