19 November 18

My tie today is very one-sided. It's a Möbius loop, to honor the birthday (on Saturday, 17 November) of August Ferdinand Möbius (1790-1868). He was a German mathematician who first explored the topology of the loop/strip that bears his name. It's a one-sided loop, meaning that you can travel the entire surface of the loop without ever crossing an edge or "getting to the other side." You can play with one on your computer monitor from this Wikipedia page, but it's even better to make your own from a wide strip of paper that is at least 11 inches long. Tape the ends together to make a loop, but include a single twist in the loop. Drawing a line down the center of the loop (like the center line on a road) will prove that the loop has only one side -- you reach your starting point again without ever turning the paper over. If you cut down that center line, to "cut the loop in half lengthwise," you get a surprise. Besides their interesting topological properties, Möbius loops have become important elements in art, jewelry, molecular synthesis, and mechanical engines and conveyor belts (where a drive belt can have a longer useful life because the friction-wearing surface is twice as long as a conventional flat belt). I Möbius-looped my tie by inserting the tail into the main part, with a single twist.