How to Make a Basic Mobius Strip.

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How to make a basic Mobius strip.
Mobius strip.
The magic circle, or Mobius strip, named after a German mathematician, is a loop with only one surface and one edge. Impossible? Well, here's how you make one:

1:
Cut a strip of paper (try to keep the width even so that you have a long thin rectangle). To make sure you tape the loop the right way, write A on the top right hand corner, B on the top left, C on the bottom right and D on the bottom left. Make the A-C edge longer than the A-B edge (the lengths don't affect the topological properties, but make it easier to fold).

2:
Hold the two ends in your hands, give the strip a half twist and tape together the short ends, A to D and B to C so that the arrows in the diagram point in the same direction. Now you have a Mobius strip.

3:
Now take a pen and starting at any point, draw a line along the middle of the strip, continuing all the way until you reach your starting point again. You have drawn a line on both sides of the loop - but without lifting your pen or crossing any edge. The paper has only one side!

4:
Now take a highlighter and colour the edge of the strip. You'll find both edges are coloured. There is only one edge!

5:
Now with scissors, cut the Mobius strip along the central line you drew earlier. It does not, as you'd expect, fall apart into two separate loops - instead you now have a single, larger one-sided loop!
6:
Draw a central line around the resulting loop and cut along it - can you predict what will happen?


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