A knot is an interwoven, closed, non-self-intersecting curve in 3D. A braid is a collection of strands crossing over or under each other. By joining the endpoints at the top of the braid diagram to the corresponding endpoints at the bottom, a braid can be associated with a knot. To do this, use the "curve braid" control.
In this Demonstration, the strands of a braid are plotted with different colors, which are carried over to the corresponding knot. The indices for the braids represent the number of crossings and how the corresponding knot can be tied.