Bowline loop may pass around or through an object during the making of the knot. The knot tightens when loaded at (pulled by) the standing part of the line. The bowline is commonly used in sailing small craft, for example to fasten a halyard to the head of a sail or to tie a jib sheet to a clew of a jib. The bowline is well known as a rescue knot for such purposes as rescuing people who might have fallen down a hole, or off a cliff onto a ledge. This knot is particularly useful in such a situation because
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