Safety: This activity uses a needle. Younger mathematicians should ask an adult to help. For more information, go to the CSIRO Education safety page.
You will need
- An open-ended zipper. If you unzip it all the way, the two sides should be completely separate.
- Pins or sticky tape
What to do
- Make sure your zipper is zipped up.
- Take the top and bottom of the zipper and put them together so the zipper forms a loop. Then, put a half twist in the loop. At the join, make sure there is at least a centimetre of overlap.
- Use pins or sticky tape to hold the join in place.
- Cut a piece of thread about 30 cm long and thread it onto your needle. Tie the ends of the thread together.
- Look at the join on one side of the zipper. Put several stitches through the material there, to hold the two ends together. Once you have enough stitches, tie the thread to a stitch, then cut it free from the needle.
- Cut a new length of thread and re-thread the needle. Stitch the join on the other side of the zipper, as above.
- Remove the pins or sticky tape. The thread will hold the loop together.
- Unzip the zipper. How many loops do you get?
- If you’re having difficulty putting your strip back together, take one side of the zipper, form a loop and add a half twist. It’s important that the twist is the same direction as when you made it!
A Möbius strip is a shape with only one side. If you trace your finger down the front of the zipper, you’ll discover that you end up on the back! Möbius strips also have only one edge. You can try tracing your finger around the edge and you’ll end up on the other side of the strip.
When you unzip your Möbius zipper, you might be surprised to get only one piece. Instead of two Möbius strips, you’ll end up with a single loop, with a full twist in it. This new band has two sides and it has two edges. If you cut the new band in half the same way, you’ll get two loops, each with two half twists. Plus, they’ll be tangled together!