Chinese button knot method that does not require a carrick bend as a first step, and does not produce a lanyard loop that needs to be reduced when used as a button. This method provides just the button, a spherical basket weave knot, in the style of Turk's head knot or diamond knot. Instructions for tying Chinese button knot in single configuration using this method as illustrated in the adjacent image, with four steps in tying it; thin red lines showing the move(s) to get to the next step: Chinese button knot Chinese button knot is essentially a diamond knot where the lanyard
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