Bowline work "A Sea Grammar" under the name Boling knot. Smith considered the knot to be strong and secure, saying, "The "Boling knot" is also so firmly made and fastened by the bridles into the cringles of the sails, they will break, or the sail split before it will slip." Another possible finding was discovered on the rigging of the Ancient Egyptian Pharaoh Khufu's solar ship during an excavation in 1954. The bowline is used to make a loop at one end of a line. It is tied with the rope's working end also known as the "tail" or "end". 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