Shawl Geometry: Pi Circles
This is the third post in a series about different shawl shapes and how to knit them. All the posts in the series can be found right here.
PI Circle from the center out
The PI Circle falls into the circular shawl shaping camp of “start with a tiny circle, and radiate concentric circles outwards.” The basic idea is that you start with a small circular cast on, then alternate expanses of straight knitting, with dramatic increases. If you work these in accordance with EZ’s concept of PI Circular Shawl Shaping, (which is based on the mathematical relationship between the rate of growth between a circle’s circumference and radius), then you’ll create a circular shawl that lays flat.
The basic concept is, if section A has X rounds and Y stitches, then section B has 2X rounds and 2Y stitches, section C has 4X rounds and 4Y stitches, section D has 8X rounds and 8Y stitches, etc.
Center Out Knitting Instructions
CO 6sts. Join in the round, being careful not to twist.
Section A: knit 1 round.
Inc Rnd: (yo, k1) around. 12sts.
Section B: knit 2 rounds.
Inc Rnd: (yo, k1) around. 24sts.
Section C: knit 4 rounds.
Inc Rnd: (yo, k1) around. 48sts.
Section D: knit 8 rounds.
Inc Rnd: (yo, k1) around. 96sts.
Section E: knit 16 rounds.
Inc Rnd: (yo, k1) around. 192sts.
Section F: knit 32 rounds.
Inc Rnd: (yo, k1) around. 384sts.
Section G: knit 64 rounds.
Inc Rnd: (yo, k1) around. 768sts.
Continue to desired dimensions.
Bind off loosely.
Pi Circles from the hem in
Knitting any shawl from the hem inwards takes a little more planning than working one from the center out. With a shawl knit from the center out you can keep increasing until you reach your desired size, or until you run out of yarn. But knitting a shawl from the hem into the center requires that you know your size information before you begin, so you can cast on an accurate number of stitches.
Calculating your round count
Determine your final gauge and desired radius of your shawl.
The radius is half the width of your final shawl, or the length from the center to the edge.
[Rnd gauge] x [desired radius] = [# of rnds total]
This will be your magic number.
Calculating your shaping using increases
Determine how many stitches you want as the bind off at the center of your shawl.
Next work out shaping for a PI Circle as you would if you were knitting it from the center out. Work out the instructions for your shawl pattern until you reach your shawl’s magic number.
Remember: Your magic number is your TOTAL number of rounds knit, NOT the number of rounds in one section.
Example calculations
We’ll use the same math we did for the center to hem version of this shawl.
So if your magic number (number of rounds total) is 100 and your desired BO number is 6sts, the calculations for your shaping would be as follows:
CO 6sts.
Section A: knit 1 round.
Inc Rnd: (yo, k1) around. 12sts.
Section B: knit 2 rounds.
Inc Rnd: (yo, k1) around. 24sts.
Section C: knit 4 rounds.
Inc Rnd: (yo, k1) around. 48sts.
Section D: knit 8 rounds.
Inc Rnd: (yo, k1) around. 96sts.
Section E: knit 16 rounds.
Inc Rnd: (yo, k1) around. 192sts.
Section F: knit 32 rounds.
Inc Rnd: (yo, k1) around. 384sts.
Section G: knit 31 rounds.
Notice how we stopped in the middle of a section?
If we hadn’t stopped at our magic number of rows (100) we would have knit 64 rounds, not 31, in that last section (section G).
We stopped because, if you add up all of the rows (not counting the CO) you get 100. Which is the magic number for this shawl.
Turning Increases into Decreases
Once you’ve worked out your calculations as though you were knitting from the center out, you knit a shawl from the edge in, by working backwards.
To do this, the number of stitches in your final increase round (when working center out) becomes your cast on number. And rather than working increase rounds that double your stitch count, you work decrease rounds that cut the number of stitches on your needles in half.
Knitting Instructions
CO 384sts. Join in the round, being careful not to twist.
Section A: knit 31 rounds.
Dec Rnd: (k2tog) around. 192sts.
Section B: knit 32 rounds.
Dec Rnd: (k2tog) around. 96sts.
Section C: knit 16 rounds.
Dec Rnd: (k2tog) around. 48sts.
Section D: knit 8 rounds.
Dec Rnd: (k2tog) around. 24sts.
Section E: knit 4 rounds.
Dec Rnd: (k2tog) around. 12sts.
Section F: knit 2 rounds.
Dec Rnd: (k2tog) around. 6sts.
Section G: knit 1 round.
Bind off loosely.
Break yarn leaving a tail, and thread tail through live stitches, pull tight and weave in your end. (The same way you would finish off the crown of a hat.)
The previous post: Wedge Circle
The next post: Octagon Circle
Shawl Geometry: Wedge Circles
This is the second post in a series about different shawl shapes and how to knit them. All the posts in the series can be found right here.
The Wedge Circle from the center out
The Wedge Circle falls into the category of shaping a circular that I call the “knit an octagon and block it into a circle.”
In this circular shawl, we use eight right triangular wedges that, when blocked, create the “swirl” effect that this shawl is sometimes named after. The eight right triangle wedges are created by working eight single, evenly spaced increases (or decreases) every other round.
Knitting Instructions
CO 8sts. Join in the round, being careful not to twist.
{8 sections}
R1: (pm, yo, k1) 8 times.
R2: knit around.
R3: (sm, yo, k to marker) 8 times.
R4: knit around.
Rep R3&4 to desired dimensions.
Bind off loosely.
This shaping actually creates an octagon, which you then block into a circle.
Note: To make the swirl curl in the opposite direction simply (yo, k to marker) every other round, rather then (k to marker, yo).
The Wedge Circle from the hem in
To work a circular shawl made up of wedges from the hem to center, use the same concept and similar formulas as working a square shawl from the hem to center.
Calculating your cast on
Determine your final gauge and the desired radius of your shawl.
The radius is half the width of your final shawl, or the length from the center to the edge of your shawl.
[Round gauge] x [desired radius] = [# of rnds]
[# of rnds] / 2 = [# of dec rnds]
[# of dec rnds] x [8sts decreased per dec rnd] = [# of sts decreased]
Make sure this number is divisible by 8.
[# of sts decreased] = [# of sts to CO]
Calculating your stitch marker placement
[# of sts decreased] / [8 shawl sections] = [# of sts in one section aka Y]
Knitting Instructions
CO [# of sts to CO].
R1: (pm, ssk, kY minus two) 8 times.
R2: knit around.
R3: (sm, ssk, k to marker) 8 times.
R4: knit around.
Rep R3&4 to 8sts.
Bind off loosely.
Break, yarn, leaving a tail, and thread the tail through all live sts, pull tight and weave in your end. (The same way you would finish off the crown of a hat.)
So if you cast on 48 sts. Join in the round, being careful not to twist.
R1: (pm, k6) 8 times.
R2: (sm, k4, k2tog) 8 times.
R3: knit around.
R4: (sm, k to 2 sts before marker, k2tog) 8 times.
Repeat R3&4.
Bind off loosely.
The previous post: Square Knit in the Round
The next post: Pi Circles
First Third of a Shawl
I’m always working on some project or another, and most weeks I talk about what I’m working on Wednesdays as part of Tami’s WIP Wednesday project. You can see past WIP Wednesdays … right this way.
Five and half repeats out of fourteen or fifteen total repeats on my stole knit in The Verdant Gryphon’s Mithril, colorway “Interior.”
Still love the yarn, the color, the pattern, the entire project.
I’m sorry this is an awful photo. You can see the color and pattern much better in this post.
If you’d like more WIP Wednesday posts from other bloggers, visit Tami’s blog.
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