More Mathematics . . .

Fun with Möbius Strips

The Möbius strip is the first example of a non-orientable surface, and it has many peculiar properties. This activity guides you through the construction of a Möbius Strip. It further illustrates some experiments you can do to discover some of the interesting traits of this bizarre little mathematical object.

The first thing you will need to do is print off the following two PDF files:

Möbius Strip with Middle Mark

Möbius Strip with Two Divisions

To assist you, the construction is illustrated below.


1. Hold the strip of paper with the printed side facing you.	2. Bring the ends around to form a loop, giving one end a half twist. The printed sides should be facing opposite directions.	3. Use tape or glue to secure the ends together.

How many sides does the Möbius Strip have? Observe your model carefully here. If the first Möbius Strip you made was the Möbius Strip with Middle Mark, your next challenge will be to cut the strip in "half" along grey line. To start the incision properly, you may want to follow the steps below.


1. Gently crease the strip, aligning the grey lines near the fold.	2. Snip across the fold along the grey line once making a small incision in the middle of the strip.	3. Insert one blade of the scissors through the hole and continue the cut along the grey line until complete.

In the file Mobius2.pdf above, the Möbius strip is divided into "thirds" by two grey lines. Use the same technique as above to cut the strip apart. There are many variations on a theme that are possible here. For example, print off another copy of the the Möbius Strip with Two Divisions and this time during assembly, insert an extra 1/2 twist before bringing the ends together. The result is not techniquely a Möbius Strip, but it is still interesting. What happens when you cut it along the grey lines? Try another half twist during another assembly, what happens then? Have fun!