Discovery Express
  • Welcome!
  • Blog
  • Ask Dr. E!
  • Check out our store!
  • 9 Apples Math Game
  • Your questions answered!
  • Events and Announcements
  • About/Contact

Mobius Strip

3/29/2017

0 Comments

 
If you are familiar with the concept of infinity, you would recognize its symbol that looks like an eight on its side. That symbol is called a lemniscate, which is Greek for “ribbon”. The lemniscate is directly related to a real-world mathematical shape: the Mobius Strip!
Picture
The Mobius strip is particularly fascinating because it is a shape that has only one side and one edge! Let’s compare it to a simple piece of paper: if you draw a line on one side of the paper, there’s nothing on the other side. There are multiple edges to this paper (or just one, if it’s a circle). For a Mobius strip, you can only draw on one side, because there is no other side. If you try to trace your finger along the edge of the strip, you’ll be able to go around and around and around, but it might look like you’re tracing the “other” side, but you never lifted your finger!

This means that a Mobius strip is “non-orientable.” Most objects and surfaces are orientable, and it can be tested by attempting to paint the sides different colors. With a cube, you can have up to six different colors, but with a Mobius strip there’s only one. There’s a famous painting, titled “Mobius Strip II” by M.C. Escher where ants are pictured walking along a Mobius strip. Just like what we’ve described above, the ants (or anything really!) could walk along the strip indefinitely!

The Mobius strip isn’t just some random shape made up for fun; it can actually be applied to real life! ​
Picture
Conveyor belts have used the Mobius strip design, which made it last twice as long. That’s because the entire surface of the strip was used, not just one side got worn down like it would in a normal ring. Manufacturers have stopped using the Mobius strip system because modern-day technology allows multiple layers to support the belt. Typewriters also used the strip’s design in their ribbons. With a ribbon twice as wide as the print head, both halves of the ribbon can be used evenly. This saved a lot of money back when typewriters were popular!

History of the Mobius Strip

In 1858, August Ferdinand Mӧbius invented this shape and named it after himself. John Benedict Listings then independently discovered it and was published following his findings. The two German mathematicians never collaborated, but both are recognized as the strip’s founders. August Mӧbius also singularly discovered the Mobius Ladder, which is an alteration of a prism graph with a twist in it. Another similar mathematical shape is the Klein Bottle, shown below the ladder.
Picture
Picture
Mobius Experiments!
You can make your very own Mobius strip at home with a piece of paper, some scissors, and tape.
  • Cut out a strip of paper about 1-2 inches wide
  • Twist one end halfway
  • Tape it together
Now you can try out the different examples from before: try to draw a line on “both” sides, or paint them two different colors. If you cut it lengthwise down the middle, what happens? There are many more videos out there that describe other interesting things you can do with a Mobius strip, like this one!


References:

Weisstein, Eric W. "Möbius Strip." MathWorld--A Wolfram Web Resource. Accessed March 25, 2017. http://mathworld.wolfram.com/MoebiusStrip.html
Teplitskiy, Abraham. “Student Corner: Mobius Strip”. The Triz Journal. January 1, 2007. https://triz-journal.com/student-corner-marvel-of-the-mobius-strip. Accessed March 26, 2017.


Image Credits:

Benbennick, David. “Mobius Strip”. Released into the public domain. Uploaded on March 26, 2017 from wikimedia.org
Kapp, J. Lehman. “Endless Belt”. Released into the public domain. Uploaded on March 26, 2017 from US Patent #3991631
Eppstein, David. “Mobius Ladder”. Released into the public domain. Uploaded on March 26, 2017 from wikimedia.org
“Structure of a Klein Bottle”. Released into the public domain. Uploaded on March 26, 2017 from wikimedia.org
0 Comments

Your comment will be posted after it is approved.


Leave a Reply.

    Follow us on Pinterest!
    Picture
    Check out our new game for math education, grades 1-7!

    Archives

    February 2019
    January 2019
    December 2018
    November 2018
    October 2018
    September 2018
    August 2018
    July 2018
    June 2018
    May 2018
    April 2018
    March 2018
    February 2018
    January 2018
    December 2017
    November 2017
    October 2017
    September 2017
    August 2017
    July 2017
    June 2017
    May 2017
    April 2017
    March 2017
    February 2017
    January 2017
    December 2016
    November 2016
    October 2016
    September 2016
    August 2016
    July 2016
    June 2016
    May 2016
    April 2016
    March 2016
    February 2016
    January 2016
    December 2015
    November 2015
    October 2015
    September 2015
    August 2015
    July 2015
    June 2015
    May 2015
    April 2015
    March 2015
    February 2015
    January 2015
    November 2014
    October 2014
    September 2014
    August 2014
    July 2014
    June 2014
    May 2014
    April 2014
    March 2014
    February 2014
    January 2014

      Tell us what interests you most, and we'll send you a free PDF of a lesson in that subject!

    Submit

    Categories

    All
    Age 10 12
    Age 12 14
    Age 14 16
    Age 16+
    Age 8 10
    Anatomy/Physiology
    Biology
    Chemistry
    Engineering
    Food Science
    Geology/Earth Science
    Health Science
    Math
    Microbiology
    Physics
    Plant Science
    Psychology
    Weather Science

Proudly powered by Weebly