The number of closed loops is called the link number . Experiment with some three-strand braids and keep track of the results. The possibilities for interesting questions multiply fast. Ask students to figure out what the components are that they can use to build braids made of four strands. Using these components, experiment with braids that have four strands.
Every knot is a closed circular braid .
This is a famous and surprising theorem of Knot Theory. It means that no matter how much a knot appears to be tangled, looped and twisted, it can be rearranged as a closed circular braid made of some number of strands. Have students experiment with some knots to see if they can always rearrange them into closed circular braids. Ideas for Discussion Comment on what the idea of braids adds to the study of knots. Have students present the results of their investigations with braids to one another.