Mobius strips are easy to make. Just glue one end of a strip of paper to the back side of the other end. Then you have a twisted strip.

Lots of knitters make Mobius cowls as well. It’s a popular and cozy style.

The author of some of the books I’ve used with students, mathematician Richard Evan Schwartz at Brown University, has been puzzling over a problem posed in the 1970s: what’s the shortest strip of paper you can use to make a Mobius strip?

After a few years of tinkering, Dr. Schwartz cracked the problem. The key to doing so: taking a paper mobius strip and cutting it, finding that the resulting shape was *not* a parallelogram as he thought, but rather a trapezoid. Then he was able to calculate what he needed to complete the proof. Scientific American wrote a story about this, where you can read more.

This is yet another example of the ways hands-on experience can lead to breakthroughs even in advanced math!

Dr. Schwartz also allowed me to reference his wonderful book *You Can Count on Monsters* in my upcoming book, with the working title *The Art of Learning Math: A Handbook for Success*. Read my review of his book here.

**Update:** Dr. Schwartz provided an explanation of his proof, with illustrations and activities, that high school students should be able to work with. You can access this here (free).