22
Jul
2013
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Shawl Geometry: Half Circles

This is the sixteenth post in a series about different shawl shapes and how to knit them. All the posts in the series can be found right here.

Shawl Geometry: all the knit shawl shapes you could even need

Today we have long post about half circles.

You can work a half circle either using the wedge, the pi circular shawl shaping, or the concentric circles of increases, simply cut everything in half.

1/2 Wedge Circle from the top down

To create a 1/2 Wedge Circle, you work half of the wedges that form the full Wedge Circle. Since the full Wedge Circle is an octagon, made up of eight wedges, then the 1/2 Wedge Circle is formed from four wedges.

Knitting Instructions

CO 8sts.
{4 border sts + 4 sections}
R1: k2, (pm, yo, k1) 4 times, k2.
R2: purl across.
R3: k2, (sm, yo, k to marker) 4 times, k2.
R4: purl across.
Rep R3&4 to desired dimensions.
Bind off loosely.

1/2 Wedge Circle from the bottom up

Calculating your cast on

Determine your final gauge and the desired depth of your shawl.
[Row gauge] x [desired depth] = [# of rows]
[# of rows] / 2 = [# of dec rows]
[# of dec rows] x [4sts decreased per dec row] = [# of sts decreased]
Make sure this number is divisible by 4.
[# of sts decreased] = [# of sts to CO]

Calculating your stitch marker placement

[# of sts to CO] / [4 shawl sections] = [# of sts in one section aka Y]

Knitting Instructions

CO [# of sts to CO].
R1: (pm, ssk, kY minus two) 4 times.
R2: purl across.
R3: (sm, ssk, k to marker) 4 times.
R4: purl across.
Rep R3&4 to 4sts.
Bind off loosely.

1/2 Pi Circle from the top down

Rather than removing wedges to turn a full PI circle, like we do with the Wedge Circle (or Octagon Circle), because there are no wedges to remove, we simply cast on for half the number of stitches in the main body of the shawl and then let the PI Shawl Shaping do the rest of the work for us.

Knitting Instructions

CO 7sts.
{4 border sts + 3 main body sts}
Section A: p1 row.
Inc Row: k2, (yo, k1) to last 2sts, k2.
Section B: St st 2 rows.
Inc Row: p2, (yo, p1) to last 2sts, p2.
Section C: St st 4 rows.
Inc Row: k2, (yo, k1) to last 2sts, k2.
Section D: St st 8 rows.
Inc Row: p2, (yo, p1) to last 2sts, p2.
Section E: St st 16 rows.
Inc Row: k2, (yo, k1) to last 2sts, k2.
Section F: St st 32 rows.
Inc Row: p2, (yo, p1) to last 2sts, p2.
Section G: St st 64 rows.
Inc Row: k2, (yo, k1) to last 2sts, k2.
Continue to desired dimensions.
Bind off loosely.

1/2 Pi Circle from the bottom up

Calculating your number of rounds

Determine your final gauge and desired depth of your shawl.
[Row gauge] x [desired depth] = [# of rows 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 rows knit, NOT the number of rows in one section.

Example calculations
We’ll use the same math we did for the top down version of this shawl.
So if your magic number (number of rows total) is 100 and your desired BO number is 3sts, the calculations for your shaping would be as follows:
CO 3sts.
Section A: St st 1 row.
Inc Row: (yo, k1). 6sts.
Section B: St st 2 rows.
Inc Row: (yo, p1). 12sts.
Section C: St st 4 rows.
Inc Row: (yo, k1). 24sts.
Section D: St st 8 rows.
Inc Row: (yo, p1). 48sts.
Section E: St st 16 rows.
Inc Row: (yo, k1). 96sts.
Section F: St st 32 rows.
Inc Row: (yo, p1). 192sts.
Section G: St st 31 rows.

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 worked 64 rows, not 31 rows, 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 particular shawl.
Turning your 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 row (when working center out) becomes your cast on number. And rather than working increase rows that double your stitch count, you work decrease rows that cut the number of stitches on your needles in half.

