Cowboy bowline Various tests of the different versions' strengths show little difference; conjecture about either knot's vulnerability to some failure remain pretty much only that – conjectures. As for the tail of a regular bowline finishing "inside the loop [ eye]", that is more a formal-image state than one of an actual knot, as the draw of the standing part will pull the tail around so that it actually points away from the eye, but there are various ways the knot can be dressed to affect this aspect. There is a rule of thumb which states that the loose end should be
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