22
Jul
2013
2

Shawl Geometry: Half Circles

This is the fifteenth post (out of 16) in a series about different shawl shapes and how to knit them. The introduction post, which lays out the game plan can be found… thisaway.

 

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.

Wedge 1/2 Circles Top Down

Half Circle Wedges Cent Out

To create a half circle top down (from the back of the neck to the hem) using wedges:
CO 8sts.
R1: P across.
R2: K2, [yo, k1, pm] 4x, k2.
R3: P across.
R4: K2, [yo, k to next marker, sm] 4x, k2.
R5: P across.
Rep R4&5 to desired dimensions.
Bind off.

DSC_5803-1

Wedge 1/2 Circles Bottom Up

Bottom up (from the hem to the back of the neck):
Determine your final gauge and the desired length from the center to the edge of your shawl.
1. [number of rows per inch] x [desired radius] = [number of rounds total]
2. [number of rounds total] / 2 = [number of decrease rounds] you divide by two because you decrease every other row
3. [number of decrease rounds] x [4sts decreased per decrease round] = [number of stitches decreased] make sure this number is divisible by 4.
4. [number of stitches decreased] + [8 bind off stitches] = [number of stitches to cast on]

CO this number and work 4 evenly spaced single decreases every other row until you have 8 sts on the needles.

So if you cast on 52 sts:
R1: P2, [pm, p12] 4x, p2.
R2: K2, [k10, k2tog, sm] 4x, k2.
R3: Purl across.
R4: K2, [K to 2 sts before marker, k2tog, sm] 4x, k2.
Repeat R3&4 until you have 8 sts on the needle.
Bind off.

Half Circle Wedges Hem In

Pi 1/2 Circles Top Down

To create a half circle top down using pi shawl shaping:
CO 7sts.
P 1 row.
K2, [yo, k1] to last 2sts, k2. 10sts.
St st 2 rows.
P2, [yo, p1] to last 2sts, p2. 16sts.
St st 4 rows.
K2, [yo, k1] to last 2sts, k2. 28sts.
St st 8 rows.
P2, [yo, p1] to last 2sts, p2. 52sts.
St st 16 rows.
K2, [yo, k1] to last 2sts, k2. 100sts.
St st 32 rows.
Continue to desired dimensions.
Bind off.

Half Circle Pi

Pi 1/2 Circles Bottom Up

To work this shawl shape bottom up, determine your gauge and your desired radius of your shawl. The radius is half the width of your final shawl, or the length from the center to the edge.
[number of rounds per inch] x [desired radius] = [number of rounds total] this will be your magic number.

Determine how many stitches you want at the center of your shawl. Then work out the rate of your shawl increases the same way you would if you were working this shawl from the center out. We’ll use the same math we did above.
Work out the rate of your shawl increases until you reach your magic number.
Remember: your magic number is your TOTAL number of rows knit, NOT the number of rows in one section.

DSC_5830-1

Work your math this way:
CO 7sts.
St st 1 row.
K2, [yo, k1] to last 2sts, k2. 10sts.
St st 2 rows.
K2, [yo, k1] to last 2sts, k2. 16sts.
St st 4 rows.
K2, [yo, k1] to last 2sts, k2. 28sts.
St st 8 rows.
K2, [yo, k1] to last 2sts, k2. 52sts.
St st 16 rows.
K2, [yo, k1] to last 2sts, k2. 100sts.
St st 32 rows.
Continue.

Knit your shawl this way:
CO 100sts.
St st 32 rows.
K2, [k2tog] to last 2sts, k2. 52sts.
St st 16 rows.
P2, [p2tog] to last 2sts, p2. 28sts.
St st 8 rows.
K2, [k2tog] to last 2sts, k2. 16sts.
St st 4 rows.
P2, [p2tog] to last 2sts, p2. 10sts.
St st 2 rows.
K2, [k2tog] to last 2sts, k2. 7sts.
St st 1 row.
Bind off.

Concentric Increases 1/2 Circles Top Down

Half Circle Concentric

To create a half circle top down using concentric circles of increases with increases every 4th row:
CO 8sts.
R1: P across.
R2: K2, [yo, k1] 4x, k1.
R3&5: P across.
R4: K across.
R6: K1, [pm, k1, yo, k1, yo] 4x, pm, k2.
R7&9: P across.
R8: K across.
R10: K1, [sm, k1, yo, k to next marker, yo] 4x,     sm, k2.
Rep R7-10 to desired dimensions.
Bind off.
(For a shawl with increases every 6th row, simply add two rows between increase rows.)

Concentric Increases 1/2 Circles Bottom Up

Half Circle Concentric Hem in

Bottom up:
Determine your final gauge and the desired depth of your shawl.
1. [number of rows per inch] x [desired depth] = [number of rows total]
2. [number of rows total] / [4 rows in a decrease repeat] = [number of decrease repeats]
3. [number of decrease repeats] x [8 sts decreased per decrease repeat] = [number of stitches decreased] make sure this number is divisible by 8.
4. [number of stitches decreased] + [12 bind off stitches] = [number of stitches to cast on]

CO this number and work 4 evenly spaced pairs of single decreases every 4th row until you have 12 sts on the needles. Then work another decrease row to get to 8 sts.
So if you cast on 88 sts.
R1: P2, pm, [p21, pm] 4x, p2.
R2: K2, sm, [k2tog, k17, ssk, sm] 4x, k2.
R3&5: P across.
R4: K across
R6: K2, sm, [k2tog, k to 2 sts before marker, ssk, sm] 4x, k2.
Rep R3-6, until you have 12 sts on the needles.
R7: P across.
R8: K2, sm, [k2tog, sm] 4x, k2.
Bind off.

DSC_6260-1

 

The books this series spawned:
Shawl Geometry I: the math of shaping shawls for non mathy people
Shawl Geometry II: 16 more shawl shapes to design and play with
Shawl Geometry III: the relationships behind the numbers

 

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

 

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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