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Moebius strip definition
Try to draw a line on both "sides" without picking up your pencil. It's actually quite simple. That is, when we define a surface normal at a point, it is impossible to extend the definition to the whole surface. The picture below illustrates that by "sliding" a given surface normal along the strip, without picking it up, we can get a surface normal that points in the opposite direction. Thus any attempt to give the surface a "front" and a "back" must fail. Imagine taking the two slices below, and bending them over so that the arrow heads coincide.
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Mobius strip | Definition of Mobius strip at tadahblog.com
It can be made using a strip of paper by gluing the two ends together with a half-twist. The Mobius strip is known for its unusual properties. A bug crawling along the center line of the loop would go around twice before coming back to its starting point. Cutting one third of the way in from the edge and parallel to it produces another amusing result. The parameter u runs around the strip while v moves from one edge to the other.
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You have most likely encountered one-sided objects hundreds of times in your daily life — like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles. This mathematical object is called a Mobius strip. Another mathematician named Listing actually described it a few months earlier, but did not publish his work until
It can be realized as a ruled surface. Its boundary is a simple closed curve, that is, homeomorphic to a circle. Some of these can be smoothly modeled in Euclidean space , and others cannot. In particular, the twisted paper model is a developable surface , having zero Gaussian curvature.