Water bowline the working end around the standing line and back through both half hitches. This is illustrated in the three pictures below. Water bowline The water bowline is a type of knot designed for use in wet conditions where other knots may slip or jam. Although similar in finished appearance to the double bowline, the water bowline is formed with a clove hitch as the loop in the standing part of the rope. This is similar to the double bowline, which puts the running end through a round turn. The additional friction from the clove hitch increases the security of this
Arf invariant of a knot graph associated to a knot diagram. This approach to the Arf invariant is by Raymond Robertello. Let be the Alexander polynomial of the knot. Then the Arf invariant is the residue of modulo 2, where "r" = 0 for "n" odd, and "r" = 1 for "n" even. Kunio Murasugi proved that the Arf invariant is zero if and only if Δ(−1) formula_8 ±1 modulo 8. From the Fox-Milnor criterion, which tells us that the Alexander polynomial of a slice knot formula_9 factors as formula_10 for some polynomial formula_11 with integer coefficients, we know that the determinant formula_12 of a