Yosemite bowline knot. A stopper knot, while serving to keep the loose end tidy, will not only help to prevent failure of the primary knot, but also act as a secondary safety knot itself. It is sometimes said that if enough of a tail is left to tie a stopper knot, the stopper becomes unnecessary. The tail should be a minimum of 40–60 cm depending on the thickness of the rope. Yosemite bowline A Yosemite bowline is loop knot often perceived as having better security than a bowline. It has been pointed out that if the knot is not dressed correctly it
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