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) endpoints of the tangle. There is also a rotation that results from composition of the reflections. A mutation replaces the original tangle by a tangle given by any of these operations. The result will always be a knot and is called a mutant of "K". Mutants can be difficult to distinguish as they have a number of the same invariants. They have the same hyperbolic volume (by a result of Ruberman), and have the same HOMFLY polynomials. Mutation (knot theory) In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots.