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Möbius Strip: Daswortgewand And Pixabay

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Mobius Strip DasWortgewand / Pixabay Some of the challenges and philosophical questions that mankind has battled with throughout history have been addressed directly by mathematics. Indeed, the study of mathematics has allowed us to pursue answers for some of the most impractical questions that are difficult or even impossible to test in reality. Although the application of some solutions are beyond what humanity is capable of at this point in time, an understanding of what they are and how they link to other mathematical and everyday principles of life grant us an extraordinary comprehension of how the world works, as well as providing insights into some of the unintuitive results of fascinating acts. This article aims to explore some of these …show more content…

Thus, for our Möbius band, we will now have a strip of paper with two edges and two boundaries. If we take this larger strip and cut it down the middle, we will get two separate pieces this time that are interlocked and which both have four half twists. What’s also interesting about the Möbius band is that if we were to cut at one third of the strip instead of the middle, we would expect to have another single strip with more twists—but the result is even more perplexing. We instead get two separate pieces this time, with the fatter piece remaining as a Möbius band with its original length—because it does not receive an extra edge from the cut—and the thinner piece having twice its original length with four half twists, two edges and two boundaries. This happens because as we draw a line down 1/3 of the band, we traverse the entire strip but we do not meet our original starting point until we have gone all the way around again. Because of this, the two strips form two separate loops that are

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