The Möbius Strip

The Möbius strip (or Möbius band) is amazing, but to find out why, you’ll need to make one.

How to make a Möbius strip

You will need:

• a strip of paper
• some sticky tape or glue
• scissors
• a pen or pencil

Take the strip of paper and lay it flat. I’ve numbered the corners to make it a bit clearer:

 
Give the paper a half twist:

 
Now stick the ends together to form a loop. Corner 1 will end up joined to corner 3 and corner 2 will be joined to corner 4. Your finished Möbius strip will look something like this:

 

Meet the amazing Möbius strip

It may have started out as an ordinary strip of paper, but because you twisted the paper, the back of the paper ended up joined to the front. This means that the Möbius strip is a one sided object. Also, because you joined the top edge to the bottom edge, it is a one-edged object.

Don’t believe it? Try these tests:

1. Use your pen or pencil to colour the edge of your Möbius Strip. Can you colour the entire edge with removing the pen?
2. Try drawing a line along the middle of the strip of paper. What happens?
3. Finally, use your scissors to cut the Möbius Strip along the centre line that you drew. What happens?
   You could repeat the process by drawing a new line and cutting along that too. It might not turn out as you expect it to!

What are Möbius strips used for?

Giant Möbius strips were once used as conveyor belts (to make them last longer, since each “side” of the strip of material gets the same amount of wear), but nowadays, better materials are available, so this isn’t necessary.

They were also used as continuous-loop recording tapes (to double the playing time).

Nowadays Möbius strips are mainly used in art. This drawing was inspired by the famous artist, M. C. Escher.

 

Möbius strips have also inspired sculptors. The granite sculpture by Max Bill and is in the sculpture gardens at the Baltimore Museum of Art. The glass Möbius sculpture is at the Cité des sciences et de l’industrie in Paris.

 

Image credits:

The three red Möbius strip diagrams (in the How to make a Möbius strip section) by Lois Lindemann are licensed under a Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales License.

Möbius Ants © iStockphoto/Floriana Barbu. Used under licence.

Photo of Max Bill’s granite ‘Endless Ribbon’ sculpture by spike55151 on Flickr. Used under Creative Commons licence.

Photo of glass Möbius sculpture by Lois Lindemann is licensed under a Creative Commons Attribution-Non-Commercial-Share Alike 2.0 UK: England & Wales License.