Thought you would never be able to see möbius strips and klein bottles in the real world? Think again.
The Mobius strip — sometimes called the Mobius band — is named after mathematician and astronomer August Ferdinand Möbius, who came up with the idea in September 1858. Curiously, German mathematician Johann Benedict Listing independently developed the same idea a few months earlier in July 1858. Unfortunately for Listing, one of the most famous surfaces in mathematics bears the name of Möbius, not Listing.
So what’s the big deal with the Mobius strip? It’s quite simple, actually. The Mobius strip is famous because it has only one side and one edge.
To see what we’re talking about, it helps to make your own Mobius strip (see today’s Try It Out! section for instructions). All you need to do is cut a long strip of paper, put a half twist in it, and glue or tape the ends together.
While the original piece of paper clearly had two sides (mathematicians would say the original piece of paper was orientable), the Mobius strip you created has just one. Don’t believe us? Try drawing a line on both “sides” of the Mobius strip without picking up your pencil. Can’t do it, can you?
That’s because the Mobius strip is non-orientable, meaning it has only one side. Most surfaces are orientable. To test whether a surface is orientable, ask whether you could paint it with two different colors. Examples of orientable surfaces include a simple sheet of paper or a sphere.