## Puzzle: Let’s (Un)Do the Twist!

Today, while walking our dog, I had an idea for the puzzle shown below. Here is a printable pdf. I hope you enjoy it. If you would like a hint as to how to solve the puzzle, read about this puzzle from the great puzzle master Sam Loyd; it was the inspiration for my puzzle.

## Make a Real Projective Plane (Boy’s Surface) out of Paper

I am teaching an undergraduate course in topology. We are now looking at what we get if we take a square and glue the sides together. (These are called identification spaces.) We are assuming that our spaces are made out of very stretchy rubber. So, if the space begins as a square, we could, for instance,…

## The Magnificent Möbius Band

As I write this blog post, we are all either struggling with the impact of the COVID-19 virus or waiting nervously as cases start to rise in our area. I am currently teaching remotely. My college students are scattered around the globe, and we are interacting through various online methods. This semester I am teaching…

## 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…

## Kindergarten Mathematics (part 2): a report

Last week I wrote a blog post asking for suggestions for math to present to my son’s kindergarten class. My readers posted many great comments. Thank you all. Today was the big day,… and it was a great success! I began by talking about what I do. My son introduced me as a math teacher….

## 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…