Bowline familiar with what to do should it come untied on the water. As noted above, the simplicity of the bowline makes it a good knot for a general purpose end-of-line loop. However, in situations that require additional security, several variants have been developed: The round turn bowline is made by the addition of an extra turn in the formation of the "rabbit hole" before the working end is threaded through. Similar to the double bowline, the water bowline is made by forming a clove hitch before the working end is threaded through. It is said to be stronger and also
Arf invariant of a knot the knot, constructed from a set of curves on a Seifert surface of genus "g" which represent a basis for the first homology of the surface. This means that "V" is a 2"g" × 2"g" matrix with the property that "V" − "V" is a symplectic matrix. The "Arf invariant" of the knot is the residue of Specifically, if formula_3, is a symplectic basis for the intersection form on the Seifert surface, then where formula_5 denotes the positive pushoff of "a". This approach to the Arf invariant is due to Louis Kauffman. We define two knots to be pass equivalent