Bowline familiar with what to do should it come untied on the water. As noted above, the simplicity of the bowline makes it a good knot for a general purpose end-of-line loop. However, in situations that require additional security, several variants have been developed: The round turn bowline is made by the addition of an extra turn in the formation of the "rabbit hole" before the working end is threaded through. Similar to the double bowline, the water bowline is made by forming a clove hitch before the working end is threaded through. It is said to be stronger and also
Arf invariant of a knot if they are related by a finite sequence of pass-moves, which are illustrated below: (no figure right now) Every knot is pass-equivalent to either the unknot or the trefoil; these two knots are not pass-equivalent and additionally, the right- and left-handed trefoils are pass-equivalent. Now we can define the Arf invariant of a knot to be 0 if it is pass-equivalent to the unknot, or 1 if it is pass-equivalent to the trefoil. This definition is equivalent to the one above. Vaughan Jones showed that the Arf invariant can be obtained by taking the partition function of a signed planar