Granny knot its possible use tying the necks of grain sacks. When attempting to tie a reef knot (square knot), it is easy to produce a granny knot accidentally. This is dangerous because the granny knot can slip when heavily loaded. A tightened granny knot can also jam and is often more difficult to untie than the reef knot. It is better to tie a reef knot in nearly all circumstances. One way to distinguish them is that in the reef knot each loop passes completely over, or completely under (not through) the neck of the other. The reef knot is commonly
Arf invariant of a knot Arf invariant of a knot In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated to a Seifert surface. If "F" is a Seifert surface of a knot, then the homology group H("F", Z/2Z) has a quadratic form whose value is the number of full twists mod 2 in a neighborhood of an imbedded circle representing an element of the homology group. The Arf invariant of this quadratic form is the Arf invariant of the knot. Let formula_1 be a Seifert matrix of