Every knot is a closed circular braid. This is a famous theorem of knot theory . But what does it mean?
It means that no matter how twisted, complex and entangled a knot might be, no matter how many crossings it has, the strands of rope can be rearranged into a single braided coil. When the knot is arranged this way and you follow the strand of rope all the way around, it will make a series of circles that cross over and under each other's strands. Every circle has the same center, there is no backtracking, and there are no extra loops.
Try reshaping some of the knots on the sheet of knot diagams into closed circular braids. For some knots, it is easy. For others it is not.
Make a huge and ridiculously complex knot out of a large piece of rope and try to rearrange it into a closed circular braid. It is possible. But why???
Because every knot is a closed circular braid, it is possible to describe any knot by listing the braid components., telling the order of their appearance, and telling how the ends are joined.
Try describing some of the knots in the sheet of knot diagrams as closed circular braids, and see if you think that this kind of description is useful for classifying knots and telling them apart.
