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 if they are related by a finite sequence of pass-moves, which are illustrated below: (no figure right now) Every knot is pass-equivalent to either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent. Now we can define the Arf invariant of a knot to be 0 if it is pass-equivalent to the unknot, or 1 if it is pass-equivalent to the trefoil. This definition is equivalent to the one above. Vaughan Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar