Mobius Strip

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Bizarre shapes and strange connections make math interesting and nothing is more strangely fascinating than the simplicity and topology of the Mobius strip. The nineteenth-century German mathematician A. F. Mobius discovered that it was possible to make a surface that has only one side and one edge.

Although such an object seems impossible to imagine, making a Mobius strip is very simple: take a strip of ordinary paper and give one end a twist, then glue the two ends together. And there it is. If you begin drawing a line lengthwise down the strip, after one full revolution you will be at the point where you started but on the opposite side of the strip! Drawing the line through another full revolution will find you back at the beginning.

Mobius strips are fun to play with, but industrial engineers have made good use of the shape as well. Conveyor belts are often designed as Mobius strips so that the surface wears out half as fast.

If you cut a mobius strip lengthwise down the center until you wind up back at the beginning, can you work out what will happen to the strip?

Posted: December 14, 2007
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