Adventures in Mathletic Knitting: Calculating the Completion of My Pi Shawl

I’m interrupting my parade of last year’s projects to bring you actual up-to-the-date knitting news!

In November, I began working on a handspun Pi Shawl:

Handspun Pi Shawl beginnings

Handspun Pi Shawl beginnings

I have absolutely adored working on this project. It’s my in-between knitting, the thing I pick up when I have a gap between binding off and casting on for other projects, or for when I need to knit something that requires little attention. It has made for good knitting in the morning when I’m still waking up…

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… and in the afternoons when I’m waiting for my kids to be done with music lessons and rehearsals…

knitting during kids' piano lessons

knitting during kids’ piano lessons

… and in the car on my many-miles holiday journeys…

with coordinated nail polish

with coordinated nail polish

It has become such a good companion, that it’s been with a bid of sad surprise to realize this week that I was nearly out of yarn and so needed to go ahead and finish the shawl.

I did a couple of rounds of faggotting and then tried out a sideways garter border.

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Though this was great fun, I didn’t like how it was looking, so after a few inches, I ripped back and tried a picot crochet cast-off:

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I like this a lot. Love it, actually. It’s so easy and fun and gives the perfect finish to this particular project. However, I am about a third of the way done with the bind-off and it turns out I still have plenty of yarn left. I hoarded one long stripe of purple yarn to save for the end and I would love to use all of it, if possible.

Time for some math! Let’s take this step-by-step.

  1. I weighed the yarn – .2 ounces. I started with 768 yards out of 4 ounces of this yarn. So .2 ounces is roughly 38 yards.
  2. I measured the radius with my measuring tape – 23 inches, stretched but unblocked.
  3. The diameter is the radius doubled – 46 inches (again, unblocked).
  4. I had to look up how to determine the circumference from the diameter, and then I felt a bit sheepish. Circumference is the diameter times pi. Of course it is! This being the Pi Shawl should have been a nice reminder to me of that basic equation. At any rate, Circumference times Pi is 46×3.14=144.44.
  5. A good rule of thumb for figuring out how much yarn you need for the bind-off is 3 times the amount of knitting you have left. Let’s round the circumference up (I always round up in knitting, to safe-side things). 145×3=435. This is how many inches of yarn I need to bind off.
  6. Let’s put it in terms of yards since that’s usually how we think of yarn. So let’s divide the number of inches of yarn required by 36, to give me the number of yards required. 435/36=12.08. Again, let’s round up to be safe. I only need 13 yards of yarn to bind off the shawl.
  7. I have 38 yards of yarn left, but I’ve already bound off about a third of the shawl. Since the circumference of the shawl is roughly 145 inches, let’s divide that by 3 to see how much I’ve bound off: 145/3=48.33. But then we multiply it by 3 to estimate how much yarn I’ve used to bind this much off: 48.33×3=145. But then we divide that by 36 to see how many yards: 145/36=4.02. Add that to the 38 I have left in the ball, and I have roughly 42 yards of yarn left.

In other words: I’m ripping back. I have 29 yards of yarn I can knit with before I need to begin the bind-off.

I’m thinking I could probably do three more rounds of faggotting before doing the bind-off, what do you think? (I’m doing a generous estimate of needing twice as much yarn as the circumference for each round of faggotting, but this could be way off.) Of course, once I’ve added a few more rounds, the circumference will have grown a bit (probably by nearly an inch), but I think I’ve allowed enough cushion in my figures to make this work.

I do so much of my knitting by intuition, but sometimes it just makes sense to sit down and deal with the numbers. In this case, I’m especially glad that I did, even though it means ripping back. I have loved the process of this shawl so much that spending a little more time with it is pure joy.

Have you begun to see the well-known geometric theory behind what you have been doing? If you are a man, you will have spotted it right away. If you are a woman (sorry, lib), you probably expunged such theories from your memory the minute you finish high school, or even college, to make room for more useful stuff. It’s Pi; the geometry of the circle hinging on the mysterious relationship of the circumference of a circle to its radius. A circle will double its circumference in infinitely themselves-doubling distances, or, in knitters’ terms, the distance between the increase rounds, in which you double the number of stitches, goes 3, 6, 12, 24, 48, 96 round, and so on to 192, 394, 788, 1576 rounds for all I know. Theory is theory, and I have no intention of putting it into practice, as I do not plan to make a lace carpet for a football field.

– Elizabeth Zimmermann, Knitter’s Almanac: Projects for Each Month of the Year

 

 

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6 thoughts on “Adventures in Mathletic Knitting: Calculating the Completion of My Pi Shawl

    • Yes, ti will definitely take more yarn but I have no idea how much more! I’m going to reweigh the ball after I’ve ripped and calculate from there how much it might use. If I need to redo the rest of my calculations then I will. We’ll see!

  1. I think picot bind offs take a lot more than a regular bind off. I did one a couple of months ago on hundreds of stitches and I was surprised how my skein dwindled. I am a math nerd and have been known to weigh, reweigh, and optimize the yardage used – have to use math when I can. Good luck Stacey!

    • Thanks, Kelly-Ann! You’re right – the picot bind-off will definitely take more and I didn’t account for that in my calculations. I’m going to reweigh the ball after I’ve ripped and try to get a good sense of how much it’s using. Then I’ll recalculate!

  2. Pingback: Or, Perhaps the Opposite Will Happen | earthchicknits

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