Here is Perko B, taken from Knotscape. Starting with crossings 11 through 20 (orientations all -ve, shown below crossing numbers). I add Q-sharings and take the diagram apart after moving to negative space as shown in detail below. Then after that I look for a congruency with Perko A, also reduced.
So sharing 17 is reduced to (a17(b17). In the other reduced diagram sharing 9 is reduced, but we can make it congruent to sharing 17 by expressing (a17(b17) as (b17(a17) and changing the orientation of that crossing. This is where the writhe changes.
So here I start with the Trefoil in three dimensional space. Then I move it to a mixed space which is described in the article on math concept sharing in this blog. I am sharing the concepts of a point and a number. We then can go back to positive space from here or on to negative space. The diagrams I draw after this are in negative space.
