Make a Mobius Strip

The magic circle, or Mobius strip, named after a German mathematician, is a loop with only one surface and no boundaries.[1] A Mobius strip can come in any shape and size. If an ant were to crawl along the surface of the Mobius strip, it would walk along both the bottom and the top in an infinite loop. You can easily construct and experiment with a Mobius strip using paper, scissors, tape, and a pencil.

Steps

Making a Mobius Strip

  1. Cut a strip of paper about {{safesubst:#invoke:convert|convert}} long and 1.5 inches in width. When cutting the strip, the measurements do not need to be accurate, these are just suggested. Try to keep the width even so that you have a long thin rectangle.[2]
    • To simplify the process, you can simply cut down the edge of a plain sheet of paper to make your strip.
  2. Label the corners of the strip A, B, C, and D. In the top left corner of the strip, write a small letter A; in the top right corner, write a small B; the bottom left, the letter C; and the bottom right, the letter D. You will use these letters to align the strip after the twist.
    • The size you make the letters doesn’t matter, but the position of each one is important for the twist step.
  3. Twist the A-C side a half turn and bring it to the B-D side. Hold the two ends in your hands, give the A-C side of the strip a half twist and join it to the B-D side. Match the letters, A to D and B to C and tape the edges together. Once the edges are taped, you have completed the Mobius strip.[2]
    • You can twist the paper more than one time and still have a Mobius strip.[3]

Experimenting with the Mobius Strip

  1. Draw a line along the middle of the strip. Using a pen or pencil, start at any point in the middle of the strip and draw a line all the way around without lifting your pen. Eventually, the pen will end up back at the point you started drawing. You have drawn a line on both sides of the loop - but without lifting your pen or crossing any edge. How did this happen? The paper has only one side![2]
    • Start at a different point in the Mobius strip and see if the same thing happens.
  2. Color the edge of the strip with a highlighter. Take a highlighter and start coloring the edge of the Mobius strip without lifting the highlighter from the strip. Continue with the marker until you reach the point at which you started. You'll find both edges are colored. This indicates that the Mobius strip has only one edge!
  3. Cut the Mobius strip along the central line you drew earlier. With a pair of scissors, poke a hole into the middle of the Mobius strip and cut along the line until you reach the beginning cut. It does not, as you'd expect, fall apart into two separate loops; instead you now have a single, larger one-sided loop![4]
  4. Cut the Mobius strip 1/3 of the way away from the edge. Like you did cutting through the center line, take the scissors and this time, cut about 1/3 of the way from the edge of the strip. Continue cutting until you reach the original cut.[4]
    • When you have finished cutting, you should have one small ring and one larger ring that are connected together.

Things You'll Need

  • Scissors
  • Tape
  • Paper
  • Pen
  • Highlighter

Related Articles

Sources and Citations

  1. ↑ https://brilliant.org/wiki/mobius-strips/
  2. ↑ 2.0 2.1 2.2 http://www.maths.ed.ac.uk/~jcollins/MobiusInstructions.pdf
  3. ↑ http://www.cut-the-knot.org/do_you_know/moebius.shtml
  4. ↑ 4.0 4.1 https://www.youtube.com/watch?v=f-19NLKxNUc
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