Today I'm celebrating the birthday (in 1790) of August Ferdinand Möbius, the German mathematician who first investigated the wonderful properties of the single-sided Möbius strip. You can make your own by taking a long narrow strip of paper, like a very long cash register tape or a strip cut from a newspaper double page, and forming a loop with a SINGLE TWIST in it, and then taping it so you can play. (It will seem that you attaching the "front side" of the paper to the "back side" of the other end.) If you now take a pencil and draw a line down the strip -- like driving down the middle of the road -- you can go completely around the loop twice without ever turning the paper over, and you wind up where you started. Your loop has a single side (surface). If you take scissors and cut on the line you just drew, to cut the loop in half "lengthwise," you get a very surprising result.
Monday, November 17, 2014
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