Knitting Instructions

CO 192sts.
Section A: St st 31 rows.
Dec Row: (p2tog) across. 96sts.
Section B: St st 32 rows.
Dec Row: (k2tog) across. 48sts.
Section C: St st 16 rows.
Dec Row: (p2tog) across. 24sts.
Section D: St st 8 rows.
Dec Row: (k2tog) across. 12sts.
Section E: St st 4 rows.
Dec Row: (p2tog) across. 6sts.
Section F: St st 2 rows.
Dec Row: (k2tog) across. 3sts.
Section G: St st 1 row.
Bind off loosely.

1/2 Octagon Circle from the top down

Since a full Octagon Circle is made up of eight wedges, the 1/2 Octagon Circle is made up of four wedges. This shawl is shaped using three pairs of increases (or decreases) plus two single increases (or decreases) along either edge.

Knitting Instructions

For a shawl with shaping every 4th round:
CO 11sts.
{4 border sts + 4 sections + 3 spines}
R1: k2, (pm, yo, k1, yo, pm, k1) 4 times, k1.
R2, 4, 6, 8: purl across.
R3, 7: knit across.
R5: k2, (sm, yo, k to marker, yo, sm, k1) 4 times, k1.
Rep R5-8 to desired dimensions.
Bind off loosely.

For a shawl with shaping every 6th round:
CO 11sts.
{4 border sts + 4 sections + 3 spines}
R1: k2, (pm, yo, k1, yo, pm, k1) 4 times, k1.
R2, 4, 6, 8, 10, 12: purl across.
R3, 5, 9, 11: knit across.
R7: k2, (sm, yo, k to marker, yo, sm, k1) 4 times, k1.
Rep R7-12 to desired dimensions.
Bind off loosely.

1/2 Octagon Circle from the bottom up

I’ve included here the calculations and instructions for working an Octagon Circle from the hem in with your shaping worked every 4th round.

Calculating your cast on

Determine your final gauge and the desired depth of your shawl.
[Row gauge] x [desired depth] = [# of rows]
[# of rows] / [4 rows in a dec rep] = [# of dec reps]
[# of dec reps] x [8sts decreased per dec rep] = [# 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] / [4 shawl sections] = [# of sts in one section aka Y]

Knitting Instructions

CO [# of sts to CO].
R1: (pm, ssk, kY minus four, k2tog) 4 times.
R2, 4, 6, 8: purl across.
R3, 7: knit across.
R5: (sm, ssk, k to 2sts before marker, k2tog) 4 times.
Rep R5-8 to 8sts.
Bind off loosely.



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The previous post: 3/4 Squares
The next post: Wedge Crescent


7 Responses

  1. Dorothy Dole

    Thank you so much for this information! I knew there was a way to knit a 1/2 circle top-down shawl that wasn’t a triangular shape. As I am 4’10” tall, that style of shawl is not the best. I couldn’t remember the math formulas as well as I used to either.

    Again, thank you for sharing.

    1. Holly

      I’m so glad this post was useful for you!! Have tons of fun knitting your half circle shawls – I think they’re one of the most wearable shapes.

  2. Pat

    Thank you for all the half circle shawl geometry. One question: The half circle top down pi shawl, after “st.st. 32 rows” would the next increase be after 64 rows? Probably a silly question but 64 rows seems an awful lot before another increase. Or do you mean to go back to the beginning again and work 4, 8 16 rows?

    1. Holly

      I’m so glad you like the post.

      Pi shawl shaping, isn’t the most intuitive, but after 32 rows without increasing, 64 rows is the correct next step (even though it feels like A LOT of rows without increases), that’s because it is the next step in the sequence that pi shawl shaping is based on.

      I talk more about how Pi shawl shaping works in the Pi Circle Shawl post of the series, and Donna Druchunas also wrote a great post on Pi Shawl Shaping over on her blog.

      Hope that helps!

  3. Pingback : Half-pi sunshine | thesheepshop

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