Zip-Apart Möbius Bands

I’ve taught topology many times. One of the highlights for the students (and for me) is the investigation of the Möbius band—the one sided, one edged, non-orientable surface with boundary. On the day we introduce the Möbius band I bring many strips of paper, clear tape, and scissors and have the students make conjectures about what…

Bubbles with knotted boundaries

We can think of a mathematical knot as a knotted piece of string (or in our case, wire) with its free ends joined. Examples are shown below. There is a remarkable theorem that every knot can be realized as the boundary of a surface. Moreover, Herbert Seifert produced a very simple algorithm for constructing an orientable…

Möbius bubble wrap

This week’s New York Times Magazine has an article called “The Year in Ideas.” One feature in the article is “Bubble Wrap That Never Ends,” by Vanessa Gregory. She writes about the popular Japanese keychain called Mugen Puchi Puchi. It has six small buttons on it, and pressing them simulates popping bubble wrap. The keychain…

Lipson’s mathematical LEGO sculptures

Ξ at the the 360 blog just posted a neat LEGO fact: it is possible to snap together two 2×4 lego bricks in 24 different ways. Given six of these LEGOs it is possible to snap them together in 915,103,765 different ways! This inspired me to post a link to a cool website by Andrew Lipson….

Cutting and folding paper

Inspired by Chaim Goodman-Strauss’s recent video about symmetries, paper snowflakes, and paper dolls, I decided to post a few other paper-related videos. First is a video showing some cutting tricks for a Möbius strip. I show this to my topology class, then have them play around with Möbius strips—twisting them various numbers of times and…