**The Math: topology**

Mobius strips are studied in an area of math called topology, sometimes called “rubber sheet geometry”, which studies properties of strings and surfaces that are allowed to bend and stretch, but not break or pass through itself. Mathematicians joke that a topologist can’t tell the difference between a donut and a coffee cup, because as this picture shows, one can be reshaped to make the other:

(This picture is from a rather silly movie by the wonderfully crazy mathematician/artist Henry Segerman, who loves to 3d print his ideas.)

Topology is only a little more than a century old, and includes knot theory, which classifies the different ways that a loop of string (or several loops) can be knotted. Here’s a fascinating video by my friend Carlo Sequin at UC Berkeley explaining the basics of knot theory.

**Movies and Instructions for making your own shapes**

- Here’s Vi Hart’s fabulous video about Möbius strip made of Fruit by the Foot. She’s a popular YouTuber who yes makes super popular and entertaining movies about math crossed with art and music, plus a good deal of rapid fire irreverence.
- Karl Schaffer shared the handout he uses with students for exploring what happens when you cut up THREE loops all joined together.
- Here are instructions for making a Möbius strip by adding a single cut to a square. Artist/sculptor Max bill made a beautiful metal sculpture in this shape, as well as making many other sculptures equivalent. I showed everyone how to do this last Monday.
- And here are my instructions for cutting and folding a Möbius strip made of just six squares and four triangles. It doesn’t look like a Möbius strip, but trace the edge and you’ll see that its one edge is in the shape of a square.
- Jeanne Lazzarini, who attends Math Monday regularly, sent me this: Have you heard of BIG Architects Group? Founded by Bjarke Ingels from Copenhagen? Ask me about him some day…Bjarke’s innovative buildings make me think of stretching the boundaries of mathematical artistry and he’s gained world-wide acclaim for his buildings! —> Be sure to check out his möbius building — https://inhabitat.com/big-unveil-massive-mobius-strip-library-for-kazakhstan/big-diag02