Choose Your Own Möbius Adventure — Part III

Geometry Level 3

What happens when you cut a Möbius strip in half (down the center)?

After cutting you will have:

Details and assumptions

This problem is part of the Choose Your Own Möbius Adventure series.

A single strip with 2 twists Two Möbius strips of the same length A single, longer Möbius strip Two strips with no twists

2 solutions

Muhammad Usman
Jan 25, 2014

i do this practical

lol. admitted it

敬全钟 - 7 years, 4 months ago

same

Daniel Wang - 7 years, 4 months ago

I tried to use the image to help me visualize. From the uncut area, if the ant is 1/4 of the distance between the two edges and walked parallel to the edge, at some point it would reach 3/4 of the distance between the two edges, on the back side of the strip (so after the paper is cut, it would be on the other half of the strip). Continuing along, it would eventually end up where it started, on the same side of the paper, so there was a single strip and 2 twists (going from front to back of strip, then going back to front).

James Shi - 7 years, 4 months ago

Hint: What happens when you cut the Mobius strip in one-third (as in part 4)? How does that explain the answer in part 3?

Calvin Lin Staff - 7 years, 4 months ago

I have never heard about the Mobius strip that's what i couldn't understand

murali dharan - 7 years, 4 months ago

It is much easy to do it practically...

Amlan Mishra - 7 years, 4 months ago

me too... its much easier

Care Phongsermsuk - 7 years ago

Ramji Varadarajan
Apr 25, 2014

A Möbius strip is formed by creating a ring with a single half-twist from a flat band. When you cut a Möbius strip in half (down the center), the ring with a single half-twist from that flat band gets cut into two halfs forming two thin twists. Since a Möbius strip has only one side a single strip with 2 twists are formed.

Choose Your Own Möbius Adventure — Part III

2 solutions

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