Yosemite bowline form a highly dangerous slip knot. Additional safety is achieved by tying with a tail (see below). When finished, the working end forms a figure eight. Because of the danger of incorrectly tying the Yosemite bowline, it may be safer and less error-prone to use a standard or double bowline with a backup stopper knot added to the tail, such as a double overhand knot tied around the loop. The Yosemite finish can be applied to other bowline variants, such as the double bowline. While the knot's versatility suggests it as a convenient tie-in for attaching a climbing rope to
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