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 the knot, constructed from a set of curves on a Seifert surface of genus "g" which represent a basis for the first homology of the surface. This means that "V" is a 2"g" × 2"g" matrix with the property that "V" − "V" is a symplectic matrix. The "Arf invariant" of the knot is the residue of Specifically, if formula_3, is a symplectic basis for the intersection form on the Seifert surface, then where formula_5 denotes the positive pushoff of "a". This approach to the Arf invariant is due to Louis Kauffman. We define two knots to be pass equivalent