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A Mobius strip is a one-sided three-dimensional object that can be made by taking a strip of paper, giving it a half twist, and taping the ends together. It can be used to demonstrate non-Euclidean geometry and the concept of a single surface.
If you take a strip of paper and tape the ends together, you’ll most likely end up with a belt. It would be a loop with an inner surface and an outer surface. But what if you take that same strip of paper and give it a half twist before taping the ends together? The result would be a fascinating geometric oddity called a mobius strip.
A Mobius strip is an example of non-Euclidean geometry made real. More often than not, non-Euclidean drawings can only be imagined or drawn as optical illusions. They could never exist outside MC Escher’s dream world. Yet the Mobius strip is really a three-dimensional object with only one side. The weirdness doesn’t end there, though.
To build a mobius strip, you’ll need a length of paper that is at least two inches wide for best results. A strip of newspaper cut lengthwise will suffice. Grab both ends of the strip with both hands and twist one end halfway. Bring the two ends together and tie them with tape.
What you should have is a paper belt with a half twist. This is now an official mobius strip. She finds a pair of scissors and a marker to perform the rest of the experiment.
The first principle to demonstrate with a mobius strip is the concept of a single surface. Using a sharpie, start drawing a line in the middle of the mobius strip without stopping. Your solid line should eventually meet up with your original starting point. This proves that the Mobius strip actually has only one side. Performing the same action on a regular paper ring would only mark the inside or outside surface.
Using scissors, cut along the line created by the pen. Instead of becoming two separate loops, a mobius strip will form a single loop twice as large as the original. Cutting the new Mobius strip will result in two interlocking rings. If you use a wider paper strip, the mobius strip will continue to form continuous or interlocking loops. You can also vary the experiment by cutting the loop into three equal sections or sections of varying length.
A mobius strip is a great way to introduce students to the world of science and geometry. The experiments are simple enough for young children to perform, but the science behind the illusion should fascinate older students as well.
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