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The Mobius Strip

Make a never-ending, one-sided shape.

The Mobius Strip

Materials

  • Strips of paper about 2cm wide
  • Sticky tape
  • Pen
  • Scissors

What to do

  1. Take a strip of paper and some sticky tape.
  2. Turn the paper into a loop but before you stick it together, flip one end of the paper over. This will give you a piece of paper with a half-twist in it. This is a Mobius Strip.
  3. Draw a line down the centre of the strip without taking the pen off the paper. Don't stop until your line meets up with your starting point.
  4. Undo the sticky tape and look at the paper. What have you done?

What happens?

  1. You have drawn on both sides of the paper without lifting your pen!
  2. Tape it back together (with a half twist), then cut the strip along the centre line that you drew. What have you got?
  3. You will make a chain that is twice as long as your original loop.

Why?

  1. When you twisted your strip, the inside and outside became one continuous surface.
  2. When you cut the strip, it became one longer chain and still had only one continuous surface.
  3. Now try the experiment again. This time give the paper a full twist. Can you guess what you will make?