Bowline the Qualified Firefighter Assessment. A mnemonic used to teach the tying of the bowline is to imagine the end of the rope as a rabbit, and where the knot will begin on the standing part, a tree trunk. First a loop is made near the end of the rope, which will act as the rabbit's hole. Then the "rabbit" comes up the hole, goes round the tree right to left, then back down the hole. This can be taught to children with the rhyme: "Up through the rabbit hole, round the big tree; down through the rabbit hole and off
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