Knots and The Ellipse II

First, let me get this over with... the answer to my math problem:

The intersection of a circle centered at either end of the minor axis' radius (the intersection of lengths A and X) with a radius of the length of the major axis' radius (length B), and the major axes would be the precise locations of F1 and F2. That seems complicated (because words like to be), but graphically, what this says is X=B (!!).

How?

I + II = B

2*I+4*II = 2*X+2*II (learned from the 'string construction' method)

2*I+2*II = 2*X (learned from Algebra 1 in 7th grade)

I + II = X = B

Who cares?

It makes finding the foci of an already drawn ellipse very easy, which was my initial dilemma. Cool, I hope you enjoyed this as much as me :-)

Now, down to the point - my knot. The first thing I did was figure out how large I could make the knot with the twine I had bought. Once I figured this out, I made a to-size elliptical layout of the knot on a piece of paper. I then strung the first pass of the knot...

Getting this right took some time and was not easy. The next step entailed tracing the overs and unders with the long piece of rope. I was able to trace the first pass three more times before the long end ran out. I was left with some slack within the knot...

The last step was cleaning up the slack and finishing the knot. This task was not hard, but took a good amount of time. I was able to get one more pass in, finishing with a 5 ply knot, as seen here:

I changed the orientation of the knot for two reasons. Firstly and from the beginning, I planned on using the plat as a door mat. It might be a little small, but we will make it work. Secondly, the knot came out not quite symmetrical. This frustrated me at first, but then I concluded this enhances its functionality; the top edge is flat, which will conveniently rest against the foot of the door. For those of you who were expecting this piece to be mounted on a wall and admired as such, I am sorry. Some times art can be functional as well!

Thanks for looking and listening, and stay tuned...