NEWS: Möbius Strip Curiosity: SATISFIED

GEEK: Möbius Strip Curiosity: SATISFIED

The first time I ever remember hearing about a thing called a Möbius Strip, I was around ten years old. I was in the middle of reading Ellen Raskin's Figgs and Phantoms, and one of the main characters -- Uncle Truman, a circus sideshow contortionist -- was attempting to fold himself into one. From what I remember, it was an extremely weird book.

But even with obscure young adult novel references aside, the Möbius Strip has long been thought of as the most mysterious shape. Looking like the concrete embodiment of the infinity symbol, it bears the unique characteristic of having only one side, the twist in its somewhat of a figure-eight shape creating a plane that loops back in on itself forever. The cool thing is that, if you have a hard time comprehending it, you can actually make one with a strip of paper and draw a line along the middle of its plane to see for yourself. If all math could be that hands-on, I'd have a doctorate in calculus.

The way it usually works in this world is that things are much more simple to explain on paper than they are to apply in real life; this is yet another way in which the Möbius Strip is quite the individual. A circle is πr2 and a trapezoid is (a+b)h/2, but since its discovery by awesomely-named August Ferdinand Möbius in 1858, no one has ever been able to define the shape of a Möbius strip in an equation.

Until now.

Gert van der Heijden and Eugene Starostin are henceforth to be worshiped as your mathematical gods. These non-linear dynamos published a study this past Sunday, and in this study they presented a solution to the Strip. This is what the abstract looks like:

Okay, so that's great and all, but what does that mean to those of us who didn't necessarily make it to the non-linear algebra phase in their mathletic careers? The simplest way to put it is that the shape of the strip can be determined by its "energy density," which is sort of another way of referring to stored-up potential energy within the folds of the strip. The fatter the strip, the wider the seams; the wider the seams, the flatter the folds; the flatter the folds, the thinner the material; et cetera and et cetera. Fascinatingly, this can be predicted algebraically by our fine friends at University College London.

So you may be saying to yourself, "All right, that's cool, but what does this have to do with me? What application does the mathematical solution to the shape of a Möbius Strip have in my everyday life?" Well, Starostin and van der Heijden do believe their work to have some practical applications. First of all, they expect it to help predict points of fabric tearing, so score one for the fashion world. Secondly, they expect pharmaceutical engineers to find it useful in modeling structures of potential new drugs. Hopefully they do, making this breakthrough useful at a fundamental sense; otherwise, I suppose, it will simply have to be content to enter the Pantheon of Theoretical Mathematics Awesomesauce.

Which, actually, would be perfectly good enough for me.


In 12th grade art class, each table was numbered. When given the freedom to "express themselves," the AP Studio Art students (including one _DictionaryGirl_) decided to number their table "infinity" and made a glitter Möbius Strip for a placard. In other words, Möbius Strips are super rad and Advanced Placement students are pretentious jerks.

While I'm not trying to debase this feat of scientific awesomesauce, I would really like to see the next fad in pubic coiffure to be the Mobious Strip.

Aaaaaand GO!

I helped carve one out of red granite once.
It was fun but easy to confuse what side you were working on.

How could confuse which side you were working on if there was only one side?!

Dear _DG_,

You rock a lot.

Love,
Me

. . . thus the " "

Ahh. I have smilies blocked.

The reality is you still have a three dimensional form. So when you look at a sculpture like this


Keizo Ushio, "Mihama". Granite, 2 m. Year 1990.
(not the one I worked on, just a nice example)

You can see clearly it is 360 degrees with many "sides" . Then contemplate the fact that truly it is one side that simply shows itself to you in different ways at different times as it follows it's path to infinity.

I've found them to be poetic and powerful visual examples of how easily we mistakenly divide things into "sides".

sweet!

i can always count on _dictionarygirl_ to provide me with the random news i so desperately seek.

Moebius?

Moebius?

Imagine how awesome you would have been if you could have played on one?

Bollocks, you're right.

It's a cool effect thought. And there should be a moebius climing frame.

i never get tired of the Curiosity Satisfied Diniosaur.

This thread is Mobius-tastic!

Awesome, awesome article.

And I must say, even though my high school didn't have any AP classes, the "mobius-glitter-infinity placard" thing totally sounds like something my friends and I would have done. Only replace glitter with, like safety pins or thumbtacks or something. Next to another placard offering "free mustache rides." Yeah, we were THOSE guys.

I don't get it. It quite obviously has two sides (if I pick a point on it, I can place each of my index fingers on either side).

If you were to put it on a desk and draw a line as far as it would go, the line would loop around, and be on both of your 'sides'.

Try it. Cut a strip of paper and put a half turn in it, tape the head to the tail, and draw your line.

Though it does really have 3 sides since the thickness of the paper creates two sides.

does it? move your fingers around the strip... they'll eventually meet because they're both on the same face.

it's a trip ain't it?

I <3 the strip.

How about a Mobius Bottle?



Perhaps a Mobius beer stein? A Kleinstein!

John Barth's short story collection Lost in the Funhouse opens with a "Frame Tale" on a thin strip of paper. One side reads "Once upon a time there" and the other side reads "was a story that began." Readers are instructed to twist the strip and tape the ends together so that you end up with a Möbius Strip that reads "Once upon a time there was a story that began once upon a time..." Check it out.