# Möbius Strip Exploration

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**Objective:**
Explore the properties of the Mobius Strip and related surfaces.

## The Mobius Strip

The Mobius Strip has some surprising features.

**Warm-up question**:
First, make a simple annulus. How many edges does the annulus have? How many sides does this figure have? Draw a loop down the middle, and cut the annulus along that loop. What do you get?

Construct a Mobius Band. (Give the strip a half twist before taping the ends together.)

- With your Mobius Strip:
- Draw a loop down the middle. What do you notice?
- How many edges does the band have?
- How many sides does the band have?
- What happens when you cut the band down the middle?

- Construct a “Double Twisted” Band. (Give the strip a full twist before taping the ends together.)
- Draw a loop down the middle. What do you notice?
- How many edges does the band have?
- How many sides does the band have?
- What happens when you cut the band down the middle? Describe the object you get.

- Complete the following table:
Number of half twists Number of edges Number of edges 0 1 2 3 4 5

- Construct a new Mobius Band. Draw a loop dividing the Mobius Band in thirds. What do you notice?
What happens when you cut the Mobius Band along this loop?
## The Mobius cross

For this activity you will need three crosses. Take two strips, and connect them in the form of a cross.

- Take one of the crosses and tape together two opposite "arms" into an untwisted loop. Then tape the other two arms in another untwisted loop. The result will look like a twisted figure eight. Cut both loops down their middles. What do you get after cutting one of the loops? What do you get after cutting the second loop?
- Take the second cross. Again tape opposite ends into loops. This time make one plain loop and one Mobius band. What do you think you will end up with after cutting? Cut the loops to find out.
- Using the third cross, tape opposite ends together to make two loops. This time twist both loops into Mobius bands. What do you think you will end up with after cutting? Cut the loops to find out.
**Handin:**A sheet with answers to all questions.

## External References

[[1] Mobius Strip] Mobius strip page from Wikipedia