## Tuesday, May 15, 2007

### Knitting Math

I've been thinking about the geometry of the knit stitch, and how needle sizing affects that. (My commute is very boring.)

First off, for this discussion, let's assume that yarn size and the tension on the yarn are perfectly constant. Makes life a lot easier. Here's a picture of what a size 0 (2mm) needle cross-section would look like next to a size 2 (3mm) needle, if they were enlarged to where 1mm=100 pixels.

A stitch is formed by wrapping the yarn around the outside of a needle, so the circumference is the important thing, even though needles are sized by diameter.

So we all remember that the circumference = pi*r^2, and r=.5(diameter). For a 2mm needle (what I usually use for socks), the circumference = pi(1^2) or 3.14 mm. Which is a handy, base reference number. The size 2 needles I bought today are 3 mm, which makes the circumference 7 mm. Three isn't a lot bigger than 2 (only 50% more!) but 7 is a lot more than 3 (125%). (Oh, and there's some rounding going on there, but y'know, close enough.)

So the difference doesn't seem like much because of the way needles are sized, but it's really pretty important. The difference between an 8 and a 10 (5 and 6 mm, respectively) is almost a centimeter in circumference. Multiply that by howevermany stitches you have in a piece and you can see why needle size matters.

All this is, of course, the verbose version of "I spent \$30 on needles today."