Wednesday, November 17, 2021

 I'm feeling very one-sided today. It's the birthday of August Ferdinand Möbius (1790-1868), who is most famous for describing the topological properties of the "Möbius loop." You can make one yourself from a long strip of paper, giving the strip a single twist before taping the ends together. (My ribbon tie is a Möbius loop.) The resulting surface has only one side, which you can prove by tracing a pencil line around the loop (lengthwise). When you reach your starting point you will have traveled twice the length of your original strip, without lifting the pencil from the surface. If you use your scissors to cut down the line, your will get a single loop twice as big, and it will have two twists. Besides these magical topological features, Möbius loops have practical applications in art, architecture, manufacturing and molecular chemistry!

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