Mobius Strip
A mobius strip has only one side. It sounds impossible, but it does. To understand it, you have to make one. Make a mobius strip by twisting a strip of paper 180 degrees and tape the ends together. If you color each side a different color before you start, the fact that it only has one side will be more obvious. If you still can’t figure it out, trace your finger all the way around it.
The Mobius Strip is named after August Ferdinand Mobius. He was an astronomer and a mathematician. Mobius was born in 1790. He found out about the mobius strip in the September of 1858. His ideas on it went in an article in 1865. Actually, the first one to both discover it and publish what he found out was Johan Benedict Listing. He lived from 1808 to 1882. He first discovered it in July 1858 and published his findings in 1861.
If you make a mobius strip, then cut it length-wise (all the way around) you will end up with a loop that is twice as long as your original mobius strip. It will have two 180 degree loops in it. If you cut it another time, there will be two of the same kind of loops interlinked. Cut it another time on each side, there will be four of those loops interlocked.
Similar to the Mobius Strip is the the Klein Bottle. It was invented by Felix Klein, who lived from 1849 to 1925. It is a three-dimensional shape that is one-sided like a mobius strip. It can only exist as a computer generated model. Cut it in half length-wise, it turns into two mobius strips.
Mobius strips have been put to use by engineers. Some conveyor belts are made with a half twist so that the wear and tear on the belt is equal on both sides - the belt only wears out half as fast. Continuous loop recording tapes were made in this way - to double the recording surface using the same amount of tape!1
The Afghan Bands is a magic trick that uses mobius strips. To perform the trick: Before the show, cut three strips of paper. For one of them, just tape the ends together. For the next one, make a mobius strip. For the last one, twist it 180 degrees in one place, and do it again in another place. During the show, cut them in half lengthwise. The first one will turn into two loops, as expected. The second one, as I have said before, will turn into a loop that is twice as long and has two 180 degree twists in it. The third one will turn into two loops that are linked together. The trick is to not let the audience know about the twists.
Mathematics in the Universe
1. BCC on the Mobius Strip
