Mobius strip experiment

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Description

A cool science experiment using only paper, pen and scissors. Great for online meetings!


Resources

A4 Paper, marker pens, scissors, sticky/masking tape

Instructions

ORIGINAL ACTIVITY
Cut the paper into a long strip about 2cm wide. Ask the Beavers if they think it is possible to draw a line on both sides of the paper, without taking the pen off the paper.

Prove that it is possible! Hold the strip out straight. Give it a half twist (180 degrees) and tape the two ends together. Hold the edge of the strip against the tip of a pen. Draw a line down the centre of the strip. Do not take the pen off the paper. Turn the paper and keep on drawing the line (I found it easier to rest the paper on a table while doing this). Do not stop until your line meets up with the starting point. Take off the tape and open out the paper. Voila! A line on both sides of the paper.

Stick it back together again how it was, with a half twist. Ask the Beavers what will happen if you cut along the line you have drawn. They will probably guess that you will make two hoops of paper. What actually happens is that you make a chain that is twice as long as your original loop.

This shape is known as a Mobius strip. When you twisted the strip, the inside and outside became one continuous surface. When you cut the strip, it became one longer chain but it still had only one continuous surface.

Try the experiment again, this time giving the paper a full, 360 degree twist. This time, you'll find that the line only appears on one side of the paper and that cutting produces two interlocking loops.

Mobius strips have been used as fan belts in cars, conveyor belts in factories and continuous loop recording tapes (it doubles the playing time of the tapes).

Video demo Link: https://www.youtube.com/watch?v=BVsIAa2XNKc


ALTERNATIVE ACTIVITY - this takes a little longer, at around 30 minutes.
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Explore mobius theory by simply cutting loops of paper and trying to predict what the result will be. HINT - it's NOT what you expect!

For each STAGE cut strips from the LONG edge of the A4 paper that is 3 or 4 fingers wide. (It needs to be wide enough to cut, but not too wide to twist).

STAGE 1 - one strip
PREPARE: Hold the strip out straight. Tape the two ends together to make a simple loop.
THINK: What will happen if you cut the loop along the centreline of the strip? Can anyone predict how many loops there will be?
DO: Cut the loop along the centreline. Do not stop until the cut meets up with the starting point.
REFLECT: Who guessed right? How many loops do you have?

STAGE 2 - one strip
PREPARE: Hold the strip out straight. Give it a HALF twist (180 degrees) and tape the two ends together to make a loop with one kink in it.
THINK: What will happen if you cut the loop along the centreline of the strip? Can anyone predict how many loops there will be?
DO: Cut the loop along the centreline. Do not stop until the cut meets up with the starting point.
REFLECT: Who guessed right? How many loops do you have?

STAGE 3 - one strip
PREPARE: Hold the strip out straight. Give it a FULL twist (360 degrees) and tape the two ends together to make a loop with a full kink within it.
THINK: What will happen if you cut the loop along the centreline of the strip? Can anyone predict how many loops there will be?
DO: Cut the loop along the centreline. Do not stop until the cut meets up with the starting point.
REFLECT: Who guessed right? How many loops do you have? What's going on?

STAGE 4 - TWO strips
PREPARE: Hold a strip out straight. Tape the two ends together to make a simple loop. Repeat to make a separate second loop. Holding the two loops together so to make a figure 8, rotate one loop 90 degrees to be at right angles with the other. Carefully tape the two loops together - put tape across both the "top" and the "bottom" of the join.
THINK: What will happen if you cut along the centreline of BOTH strips? Can anyone predict how many loops there will be?
DO: Cut the BOTH loops along the centreline. It works best if you cut leaving just the joint until the very end. Ensure everyone is at the same point (two loops also cut completely) then have everyone finish the cuts - in a cross shape across the join. THIS IS TRICKY! Carefully stretch out the shape.
REFLECT: Who guessed right? How many loops do you have? What's going on?


Tags

  • at home programme
  • beavers
  • beavers and cubs
  • cubs
  • experiment
  • Indoor
  • Indoor activity
  • Mobius strip
  • online
  • paper experiment
  • science
  • Zoom
  • Zoom meeting

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