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How to make a paper Möbius strip

One of the most famous surfaces in mathematics, the Möbius strip can be constructed by cutting a long strip of paper, putting a half twist in it, and gluing the ends of the strip together. What makes this seemingly ordinary construct so fascinating is that, while the original strip of paper clearly had two sides, the Möbius strip seems to have only one. Try to draw a line on both “sides” without picking up your pencil. It’s actually quite simple.

Then you take some scissors to it… and it gets even more interesting!

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