6
May
2013
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Shawl Geometry: Pi Circles

This is the third post (out of 15) 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.

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

PI Circle Center Out

The second way to knit a circular shawl is based around the mathematical concept of pi.
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.

CO 6sts. Join in round, being careful not to twist.
Knit 1 round.
[yo, k1] around. 12sts.
Knit 2 rounds.
[yo, k1] around. 24sts.
Knit 4 rounds.
[yo, k1] around. 48sts.
Knit 8 rounds.
[yo, k1] around. 96sts.
Knit 16 rounds.
[yo, k1] around. 192sts.
Knit 32 rounds.
[yo, k1] around. 384sts.
Knit 64 rounds.
[yo, k1] around 768sts.
Continue to desired size.

Pi Circles Hem In

To work this shawl shape from the hem in, 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 rounds knit, NOT the number of rounds in one section.

So if your magic number is 100 and your CO number is 6 sts, your shaping would be as follows:
CO 6sts.
Knit 1 round.
[yo, k1] around. 12sts.
Knit 2 rounds.
[yo, k1] around. 24sts.
Knit 4 rounds.
[yo, k1] around. 48sts.
Knit 8 rounds.
[yo, k1] around. 96sts.
Knit 16 rounds.
[yo, k1] around. 192sts.
Knit 32 rounds.
[yo, k1] around. 384sts.
Knit 31 rounds.

Notice how we stopped in the middle of a section? If we hadn’t stopped at our magic number we would have knit 64 rounds, not 31.
This is because, if you add up all of the rows (not counting the CO) you get 100. Which is your magic number for this shawl.

Once you’ve worked out your rate of increases, you turn it into your rate of decreases simply by working backwards.
So you start by casting on the number of stitches in your last increase, and beginning at the end, you start knitting. Every time your math says to double your stitches, you decrease half of them away.
CO 384sts.
Knit 31 rounds.
[k2tog] around. 192sts.
Knit 32 rounds.
[k2tog] around. 96sts.
Knit 16 rounds.
[k2tog] around. 48sts.
Knit 8 rounds.
[k2tog] around. 24sts.
Knit 4 rounds.
[k2tog] around. 12sts.
Knit 2 rounds.
[k2tog] around. 6sts.
Knit 1 round.
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 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: Wedge Circles
The next post: Circle with Concentric Circles of Increases



Get All the Shawl Shapes You'll Ever Need

Collectively the Shawl Geometry Series of books cover 75 shawl shapes from beginner to advanced, plus shawl shaping principles and theory. If you’ve enjoyed this blog post then check out the books, they cover enough shawl shaping to keep you happily knitting for a lifetime or two.

Get a lifetime's worth of shawl shapes!

 

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