The Meaning of Moebius

If you weave, knit, or crochet scarves chances are you’ve come across a pattern or two for Möbius (sometimes spelled Moebius) scarves. For those not in the know, a Moebius scarf is an infinity scarf with a twist—literally. Basic infinity scarves are scarves where both ends are sewn together to form a circular scarf; with a Möbius you put a twist in the scarf before sewing the ends together. The Möbius scarf is named after the Möbius strip which in turn is named after August Ferdinand Möbius, a German mathematician who first wrote about it. Just as with the scarf, Möbius strip is a flat rectangle which is then twisted and the two ends attached. If an ant were to travel the length of the strip returning to its original start point, it would have crawled along both sides of the entire strip—without going over an edge. Along with making very cool looking scarves, Möbius strips have been used in conveyor belts, as continuous loop recording tapes (which provides double the playing time), and in the symbol for recycling. There are also a lot of other scientific and mathematic applications for Möbius strips—they’re even a part of music theory. So when you wear a Möbius scarf you’re not just wearing a fabulous piece of cloth, you’re wearing a bit of math.  

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