17 November 11

Happy Birthday, Mr. Möbius! August Ferdinand Möbius (November 17, 1790 - September 26, 1868) was a German mathematician who discovered the unusual properties of the one-sided "Möbius strip" in 1858. You can make one for yourself by looping a long strip of paper, twisting the paper once before fastening it (e.g., with tape) to complete the loop. The surface of this object now has only one side, as you can prove by drawing a continuous pencil line around the loop. The technical definition is "a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space" (Wikipedia, article on Möbius). Möbius-loop patterns are famous in art, particularly in many designs by M. C. Escher, and they are also of increasing interest in chemistry. My tie recreates a one-sided loop to celebrate Möbius' birthday, with animals parading in all possible directions.