Granny knot its possible use tying the necks of grain sacks. When attempting to tie a reef knot (square knot), it is easy to produce a granny knot accidentally. This is dangerous because the granny knot can slip when heavily loaded. A tightened granny knot can also jam and is often more difficult to untie than the reef knot. It is better to tie a reef knot in nearly all circumstances. One way to distinguish them is that in the reef knot each loop passes completely over, or completely under (not through) the neck of the other. The reef knot is commonly
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