NCTM Meeting in San Diego

Mobius Strips

Paul Kelley
Anoka High School
Anoka, MN 55303
pkelley@informns.k12.mn.us

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Back to NCTM San Diego: Presentation Summary
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Mobius Strips

For this activity, you will need five strips of paper per student. Each strip should be approximately 3 x 14 inches. Each student will also need about two feet of tape (either transparent tape or masking tape will work), a pair of scissors and a pen or pencil.
  1. First, make a Mobius strip. Use one strip of paper. Put the two ends together, and give one end a half-twist. Tape the paper together this way, being sure to tape across the entire strip.

  2. Draw a line down the middle of the strip. Continue drawing until you meet up with your starting point. Could you have drawn this line without lifting your pencil from the paper? Without turning the paper over? Could an ant walking along your line walk until he met his starting point, without walking over an edge of the paper? How many sides does a Mobius strip have? What do you think will happen if you cut along that line?

  3. Cut along the line. What happens? What would happen if you cut in half again? Try it and see.

  4. Make another Mobius strip. If you cut 1/3 of the way, what will happen? Do it. Note: By this time, many students will give up on the "guessing" part of the activity, or else give absurd opinions.

  5. Make another strip, but use a full twist on the end this time, instead of a half-twist. Cut in half. Note what happens. Then, cut again.

  6. Put two of your strips together - one should be a Mobius strip, the other a regular loop. Tape them together at right angles, bisecting each other. What happens if you cut along the middle of both? Do it.
Although this is a "fun" activity for students, it should be pointed out that there are real-life applications of Mobius-type strips. For instance, many ribbons for typewriters or computer printer cartridges are Mobius strips, the better to utilize both sides of the ribbon. Also, some belts on cars and farm machinery are put together in this way, in order to provide for more uniform wear and tear on the belts.


Paul Kelley
Anoka High School
Anoka, MN 55303
pkelley@informns.k12.mn.us

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