Although the Möbius strip is named for German mathematician August Möbius, it was co-discovered independently by Johann Benedict Listing, a completely different German mathematician, but at around the same time in 1858. Weird, right? But that’s not the only strange thing about the Möbius strip. It’s a non-orientable surface. This means it has a path that will take a traveler back to their point of origin. Are you completely confused now? That’s okay! Just watch the video and I’ll explain.


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Download Student Worksheet & Exercises


So a paradox is something that seems to contradict itself – it sort of makes sense, but then again it doesn’t really make sense. It seems odd that a paradox fits into a math lesson, yet they do exist in mathematics. The Möbius strip is a fun example of a paradox that you can actually touch. What happens when you cut the Möbius strip like I show in the video?


Exercises


Identify the figures shown below:


1. mobius-strip-1 2. mobius-strip-2 3. mobius-strip-3 4. mobius-strip-4
  1. How many faces does a Möbius strip have?
  2. How many edges does a Möbius strip have?
  3. Given a strip of paper, at which angle should one rotate one of its ends before connecting to form a Möbius strip?
  4. When a person cuts along the length of the Möbius strip to come up with a longer one, how many twists does he observe in the final strip?
  5. Say you want to get two Möbius strips from an existing one. How would you do it?

mobius-strip-9


  1. If you cut the Möbius strip along its length as shown in 9 above, how many connected strips would you get?

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Comments

2 Responses to “Möbius Strip”

  1. Isn’t that cool? I Love this experiment!

  2. Michelle Stevens says:

    I cut the strip again after the first cut and I got two strips linked together!!!! 🙂