The Magic of Möbius Strips

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For: Nice activity for primary pupils but will amaze all ages

Thursday 26/03/20

Hands-on activity: a Mobius Strip is an object that defies common sense and has some curious mathematical properties

The  Möbius Strip is called after German Mathematician August Ferdinand Möbius (1790 – 1868) but it is believed to have been known in Roman times.

You can see our friend Douglas Buchanan’s expert demonstration of  Möbius Strips.

What you will need:

  • Paper
  • Ruler
  • Pencil
  • Scissors
  • Sellotape

INSTRUCTIONS:

  1. Cut a strip of paper approximately 30 cm long and 4 cm wide. (Divide an A4 page into 5 long strips)
  2. With a pencil and ruler draw a dashed line along the centre of the strip, lengthways
  3. You are going to join the two narrow ends of the paper together but first make a half a twist with one end.
  4. Tape the two ends together. This is called a Möbius Strip
  5. Trace along the centre of the strip: do you come back to where you started?

In Mathematics the Möbius Strip is considered to have only one side, because you can travel around a Möbius Strip and arraive back at your starting point.

Extensions

Activity 2

  1. With a scissors cut along the centre of the Möbius Strip. First predict what you expect to end up with.
  2. Use another strip of paper and create another Möbius Strip. This time instead of cutting it along the centre, cut in into three strips. First predict what will happen.

Q. What is the relationship between the larger loop and the Möbius Strip?

Activity 3:

  1. Tape two strips of paper on top of each other to form an X shape
  2. Create the first loop by taping the two narrow ends together normally
  3. With the other loop,tape the narrow ends together with a half a twist
  4. Cut the möbius strip in half, going over the intersection of the two strips too.
  5. Next cut along the centre of the normal loop.

Q What shape are you left with this time?