Cowboy bowline Cowboy bowline The cowboy bowline (also left-hand bowline, Dutch marine bowline or winter bowline) is a variation of the bowline loop knot. The cowboy bowline has the working end go around the standing part on the side closer to the loop and results with the working end outside the loop. In contrast, a regular bowline has the working end finishing inside the loop. (The "rabbit" goes around the "tree" in the opposite direction from normal.) Some hearsay suggest the Dutch Navy uses (or used) this variant of the bowline because they consider it superior since the working end is not
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