Making a Moebius strip

Follow these instructions to make your own Moebius strip and learn about topology.

• 19 June 2006 | Updated 14 October 2011

• What you need 
• What to do 
• What's happening 

This loopy structure was invented by a German mathematician named August Moebius. Its amazing properties arise from the fact that this strip of paper has only one edge and one side!

What you need

To do this activity you will need:

• paper
• scissors
• a pencil
• adhesive tape.

What to do

1. Cut a strip of paper 30 cm long by 5 cm wide (or something like these proportions - it doesn’t need to be exact!).
2. Join the ends to make a hoop, but give the strip a half twist before you tape it together.
3. Draw a line along the centre of the strip.
4. Cut the strip in half along its length.

How much bigger is your loop than the one you started with? How much bigger is the loop if you cut the strip into thirds or quarters? Can you draw on only one side of a Moebius strip?

What's happening

Moebius strips are often used as belts in machinery because they last longer - they wear out both ‘sides’ at once.

This useful strip is part of a branch of mathematics called topology. Topology can be hard to explain, because in it straight lines or edges aren’t important, and a circle is considered to be the same as a square. In topology, one is just a distorted or deformed version of the other!

For more hands-on science fun, join CSIRO's Double Helix Science Club.