Mobius Strip Activities

Instructor: Nora Jarvis

Nora has a Master's degree in teaching, and has taught a variety of elementary grades.

What exactly is a Mobius strip? What does this little strip tell us about physics? While doing the activities in this lesson, your students will grapple with those questions and get to know all about Mobius strips.

What Is a Mobius Strip?

Albert Mobius, a 19th century astronomer, developed the Mobius strip as a representation of a mathematical puzzle. The Mobius strip is a rectangular strip that has been joined at each end after one end is twisted 180 degrees. The end result is a loop that looks like it's two-sided, but actually only has one side.

The following activities will allow your students to make their own Mobius strip and learn more about this one-sided nonorientable surface. As your students work, be sure to help them make connections between this curious optical illusion and other concepts in math and physics.

How to Make a Mobius Strip

Give your students the following directions to make their own Mobius strips:

  • Use paper to create a thin rectangular strip (imagine that you are making a paper bracelet for your wrist to get the shape right)
  • Turn one end 180 degrees
  • Tape the two ends together

cap=An example of a Mobius strip

After your students have made their strips, ask them to choose a starting point and draw a continuous line until they reach their starting point again. Help your students notice that they were able to draw on just one side of the strip even though it is twisted.

Ask your students:

  • How is it that the Mobius strip looks like it's twisted but has one continuous side?
  • Is there a way you could alter your Mobius strip to have two sides?

Cut Up Your Mobius Strip

This activity is intended to be done after your students have created their first Mobius strip. Pass out scissors and ask your students to cut along the line they drew in the previous activity. Ask your students the following discussion questions:

  • What happened to your Mobius strip when you cut it in half?
  • Do you think there's any way you could cut your Mobius strip and have the two pieces separate?

Listen to your students theories about how they might cut the strip so that the loops would separate. Encourage your students to test out their theories. You should include additional paper and tape for your students to keep creating and testing their Mobius strips. Encourage your students to notice patterns in their Mobius strip exploration.

Mobius Strip in Art

Pass out photographs of the following art:

  • Mobius Strip by Robert R. Wilson
  • Endless Ribbon by Max Bill
  • Parade of Ants by M.C. Escher

In small groups, have your students examine the artwork and identify the places where they see Mobius strips. Have your students discuss why they think each artist chose to use Mobius strips in their art. Pass out a Venn diagram and have your students compare and contrast the different ways that the artists use Mobius strips.

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