Double bowline a climbing harness and provides more strength and security than the double bowline. Double bowline A double bowline (or round turn bowline) is a type of loop knot. Instead of the single turn of the regular bowline, the double bowline uses a round turn. This forms a more secure loop than a standard bowline. Though called "double bowline" by Clifford Ashley, this name is also reasonably descriptive of a different knot: the bowline on a bight. Because of this ambiguity some sources differentiate by using one of the alternate names above. And at least one other source uses the name
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