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 topology, one of my favorite classes to teach. The students are second-semester seniors or junior. So for many of them, this is their last mathematics class. Near the end of the semester, I often take a break from the theory and proofs and have a class where the students play with Möbius bands and related objects—making them out of paper, cutting them apart, forming conjectures, and so on. It is usually a welcome April stress-reliever. This year, they will have to do it at home on their own. I made the following video for them to follow along.

I made the video for my advanced mathematics students, but I hope that the video could also be enjoyed by people of all ages and mathematical backgrounds. I have done this activity with kids as young as kindergarten. Everyone seems to enjoy it. I can’t stress this enough that it is best when you do the activity. It makes much more of an impact than watching it. By the way, when I do the activity for younger kids I tell them a story (about a circus coming to town) to go along with the activity. (I wrote about it here.)

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Have fun, and if you do this with your kids or students, leave a comment (or a photo!) below.

If you would like another take on this idea, you can read my post about making zip-apart Möbius bands.

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Or you can read about making Möbius band ambigrams.

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2 Comments

  1. Frank Richeson says:

    Mom and I watched the video a few days ago and were very impressed! I’ll check out the other exercises…

    Love, Dad

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