Wonder Friends who remember learning about infinity might recall the unique symbol for infinity called the lemniscate, which means “ribbon.” Did you know that the lemniscate is similar to a real-world mathematical shape? It’s true? Drumroll please…Wonder Friends, meet the Mobius strip!
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.
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.
When you look closely at a Mobius strip, you’ll see that it would be impossible to paint it with two different colors. It might also help you to imagine ants walking along the Mobius strip. As M.C. Escher showed in his famous picture, Möbius Strip II (Red Ants), ants could walk on a Mobius strip on a single surface indefinitely!
Perhaps it’s the possibility of traveling indefinitely in a loop along a Mobius strip that makes some people associate the Mobius strip with the concept of infinity. Perhaps that’s also why the lemniscate symbol for infinity resembles a Mobius strip!
If you’re WONDERing whether the Mobius strip is simply a mathematical curiosity, it’s not! It has practical applications. For example, conveyor belts have been designed as giant Mobius strips. Why? They last longer because the entire (singular) surface area gets the same amount of wear and tear. Similar applications have been used in recording tapes and printer and typewriter ribbons.