Mobius strip importance

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  • 22.05.2018
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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. A system of differential-algebraic equations that describes models of this type was published in together with its numerical solution.
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Möbius strip

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Quanta Magazine

In math, three-dimensional space sprawls out to infinity in every direction. With an infinite amount of room, it should be able to hold an infinite number of things inside of it — pearls, peacocks or even planets. The result underscores the delicate endeavor of situating surfaces in space, as well as the intuition-challenging nature of infinities. The smallest infinity is something like the set of natural numbers — what you would get if you started counting 1, 2, 3 and never stopped. The set of natural numbers is countable, as is any group of objects that can be placed in an infinite list. If you were to place an infinite number of pearls or peacocks, or planets into three-dimensional space, those pearls would be countably infinite — you could, in theory, list them all, as if each had a serial number scraped onto its side. Some sets of numbers are too big to be made into a list.
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Möbius Strips Defy a Link With Infinity

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 The concept of a one-sided object inspired artists like Dutch graphic designer M.
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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.
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