I am officially crazy about knitting doilies. I am most fascinated with their construction. It's probably my math teacher brain that is so intrigued with them. Well, not probably, it is. I love all of the symmetry and constructions and proportions. For example, here is a doily:
Not overly unique but it illustrates the basics. The whole thing is made up of repeating sections. All you are ever doing is knitting this section of knitting eight times.
This doily has a cast on of 8. Eight pattern repetitions equals eight cast on stitches. Basically, what you are doing is building a piece of pie from the point up, or for math teachers, a sector from the center to the circle's edge.
I have been trying to find a set formula for the amount of increases necessary to have a flat piece of work. This is my thinking. Let's say that I cast on 6 sts and just keep knitting round after round after round; my finished product will be a tube. If I add increases, evenly spaced and every round or every few rounds, my piece will grow outwards and lie flat. The problem is here, if I increase too little, my work will start to look like a bowl; if I increase too much, my work will have ripples. So, what is the right amount of increase?
I'm finding that there is not one set answer, rather a range of possibilities. This bugs me. I like my math to have a nice clean answer (this is probably why I don't teach that fake math, Statistics).
Designing is another level unto itself. I sort of played with a simple design using constructions and symmetry. I ended up with a nice little picture. But how to translate that into a pattern? When do you know to end a motif and continue with a new one? I was banging my head against that wall trying to figure this one out and after almost a bottle of wine and several sheets of paper, the math bubble broke open in my brain...Proportions! The thing I use consistently in knitting and cooking eluded me for most of the evening. Obviously, I was trying to make things WAY to hard.
So, now I'm at the point of trying to put it all together. Tomorrow I'll start the knitting and charting.