Investigating Möbius Bands

Question: How do the combinations of twists and cuts affect a Möbius band?

Hypothesis:

Materials: · scissors · tape

Procedure:

1. Construct a Möbius strip with zero twists.
2. Predict what would happen if you cut the band in half. Record your prediction.
3. Cut the band in half. Record the result.
4. Again, construct a Möbius strip with no twists. Predict and record what would happen if you cut the band one-third from the edge.
5. Cut the band one-third from the edge. Record the result.
6. Repeat Steps #1 – #5. But this time, add a half twist to the Möbius band.
7. Continue until you notice a pattern emerge.

Cutting Mobius Bands in Half

Number of ½ twists	Number of Sides	Prediction	Result ( # of loops, length, width)
0
1
2
3
4
5