Mobius strip klein bottle

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It locally looks like any other surface. Close-up we see a 2-dimensional object. The surface becomes more interesting when we try to decide how many sides this surface has.

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Klein bottletopological spacenamed for the German mathematician Felix Kleinobtained by identifying two ends of a cylindrical surface in the direction opposite that is necessary to obtain a torus. Klein bottle. Article Media.

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The Klein bottle is a closed nonorientable surface of Euler characteristic 0 Dodson and Parkerp. It can be constructed by gluing both pairs of opposite edges of a rectangle together giving one pair a half-twist, but can be physically realized only in four dimensions, since it must pass through itself without the presence of a hole. Its topology is equivalent to a pair of cross-caps with coinciding boundaries Francis and Weeks

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If you like a drink, then a Klein bottle is not a recommended receptacle. It may look vaguely like a bottle, but it doesn't enclose any volume, which means that it can't actually hold any liquid. Whatever you pour "in" will just come back out again. How do you construct such a strange thing and why would you want to construct it?

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Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. The Klein bottle was first described in by the German mathematician Felix Klein. The following square is a fundamental polygon of the Klein bottle.

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Specifically, they have only one side although it seems to be two sides. But the interesting thing about it is that it has only one side. Locally, it seems to have two sides.

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Click to get a printable template for five Mobius strips. Print this with as small margins as your printer will allow, and cut along the solid lines to get basic Mobius strip shapes. Do the Mobius twist!

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In the last tutorial we constructed certain minimal surfaces in hyperbolic space. It turns out that the very same procedure applied to the 3-sphere yields minimal surfaces, too. Thus we end up with a family of circles.

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By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. So glueing together two of them, does it matter whether they are mirrored versions of each other or not?

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