Yosemite bowline 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 can potentially collapse into a noose, however testing reveals this alternative configuration to be strong and safe as a climbing tie-in. A Yosemite bowline is made from a bowline with the free end wrapped around one leg of the loop and tucked back through the knot, a final round turn and reeve commonly known as a "Yosemite finish." The knot's security is enhanced by preventing the bowline capsizing to
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