Bowline on a bight Bowline on a bight The Bowline on a bight is a knot which makes a pair of fixed-size loops in the middle of a rope. Its advantage is that it is reasonably easy to untie after being exposed to a strain. This knot can replace the figure-eight knot when tying into a climbing harness. However, it is critical to use a strong backup knot with plenty of tail beyond the knot. 2011 testing shows that the knot might slip when only one loop is loaded. Cavers and canyoneers ought to fasten their cow-tail carabiner through both loops. European cavers widely
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