Bowline work "A Sea Grammar" under the name Boling knot. Smith considered the knot to be strong and secure, saying, "The "Boling knot" is also so firmly made and fastened by the bridles into the cringles of the sails, they will break, or the sail split before it will slip." Another possible finding was discovered on the rigging of the Ancient Egyptian Pharaoh Khufu's solar ship during an excavation in 1954. The bowline is used to make a loop at one end of a line. It is tied with the rope's working end also known as the "tail" or "end". The
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.