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?