10 Things You Probably Don't Know About Möbius Strips

Sterling Silver Mobius Strip PendantYou are probably aware that a model of a Möbius strip can be created by taking a paper strip, giving it a half-twist, and then joining the ends of the strip to form a loop with just one surface and one edge.

And you may also be aware that the Möbius strip gets its name from German mathematician and astronomer August Ferdinand Möbius who discovered it in 1858.

But here are ten things about that you probably didn’t know about Möbius strips:

1. The strip was almost simultaneously discovered by mathematician, physicist and surveyor Johann Benedict Listing. So it could easily have ended up being called a Listing Strip. Not quite so funky eh? ;-)

The oldest surviving depiction of a Möbius strip dates from Roman times.

2. The oldest surviving depiction of a Möbius strip predates Möbius’ and Listing’s “discovery” by more than 1500 years, appearing as it does on a Roman floor mosaic from the ancient town of Sentinum in Italy, depicting Aeon with Zodiac. The mosaic dates back to the 3rd century A.D.

3. Cutting a Möbius strip along the centre line with a pair of scissors yields one long strip with two full twists in it, rather than two separate strips; the result is not a Möbius strip. On the other hand, cutting along a Möbius strip a third of the way in from the edge, creates two strips. One is a thinner Möbius strip while the other is a longer but thinner strip with two full twists in it.

A depiction of a Klein Bottle4. A closely related and equally curious geometrical object is the Klein bottle. While a Möbius Strip has one surface and one edge, a Klein Bottle has a single surface and no edges. Alas this means it can't exist in 3-dimensional space. So this 2D image merely shows a 3D model. An actual Klein Bottle would need 4D and would not have the intersection shown on the 3D model i.e. the "spout" would not pass through the "wall" of the "bottle".

5. Practical applications of Möbius strips include conveyor and belt drives that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the recording time).

6. The Möbius strip can be found in several natural phenomena, including the trajectory of charged particles trapped in the magnetic field of the Earth, as in the van Allen belts. Some protein molecules have the shape of a Möbius strip.

Möbius Strip II by M.C. Escher

7. The Dutch artist M C Escher, famous for his work depicting mathematical and impossible objects, produced a number of works featuring Möbius strips, with Möbius Strip II, depicting red ants walking on a Möbius strip, probably being the best known.

8. You will often see a Möbius strip described as a nonorientable surface but this is rarely explained. The key is to think of the strip not as a strip of paper (which has thickness) but as a rectangular tunnel through which you can travel. If you begin to travel though this tunnel you will get back to where you started, but when you get there what was the floor will now be the ceiling (and vice versa) and the wall that was to your left will now be to your right (and vice versa). A true Möbius strip has no thickness.

9. Möbius strips occur in various works of fiction including Sylvie and Bruno Concluded (1893) by Lewis Carroll (best know for Alice's Adventures in Wonderland (1865) and Through the Looking-Glass, and What Alice Found There (1871)) and The Wall of Darkness (1946) by Arthur C Clarke (best known for 2001: A Space Odyssey (1968)). My own personal favourite is Star, Bright (1952) by Mark Clifton in which two gifted children use a Möbius strip as a stepping stone to discovering time travel.

A number of Möbius strips on my workbench10. There are several ways of depicting a Möbius strip. As we have seen from M C Escher’s artwork, one of them looks, rather appropriately, like the mathematical symbol for infinity (although this not where the symbol originates). Others look like a ring with a twist. For my Möbius strip pendants, each of which is hand made, I aim for a slightly more random shape such that no two are exactly the same.
So how many did you know?

I have to confess that although I knew most of them, having been fascinated by Möbius strips since I read Star, Bright while in junior school, I wasn't aware of the Aeon with Zodiac mosaic until I stumbled across it while checking some details for this article. I always figured that people would have been aware of the strip before Möbius, but a Roman mosaic associating it with the zodiac... Wow!

I hope you enjoyed this article. Please comment if you know of any more Möbius strip related facts and be sure to check out my sterling silver pendant version at:

https://www.etsy.com/uk/listing/561961082/sterling-silver-mobius-strip-pendant


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