Möbius Strips

Our next classroom activity was an investigation of Möbius strips -  surfaces that have only one side and one boundary. An easy way to create a Möbius strip is to take a paper strip, give it a half-twist and join the ends of the strip to form a loop.

We started class by going over the basics of Möbius strips with 1, 2, 3, 4 and 5 twists - counting the number of faces and edges. Next, we analysed the behaviour of Möbius strips with a single twist when they are cut in different ways (at distances of ½, ⅓ and ¼ from the centre) and made conjectures prior to cutting about the nature of the resulting strips that would be formed. Once they had had a chance to play around with the strips themselves, we showed them a video lecture by Dr. Tadashi Tokieda, a professor of mathematics at Stanford University.

Our kids were fascinated by the Möbius strip - particularly with trying to identify patterns regarding cutting a 1-twist Möbius strip at different distances from the edge including the case where bisection implied that the width of the middle strip was zero. They were keen on exploring cases outside the class dealing with multiple twists and cuts so we went deeper into the topic than we initially planned! Since making smart conjectures was one of the key elements of the course, cutting the Möbius strip and its variants lent itself well to that goal.

The Möbius strips activity - observe the piles of cut out strips with different twists on the floor of the class! Our little mathematicians hard at work :-)

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