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Once you've made your Möbius Strip you can cut it along the middle down the whole length of the strip. M.C. Escher's "Mobius band II". Construct a Möbius band by giving a paper strip a half twist before taping the ends together. With your Möbius Strip: Draw a loop down the middle. What do you notice? How many edges does the band have? How many sides does the band have? What happens when you cut the band down the middle?

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Photo coming soon. However if we trace this resulting strip in the same way we did above we realize that this strip is not a möbius band, it has two sides and two edges.

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s. 1000 × 481, JPG 8.47 × 4.07cm, (3.33 × 1.60") 300 dpi Standard License Cut your loop in half.
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Have the students cut their Mobius bands in half. Make sure they begin with a hole in the middle. I just wanted to clarify our terminology. After we understood what the word orientable means we of course started to cut the strips in half. The ring, cut along the centerline gave two similar rings, the Möbius strip gave a longer $4$ times twisted strip which is orientable.

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Make some more Möbius bands but this time make one with two half twists, This shape should have two edges and two faces.

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Cut the Mobius strip in thirds and you make two linked loops one with one half twist and one with 4 half twists. Mark a line 1/n from one side of a Mobius band of width W, then cut along this line. There will be a strip left in the middle of width W - W/n-W/n.

If you cut such a thing in half, you get two links of the same sort interlinked. Mobius Bands / Mobius Strips (VIDEO!) Everyone, at some point in one’s life, simply must cut a Mobius band in half. This little video gives a tiny discussion as to what is going on when one does.