Triple bowline Triple bowline The triple bowline knot is a variation of the bowline knot. The knot can be applied to emergency situations, such as mountain rescue. The name comes from the three loops that would be formed by tying this knot. The knot is tied in the same way the original bowline is, except with a doubled rope (using a bight). An overhand loop is formed in the rope, the working end is passed back through that loop, behind the standing part of the rope, back through the loop and pulled tight. The working end (bight) forms a third loop, often
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