17 November 23

August Ferdinand Möbius was born on 17 November 1790. He is most famous for investigating the amazing mathematical and topological properties of what we call Möbius loops. The simplest example is a circular ribbon formed with a single twist. This object has a single side and a single edge, which you can prove by working to paint the loop or to trace along the edge; as you progress in your work, continuing down the path, you eventually reach the point where you started, having traveled twice the circumference of the loop. If you try to cut this loop in half (lengthwise), you get another single loop, twice as big as the original -- but the double-sized loop now has two twists, and has two sides and two edges. That may sound like magic or "child's play" but the fascinating properties have applications in mechanical engineering, biology, chemistry and art. Many works by M. C. Escher involve Möbius loops; you can watch a video recreating Escher's red fire ants crawling on a loop! Dr. Möbius made many other contributions to topology and theoretical mathematics. My tie is a Möbius ribbon. Today in my Beginning Ethics class I'm helping my students appreciate the wonders of Möbius loops using long paper strips, tape, pencils and scissors!