If you took a strip of paper and taped the ends together, you would most likely end up with a belt. It would be a loop with an inside surface and an outside surface. But what if you took that same strip of paper and gave 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. Most of the time, non-Euclidean designs can only be imagined, or drawn like optical illusions. They could never exist outside of an M.C. Escher dream world. Yet the mobius strip is indeed a three dimensional object with only one side. The strangeness doesn't end there, however.
To construct a mobius strip, you will need a length of paper at least two inches wide for best results. A strip of newspaper cut lengthwise will suffice. Take the two ends of the strip in both hands and give one end a half-twist. Bring the two ends together and bind them with tape.
What you should have is a belt of paper with a half-twist. This is now an official mobius strip. Find a pair of scissors and a marking pen 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 marking pen, start drawing a line down the middle of the mobius strip without stopping. Your continuous line should eventually meet up with your original starting point. This proves that the mobius strip does indeed only have one side. Performing the same action on a normal paper loop would only mark the inside or outside surface.
Using the 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 down the new mobius strip will result in two interlocking loops. If you use a wider strip of paper, 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 lengths.
A mobius strip is an excellent way to introduce students to the worlds 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.
By Michael Pollick