Shoelace knot the granny (or duffer's) knot. This version will also produce asymmetrical slips; one pointing down the other up. Shoelace knot The shoelace knot, or bow knot, is commonly used for tying shoelaces and bow ties. The shoelace knot is a doubly slipped reef knot formed by joining the ends of whatever is being tied with a half hitch, folding each of the exposed ends into a loop (bight) and joining the loops with a second half hitch. The size of the loops and the length of the exposed ends are adjusted when the knot is tied. It has the stability
Mutation (knot theory) Mutation (knot theory) In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose "K" is a knot given in the form of a knot diagram. Consider a disc "D" in the projection plane of the diagram whose boundary circle intersects "K" exactly four times. We may suppose that (after planar isotopy) the disc is geometrically round and the four points of intersection on its boundary with "K" are equally spaced. The part of the knot inside the disc is a tangle. There are two reflections that switch pairs of