Ep. 9 - The (Very Short) History of the Mobius Strip

Introduction

It's either a famous discovery of mathematical wonder or an obscure piece of trivia that you use to win bets against your less informed friends - either way, the Mobius strip, invented by August Ferdinand Mobius and Johann Benedict Listing, is a strange yet accessible piece of topology (which is the study of problems in space that are just as strange as these). Personally, I find it beautiful for the fact that it's ONE SIDED and will spend this whole blog post informing you of its history, quirks, and other trivia. Enjoy?

What is a Mobius Strip?

A Mobius strip, also known as a Mobius band, is a loop that has any odd number of half-twists in it (though usually just one) which turns both 'sides' of the strip into one. You can try this at home with a piece of paper and tape, and then draw a line along the middle. You'll see that, after you are done, both 'sides' will have that line! Some other things you should try are cutting a Mobius strip in half (also try making the cut about one-third to one side of the strip, and see what happens), making a Mobius strip comic strip (bonus points if it includes time travel!), knitting a Mobius strip, Making a Mobius strip with a 360 degree twist instead, writing an endless Mobius strip poem....the possibilities are endless! There are plenty of websites out there that show incredible crafts and art about Mobius strips, some of which I will list at the bottom of the page.

History of the Mobius strip

The Mobius strip was independently 'discovered' by German mathematicians August Ferdinand Mobius and Johann Benedict Listing. August Ferdinand Mobius was a German mathematician who studied under Carl Friedrich Gauss and worked at the University of Leizpig. He 'discovered' the Mobius strip in his 1858 (in his sixties by that time) while he was studying polyhedra (plural of polyhedron), which are any solid figures with edges, vertices, and flat faces (think of a six-sided die or a pyramid.) Johann Benedict Listing was a younger mathematician of Czech descent who also studied under (and made friends with) Gauss. Benedict described the strip earlier, but did not publish his ideas until 1861. The Mobius strip became a catalyst for the advances of a new field of mathematics called topology (a term coined by Listing), which deals with geometry and shapes without considering shape or size. An idea that the Mobius strip helped define was orientability, which we won't get into but is certainly fascinating, especially when you delve deeper into the theories of how all shapes can be categorised as spheres or many-holed donuts. Search it up and see for yourself! In real life, the Mobius strip has been used in recording tapes, conveyor belts, electronic resistors, typewriter ribbons, and computer print cartridges. There are numerous art pieces based on the Mobius strip, such as Mobius Strip II by Maurits Escher. 

Mobius Tidbits for your friends

Joke 1: (From Ian Stewart's Professor Stewart's Cabinet of Mathematical Curiosities)

Q: Why did the chicken cross the Mobius band?

A: To get to the other....?

Joke 2: (That I invented myself)

Q: Why did the teachers find essays written on Mobius strips biased?

A: Because they only showed one side of the story!

No? Not funny?

Joke 3: (Also of my own invention, though I might have heard it from somewhere?)

Q: Why did everyone read the Mobius strip book?

A: It had the saddest half-twist of all time.

Still not funny?

...

Limerick: (From Ian Stewart's Professor Stewart's Cabinet of Mathematical Curiosities)

A mathematician confided

That a Mobius strip is one sided

               You'll get quite a laugh

               If you cut it in half.

For it stays in one piece when divided.

Fact: The recycling symbol, designed by Gary Anderson, is a Mobius strip.

In conclusion....

It's amazing what humanity can understand with time one their hands - It brings me a little hope for the intelligence of humanity. In the future, I hope that that intelligence is put to the best use, to benefit the world and the environment. This world is full of challenges and problems waiting to be solved. But sometimes, it's nice to just play with paper loops.

-Tomatobean

Sources

Alagappan, Serena. “The Timeless Journey of the Möbius Strip.” Scientific American, Jan. 2021, www.scientificamerican.com/article/the-timeless-journey-of-the-moebius-strip/#:~:text=The%20M%C3%B6bius%20strip%20was%20independently,into%20%E2%80%9Cprojective%20geometry%E2%80%9D). Accessed 9 June 2024.

Ashworth, William. “August Möbius.” The Linda Hall Library, 17 Nov. 2014, www.lindahall.org/about/news/scientist-of-the-day/august-mobius/. Accessed 9 June 2024.

Britannica, The Editors of Encyclopedia. “August Ferdinand Möbius.” Encyclopedia Britannica, 27 Mar. 2024, www.britannica.com/biography/August-Ferdinand-Mobius. Accessed 9 June 2024.

Gunderman, David, and Richard Gunderman. “The Mathematical Madness of Möbius Strips and Other One-Sided Objects.” Smithsonian Magazine, Sept. 2018, www.smithsonianmag.com/science-nature/mathematical-madness-mobius-strips-and-other-one-sided-objects-180970394/. Accessed 9 June 2024.

O’Connor, J. J., and E. F. Robertson. “Johann Benedict Listing - Biography.” Maths History, Sept. 2000, mathshistory.st-andrews.ac.uk/Biographies/Listing/. Accessed 9 June 2024.