##

## the MOBIUS STRIP and the ANNULUS

which is this?

1) How do you make a mobius strip?
How do you make an annulus?
2) Why does a mobius strip have only one side?
3) How many sides does a strip made with 2 half twists have?
One with 3 half twists?
How many sides does a strip with 46 half twists have?
One with 511?
4) How many edges does the annulus have?
How many edges does the mobius strip have?
How many edges do the strips with 2, 3 46 or
511 half twists have?
5) a) Is there a connection with the number of sides
and the number of edges? Explain.
b) What is the connection to the number of
half twists and the number of sides?
c) What is the connection to the number of
half twists and the number of edges?

#### Answer the following for (a) the annulus (b) the strip with two half
twists and (c) the mobius strip.

6) What results when you cut the strip down the middle?
Explain precisely.
(What are the pieces, how are they linked, etc)
7) What if you cut the pieces resulting from above down the middle
(i.e. cut the original strip into fourths)?
8) What if you cut the original strip into thirds?
How many cuts does this require?
9) Summarize the overall pattern and give
as many conclusions as you can.

#### BONUS: the KLEIN BOTTLE

##### A SURFACE WITH ONLY ONE SIDE!!!

It passes through itself like a ghost through a wall!

##### DOUBLE BONUS:

The Klein bottle results from sewing together two mobius strips along
their single edge.EXPLAIN.

**Chaim Goodman-Strauss**
Dept. Mathematics
Univ. Arkansas
Fayetteville, AR 72701
*cgstraus@comp.uark.edu*
* 501-575-6332*

(c)1992-1994 Chaim Goodman-Strauss

Original paper masters available on request.