Cut a 5-cm strip lengthwise from an old newspaper. Holding the strip out straight, give it a half twist (180 degrees) and glue the two ends together. Take a pen and carefully draw a line along the centre of the strip. Where do you end up? Is the line drawn on the inside or outside of the paper? Now cut the strip along the line you drew. How many chains do you get? Now try cutting a half-twist strip, one-third of the way from one edge.
Your piece of paper is called a Mobius strip, which is a shape described by a branch of mathematics called topology. When you twisted your strip, the inside and outside became one continuous surface. And when you cut the strip, it became one longer chain but still had only one continuous surface.
Try the experiment again and give the paper a full twist. Then try one and a half twists, and see what happens.
Sunday, December 16, 2007