## 24 October 2006

### Math for doilies (and shawls) knitted in the round, part 1

Say your doily is 100 rounds. You have just finished round 50 and are "halfway" through the pattern, but of course you're not actually halfway through the knitting because the rounds so far have been relatively small and are only getting bigger and bigger. Question #1: Well, how much of the doily have you completed, then? Question #2: How many rounds will you have to finish before you're really at the halfway point?

For exact answers, you can count up all the stitches in the doily round by round (a spreadsheet would help!). You can then divide the number of total stitches by the number of stitches completed so far to find out how much of the knitting you've done. However, there is an easier way to estimate the answer instead, based on the fact that the area of a circle is equal to pi times the square of its radius. Think of comparing two circles—one circle is the finished, whole doily; the other circle is the doily in progress.

Note that we also have to assume that the doily is flat and increases more or less evenly and gradually (like eight stitches increased every other round—but the exact numbers are not critical). This math doesn't quite apply so well to an Elizabeth Zimmermann "Pi shawl," where there are many rounds with no stitch increases and a few rounds where the stitch count suddenly doubles. (I'll have to look into pi-shawl math some other time!)

Estimated answer to question #1:

• The fraction of the finished doily you have so far is equal to about (the number of rounds completed so far)²/(the number of total rounds in the finished doily)².
Plugging in the numbers from our example: 50²/100² = 2500/10000 = .25 (i.e., 25%)

So, in a doily with 100 total rounds, you have knitted about one fourth of the doily when you have finished round 50.

Estimated answer to question #2:

• The number of rounds completed before you get to a certain fraction of the finished doily is equal to about (the square root of fraction of the finished doily)*(the number of total rounds in the finished doily).

Plugging in the numbers from our example, √.5 * 100 rounds = .707 * 100 rounds = 70.7 rounds

For a doily with 100 total rounds, you have knitted about half when you have finished round 70 or 71.

Based on the results above, here are some easy to remember generalizations:

• When you have knitted half of the total number of rounds, you have knitted about one fourth of the total doily.
• You have knitted half of the total doily when you have knitted about 70% of the number of total rounds.

Other examples:

To estimate how many rounds it takes to complete 80% of a 125-round doily, use equation #2: √.8 * 125 rounds = 111.8 rounds.
Or, to estimate how far along you are when you have just finished round 85 in a 96-round doily, use equation #1: 85²/96² = .78 (i.e., 78%)

Remember that every pattern is different and these are just general estimates. However, if anything, the math demonstrates that you should not understimate the amount of time (and thread!) you still need when you may be "only" a dozen rounds from finishing a large doily.