Bight (knot) be used in situations where the ends of the rope are inaccessible, such as forming a fixed loop in the middle of a long climbing rope. Many knots normally tied with an end also have a form which is tied in the bight (for example, the bowline and the bowline on a bight). In other cases, a knot being tied in the bight is a matter of the method of tying rather than a difference in the completed form of the knot. For example, the clove hitch can be made "in the bight" if it is being slipped over 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