Today Polish readers of “Gazeta Wyborcza” (most popular newspaper in my country) can read about experiments with Möbius strip, together with the information about my blog.
Since it’s not available for non-Polish speakers, I decided to describe these experiments here as well.
- Take a strip of paper (for example cut it out from a sheet of paper), twist one end by 180 degrees and join two ends (use glue or a stapler). You just made your own Möbius strip.
- Draw a line lengthwise around the strip, in the middle of its width, as long as you can. Where did you finish?
- Now take scissors and cut along this line. Did you get two thinner strips?
- Prepare a Möbius strip as before.
- This time draw a line in one third of its width. Where did you end up?
- Now cut along this line. Did you get the same result as in the previous experiment?
Pretty cool, right? According to Matt Parker, 19th century German mathematician August Ferdinand Möbius loved this strip so much that named himself after it 🙂 This figure has only one side and one edge, unlike the strip without a twist. This is why when we draw a line, we end up in the same point. We can colour the whole strip without lifting the pen!
You can experiment with Möbius strip by adding more twists before attaching ends or glueing together two strips. Enjoy!