Spanish bowline complicated knot however and if not properly tightened, it can slip. A fireman's chair knot is another double loop knot which is more practical, easier to tie and less prone to slipping although it lacks the elegance of a Spanish bowline. Spanish bowline The Spanish bowline is a double loop knot that can be used to lift a person. For a conscious person, each loop is placed around a leg and the person holds onto the standing part of the rope. This knot can serve as a makeshift Bosun's chair. For an unconscious person one loop is placed around the
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