# High School Math

MISSION STATEMENT: To encourage and promote a greater use of the internet and computer technology in the math classroom. For educators, students, parents and homeschoolers.

## Saturday, February 26, 2005

### Mobius Strip

Take a strip of paper and some sticky tape. Turn the paper into a loop, but before you stick it down, flip one end of the paper over. This should give you a piece of paper with a half-twist in it. This is a Möbius strip (see diagram).

The Möbius strip has only got one side. If you draw a line down the middle of the strip until you get back to your starting point, you will find that you draw on both sides of the paper.

Cut down the middle of the strip. Instead of getting two separate strips, the Möbius strip becomes one long strip. (To start the cut off, fold the strip and make a small cut, then unfold the strip and use the hole as a starting point.) This long strip has four half-twists in it. If you cut it down the middle, you get two strips wound around each other.

Using a new strip, cut about a third of the way in from the edge (you will need to go around the loop twice). You will get two strips. One is a thinner Möbius strip, the other is a long strip with four twists in it.

This time flip the strip twice before sticking it down. This will give you a strip with two half-twists in it. This strip has two sides and two edges. When you cut down the middle of the strip it will split into two linked rings.

Now, make a strip with three half-twists. This strip will have only one side and one edge. When you cut down the middle, the strip will become a knotted loop.