I was talking about math and design with my friend Lori, who designs crochet motifs (and uses a lot of geometry as a result) and I thought I’d collect my posts on the topic so far in one place as well as talking about areas of concentric stripes in circles (and therefore calculating relative yarn quantities).
Summary: if a is the number of rounds you’ve worked so far (from the center out) and b is the total number of rounds in the circle, do this math: (a*a)/(b*b) to see how far you are.
Alternately, you’ll be approximately halfway done when you’ve worked 70% of the rounds.
All this assumes a fairly regular density of stitches.
I wasn’t expecting to find as handy a visual pattern as I did for the triangle shawl, and indeed I didn’t. But I found a more useful rule of thumb than I expected, which I will summarize before showing my work.
If your center circle takes exactly one skein of yarn, the second stripe will take approximately 3 skeins; the third stripe will take approximately 5; the fourth, 7; the fifth, 9; and so on. Count by odd numbers and you’ll get a good rough estimate. The more stripes you go, the less accurate the approximation will be at the outer edges, but it’s a good starting point.
This calculation assumes that the stripes each contain an equal number of rounds and are approximately the same density of stitches.
Here’s the math: