Ok, so I'll spill the beans on how to do these.

1) Make a grid. I just replicate boxes for this, use shift to make them square... though they dont' have to be. For some reson, the animation doesn't show the grid i made properly. If there's a grid lock, someone tell me where it is and save my fingers.
2) Make really thick lines to lay down a path for your knot. This is where experience and familiarity with knots helps. Turn down the line width by two points, or four or even six if you want weightier lines, and trace over what you just laid down again, as I did in red. Or white, or blue or whatever. Pick a lighter color than the first one whatever you choose.
3) Go over the whole thing again, this time with the line tool at 1 px (2 if you reduced the inner line by 4 points, 3 if you reduced it by 6, etc...) and fill in the cross over points. Easiest way to do this is to follow one path and alternate between over and under. That is your mantra when you're making these things: Over, under. Over, under. If you get two unders/overs in a row, you screwed up somehow.
4) You're done. You can add cosmetic touches like I did to make it not look so flat, but that's not necessary. Erase the grid and they'll never know better.

Adding corners using curves involves laying two elipses, one with lighter line width, and copying the relevant portion of the curve. I wish there was an arc tool.

This method IS NOT how you do it with paper and pencil. It's similar, but a different process.

This knot has three lines, but there are rules to follow when doing these things to get huge panels with only one line. I know these rules. I'm keeping those.

Doing these takes a perfectionist mentality to make them look nice. If you're cursor placement is off by one pixel, hit the undo. Hell, I see two places i screwed up (both corners) and they irk the hell out of me. Still, this is the practice board.

I told you these things are a lot less impressive when you know how to do them...