Tom fool's knot under and through the outer side of the opposite loop. Tom fool's knot The Tom fool's knot is sometimes considered a handcuff knot but is somewhat inferior for this purpose to the knot which usually bears that name. It is a good knot with which to commence a slightly fancy sheepshank. It is also used as a trick knot due to the speed with which it can be made. Tom fool's knot is believed to be the knot "epankylotos brokhos" described by the 1st Century Greek physician Heraklas. It is formed by making two loops, not exactly overlaying each other.
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