Bowline more resistant to jamming than the other variations, especially when wet. In this variation the knot's working end is taken round the loop in the direction of the original round turn, then threaded back up through the original round turn before the knot is drawn tight. The Yosemite bowline is often used in climbing. The cowboy bowline (also called Dutch bowline), French bowline, and Portuguese bowline are variations of the bowline, each of which makes one loop. (Names of knots are mostly traditional and may not reflect their origins.) A running bowline can be used to make a noose which
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