Bowline on a bight advocate the use of a figure eight twisted version of the Bowline on a bight. This knot can be used to provide a toe hold in the middle of a rope; to make an emergency bosun's chair; and to create an upper rope "block" to make a crude purchase by threading the rope round an anchor point and then back up through the loop. It is sometimes used in sport climbing to tie into two anchor bolts independently. This knot is convenient when a dependable loop is required but neither end of the line is available. It's also commonly used
Arf invariant of a knot Arf invariant of a knot In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated to a Seifert surface. If "F" is a Seifert surface of a knot, then the homology group H("F", Z/2Z) has a quadratic form whose value is the number of full twists mod 2 in a neighborhood of an imbedded circle representing an element of the homology group. The Arf invariant of this quadratic form is the Arf invariant of the knot. Let formula_1 be a Seifert matrix of