Knot cavers, arborists, rescue professionals, stagehands, fishermen, linemen and surgeons. The International Guild of Knot Tyers is an organization dedicated to the Promotion of Knot tying. Truckers in need of securing a load may use a trucker's hitch, gaining mechanical advantage. Knots can save spelunkers from being buried under rock. Many knots can also be used as makeshift tools, for example, the bowline can be used as a rescue loop, and the munter hitch can be used for belaying. The diamond hitch was widely used to tie packages on to donkeys and mules. In hazardous environments such as mountains, knots are
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