In the mid-nineteenth century mathematicians August Ferdinand Möbius and Johann Benedict Listing found that if you take a strip of paper, give it a half twist, and attach the ends, you create an interesting object. If you follow your finger along the surface you will find that it has only one continuous surface (that is, as you follow along you will end up covering both sides of the strip. If you try to cut it in half, you only end up with a longer strip with two full twists. The mathematics describing this, and similar objects, gets quite complex. Möbius strips have found applications beyond being mathematical oddities. For instance, conveyer belts are often built as Möbius strips so that they have even wear and tear. In chemistry, Möbius aromaticity involves a ring of atoms that incorporates a half twist. Crazyjoe579 made this LEGO version.

I have to make a correction: if you cut the Möbius strip in half, you will NOT get another Möbius strip. You will get something like a Möbius strip: it is a strip of paper with a full twist. If you don't believe, try it out with a piece of paper: the half-cut Möbius strip will have two surfaces.

ReplyDeleteYou're right, of course. It's been since gradeschool that I played with a Möbius strip, but I should have checked before typing that up. I'll correct the original post.

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