17 November 21

 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!

17 November 20

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).

17 November 19

Today is the birthday of August Ferdinand Möbius (1790-1868), most famous for investigating the properties of "Möbius loops." 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). My neckwear for today is a Möbius ribbon!

16-17 November 17

November 17 marks the birthday of August Ferdinand Möbius, 1790-1868. He is most famous for his mathematical description of the Möbius strip (or loop), which is a looped surface that has only one side. I hope you have had a chance to play with Möbius loops! My tie is made from wide ribbon, and it has only one side. I mean that if you were painting my tie, you could brush smoothly all around the loop until you reached your starting point -- and you would have painted the entire loop -- it has no "inside" versus "outside." Here's your topological/philosophical puzzle for today: In what sense does my tie tack go "through" the loop? We can't say it pokes through "one side" and comes out of the "other side," because the loop has only one side . . . even when I cross the loop over itself . . .