Found Math

Maybe you didn’t notice, but the poster hanging up around campus for Dorian Small‘s recent concert in Norman was highly mathematical.  It was the Klein Bottle Fish:

doriansmall1

Dorian Small is unorientable.

What is a Klein Bottle?  It’s a non-orientable surface; which means there is no uniform way to assign directions on the surface.  In particular, that means the Klein Bottle has no inside!  But that doesn’t stop people from selling Klein Bottle bottles and Klein steins!

Another more easily imagined example of a unorientable surface is a Mobius strip:

The Mobius Strip

The Mobius Strip

If you were to paint a Mobius strip by starting somewhere, merrily painting along until you’ve done one side, you’d discover that you’ve actually painted the whole thing! The same is true for a Klein Bottle.  These videos give a very nice explanation:

P.S.  For a neat trick, make a paper Mobius strip and cut it down the center all the way around.  But before you actually do it, double points if you can figure out what will happen!

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8 thoughts on “Found Math

  1. The 3-d animation of the klein bottle was fantastic and a lot easier to visualize than the pipe cleaners. This is cool stuff. Another cool example is the figure 8 klein bottle. Worth checking out.

  2. I have never heard of a klein bottle before. I didnt really understand what they meant by it has only one side until the first youtube video. When the lady ran her fingers around the mobius strip and ended up where she started (on the same side) was awesome. The 3-D animation also helped me get a grasp of the figure. That was an interesting blog! Definitely going to try to make my own Mobius strip!

  3. Has anyone read Martin Gardner’s “The No-sided Professor”? It’s a short story based on the Möbius Strip… Gardner is an Oklahoman, and I think his son is an Education professor here at OU.

  4. Right, not only is Martin Gardner an Okie, he lives right here in Norman. He’s this amazing guy who’s in his 90’s and is still writing books like crazy. I’ll have to check this one out – thanks for the recommendation!

  5. Pretty interesting post… somewhat tricky to visualize beforehand. You can cut the mobius strip several more times and get new results. There’s a website here, with pictures for 2 and 3rd cut as well as a short explanation of what is happening.
    http://www.exo.net/~pauld/activities/mobius/mobiusdissection.html

    On a side note, I find it funny that pizza is of equal importance to math, based on the tag cloud 🙂

    • Alex,

      Thanks for the link!

      As a side note, pizza is of equal importance! 🙂

  6. I was actually not introduced to a mobius strip until this past semester. I had heard of it before, but it was never explained. At a conference I attended, a peer showed me her ring and how it was a mobius ring. In fact, it was her engagement ring! It’s tempting to have my ring this way, also, so no matter where I go or what I do, I’ll have a little bit of math on hand. Like others above, I hadn’t heard of a Klein bottle either until this post. I checked out the figure 8 Klein bottle Derek suggested, too, and it’s pretty cool!

  7. When I was in middle school, we used to make mobius strips out of newspaper all the time. I know I didn’t understand how cool they really were at the time and how much math they had involved in them, but it was wild that you could make something so seemingly complicated out of a simple (and straight) strip of newspaper!

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