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!
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.
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
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.
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