Today is the birthday of August Ferdinand Möbius (1790-1868), most
famous for investigating the properties of "Möbius loops." My neckwear for today is a Möbius ribbon! It looks like it has two sides, but it really has just a single surface. (And so it's impossible to put it on "upside down" or "inside out" or "backwards.") You can make
one yourself from a long strip of paper that you tape into a loop,
including a half-twist. The most significant feature of this object is
that it has exactly one side, which you can prove by tracing a line
around the loop; without lifting your pencil/crayon at all, you will
arrive back where you started. And if you then use scissors to cut down
that line, expecting to cut the loop in half (lengthwise), you get the
surprising result of a single loop that is twice as big. Möbius loops
are famous in art, science and fashion design (particularly for knitted
or crocheted scarves).
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