Math Art: Mobius Strips

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Art and Science: Mobius Strips •


I wish math art was a big part of my math education when I was a kid. It’s not that I was bad at math. On the contrary, I did quite well in math, but that’s just because I was good at remembering the rules. Being able to physically make some math would have rendered it far more interesting, though, and perhaps math would have lingered as something I wanted to pursue instead of leave behind as a series of boring tests.

Have you ever made a Mobius strip? It’s a simple thing to make, but it will blow your (and your kids’) minds. In case you don’t know what it is, here’s what you do: take a strip of paper. Fasten the ends together, but give the paper a little twist first.

Art and Science: Mobius Strips •


Take your finger (or use a pen), and run it along one side of the strip. Follow it all around, and you’ll find that you end up on the opposite side of the paper, without having lifted your finger (pen) up off the paper. That one little twist turns the strip into what is called a nonorientable surface.

That’s as mathy as I will get here, because this hurts my brain:

Mobius Math


As if the regular Mobius strip weren’t cool enough, grab a pair of scissors, and cut it lengthwise, all around the strip. This is what you get:

Math Art - Mobius Strips •


Is that not mind-boggling? One big loop! This loop contains 2 twists. But don’t stop there; cut this strip down the middle and get…

Math Art - Mobius strips •

…which is 2 strips, each with 2 full twists.


Don’t stop cutting! It’s still wide enough to cut!

Math Art - Mobius Strips •

Not sure what this is, but it’s fun to throw it around in the air and pretend it is a monster.


The work of M.C. Escher is always a favorite with kids because of the optical illusions he wove into his pieces. Check out his 2 works based directly on Mobius strips:


Escher Moebius Strip1 •

Moebius Strip I
wood engraving and woodcut
photo credit:

Escher Red Ants Mobius Strip •

Moebius Strip II (Red Ants)
Woodcut printed from three blocks
photo credit:


Looking for more Escher inspiration? Try these books:




  1. Audrey
    06/03/2013 / 4:57 pm

    I totally agree. Visual math makes math so much more intriguing and accessible. I love the YouTube videos of that genius math girl and the things she does for that very reason.

  2. 06/04/2013 / 2:46 am

    Alright, we gotta do this. This is way cool!

    Way way cool!

    Thanks for sharing!

    • 06/04/2013 / 3:51 pm

      Yay! Make many. They’re fun to just stare at for a while, even.

  3. 06/04/2013 / 8:28 am

    That is so cool and the math equation hurts my brain too!

    • 06/04/2013 / 3:48 pm

      Yep, total shut down when I see math like that- I’m scared about 5th grade math…

    • 06/04/2013 / 4:16 pm

      That’s a lotta love. I love it, too- it’s so simple and wonderful.

  4. 06/04/2013 / 9:51 pm

    I don’t understand the maths part of this at all… but mobius strips are just way cool, even if you don’t understand them! LOL

    • 06/05/2013 / 10:47 am

      Maybe they’re even better when you don’t understand them- more mystery!

  5. 06/05/2013 / 6:00 am

    Wow, awesome! I don’t understand the maths either. I thought I’d left cos and sin behind me, oh, twenty years ago… 😉

    • 06/05/2013 / 10:48 am

      It’s okay. You can leave them far behind- all you need now is some paper and a little tape- no thinking required!

  6. 06/05/2013 / 10:06 am

    My math whiz kids will love this. As for me? Mind blown.

    • 06/05/2013 / 10:49 am

      Oh, I’m so glad they’ll love it! I wasn’t sure if this was one of those, “Oh yeah, Jeanette. We all already know about this. What else ya got?” things. I’m glad I could blow your mind a little, too.

  7. Sarah Ozurumba
    06/14/2013 / 7:53 am

    You could take this project a step farther and have kids create an abstract relief sculpture with mobius strip pieces by gluing them to a background paper and also to each other. It helps kids understand the concept of space as an element of art.

    • 06/17/2013 / 8:17 pm

      I LOVE this idea- I think we may need to try it, and I know it will be a great process that ends up looking really great, too. I love when people creatively brainstorm here!

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