What Are the Connections Within Mathematical Theory?

Knots are made from a bunch of little sticks that are glued end to end. You're not allowed to increase the number of sticks without bound. So it becomes smaller and smaller and smaller until it just becomes, as you can on your shoe lace. The trivial knot is the only knot zero crossings. And there's over 300 million of those knots up to 19 crossings.