This is probably the best known of the topological shapes. Take a strip of paper. Give it one twist. Tape or glue the ends together. How many sides does the shape have? Check your guess by placing your pencil on the center of a side.

  1. What when you draw a line down the center until you get back to the point where you started.? How many sides does your Mobius strip have? Explain.
  2. What happens when you cut along the line that you drew? Call this shape “Cut 2”
  3. What happens if you cut down the center of Cut 2?
  4. What would happen if you repeated the experiment with two twists in the strip of paper?
  5. Complete the following table. Remember to include a zero twist loop in your chart.

  1. What pattern do you see in the number of twists and the number of pieces?
  2. What do you predict will occur when there are 4 twists in the strip?
  3. Make a 4 twist loop and check your prediction. Was it a correct prediction?