A Möbius strip is a surface with only one side and only one edge.

To make one, take a strip of paper and make a loop as if forming a link in a paperchain but before joining the ends, give the strip half a twist. Whilst the shape has been known since ancient times, it is named after the German Mathematician August Ferdinand Möbius.

The Möbius strip has interesting properties. If you cut it in half, lengthways, you get not two loops but rather, one long loop with one whole twist. If you cut the strip one third of the way from the edge, you end up going round "twice" before reaching the point where you started and you end up with two loops, that are linked.

This animation designed and rendered by Andrew Beattie of Möbius shows the twist being added and the cuts described above.