Triple bowline larger than the two equal-sized loops. The size of the third loop depends on the length of the bight pulled through the loop. A bowline on the bight is a similar knot to the triple bowline. Instead of wrapping the bight around the standing end and then passing it back through the nipping loop, the two loops are passed through the bight so that it tightens on the standing end. It has only two active or available loops. This is used in rescue situations, especially in a case where there might be an injured person or people, as it forms
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