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: Square Knit in the Round
This is the first 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 easiest way to think about shawl shapes is to understand the basic geometric shapes: square, triangle, and circle, and then manipulate and decorate them to get all these other shawl shapes and styles.
But there are also multiple ways to create each basic shape: backwards, forwards, and sideways.
The Square Knit in the Round, is knit in the round. This shawl is shaped with four pairs (eight total) of evenly spaced increases (or decreases), worked every other round. The pairs of increases (or decreases) radiate outwards (or inwards) from the center of your shawl to the hem pushing (or pulling) the fabric to form the four corners of your square.
The Square Knit in the Round from the center out
The most traditional way to create a square is in the round from the center out. To do this you increase 8 stitches in pairs every other round.
Center Out Knitting Instructions
CO 8sts. Join in the round, being careful not to twist.
{4 sections + 4 spines}
R1: (pm, yo, k1, yo, pm, k1) 4 times.
R2: knit around.
R3: (sm, yo, k to marker, yo, sm, k1) 4 times.
R4: knit around.
Rep R3&4 to desired dimensions.
Bind off loosely.
The Square Knit in the Round from the hem out
You can also knit from the hem to the center by decreasing 8 stitches in pairs every other round.
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 cast on
Determine your final gauge and desired width.
[Desired width] / 2 = [width from CO to BO]
[Width from CO to BO] x [rnd gauge] = [# 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 to CO] / [4 shawl sections] = [# of sts in one section aka Y]
Center Out Knitting Instructions
CO [# of sts to CO]. Join in the round, being careful not to twist.
R1: (pm, ssk, kY minus four, k2tog) 4 times.
R2: knit around.
R3: (sm, ssk, k to 2sts before marker, k2tog) 4 times.
R4: knit around.
Rep R3&4 to 8sts.
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.)
So if you CO 48 sts. Join in the round, being careful not to twist. (This step is a total PITA.)
R1: (pm, k12) 4 times.
R2: (sm, k2tog, k8, ssk) 4 times.
R3: knit around.
R4: (sm, k2tog, k to 2sts before marker, ssk) 4 times.
Repeat R3&4 to 8sts.
Bind off loosely.
The previous post: Shawl Geometry Introduction
The next post: Wedge Circle
Shawl Geometry Introduction
Ages and ages ago I mentioned working on a couple swatches to illustrate shawl shapes, primarily for my own reference, but thought that it might be interesting to write up a blog post about how to shape different types of shawls.
Well, a couple swatches became many more than a couple, and a single blog post quickly became far too long, and the whole idea grew in leaps and bounds until it became a series, and that series grew so long that it made sense to have an accompanying series of ebooks.
So here we have it, a series of blog posts about the ins and outs of shaping knitted shawls, and here’s the game plan.
This series of posts covers the basic shawl shapes (circles, squares, triangles) and beyond (shallow triangles, 3/4 squares, crescents, etc).
The shawl shapes we’ll cover are:
Squares: center out, hem in, edge to edge, and on the bias
Circles: made up of wedges, and using pi shaping
Triangles: right triangles, shallow triangles, winged (heart) triangles, side to side triangles
Rectangles: width-wise and lengthwise (with and without provisional cast ons)
Squares and Circles with slits from the center to hem
3/4s of a Square
1/2 Circles
and
Wedged Crescents
Phew. (remember what I said about leaps and bounds?)
See you next Monday! We’ll start with the square from the center out, and make our way from there.
Table of Contents/Index:
(Just click the links below to go directly to the post.)
1. Square Knit in the Round
2. Wedge Circle
3. Pi Circle
4. Octagon Circle
5. Right Triangle
6. Shallower Triangle
7. Triangle with Wings #1
8. Side to Side Triangles
9. Edge to Edge Square
10. Bias Square
11. Rectangles
12. Squares with a Diagonal Slit
13. Wedge Circle with a Slit
14. 3/4 Square
15. 3 methods of shaping 1/2 Circles
16. Eight Equal Wedge Crescent
The Shawl Geometry Books. They’re the math of shaping shawls for non mathy people.
Stitch abbreviations:
These are the stitch abbreviations that will be used throughout the series.
BO- bind off: [k2tog, sl st on RH needle back to LH needle] Repeat until desired number of sts are bound off.
CB- center back. In this context usually (though not always) used in reference to spine at the center of a shawl.
CO- Cable cast on: starting with a slip knot on LH needle, knit one st into the slip knot and place on LH needle. [Insert RH needle between the 2 sts, wrap and bring through as though to knit, slip look from RH needle onto LH needle creating a new st.] Repeat until desired number of sts are cast on.
Provisional cast on: great instructions for a provisional cast can be found here: http://knitty.com/ISSUEfall05/FEATfall05TT.html
kfbf- knit front, back, front into the same stitch
k- knit
k2tog- knit two together
k2togtbl- knit two sts together though the back of the loops
LH- left hand
p- purl
psso- pass slipped st over
PM- place marker
R(s)- row(s)/rnd(s)
RS- right side
sk2p- slip 1, knit two together, pass slipped st over the knit two together; 2 sts decreased
sl- slip
sm- slip marker
ssk- slip 1 st, slip 1 more st, knit these two together thought the back of the loops
st(s)- stitch(es)
WS- wrong side
yo- yarn over
Schematic Color Guide:
The schematics included have arrows to show the paths of increases/decreases. These arrows are color coded with the following colors, and they arrows tips point in the direction of the increases/decreases.
Black = basic shape of shawl
Green= 1 st increased/decreased every row/round.
Purple= 2 sts increased/decreased every third row/round.
Orange= some other rate of increase/decrease
Red= 1 st increased/decreased every other row/round.
Blue= 2 sts increased/decreased every other row/round.
These last two colors are the most commonly used.
This Series Spawned 3 Books:
Shawl Geometry Book One: the math of shaping shawls for non mathy people
Shawl Geometry Book Two: fresh shawl shapes to add to your knitting library
Shawl Geometry Book Three: the principles and theories of shaping (and transforming) knitted shawls
Next: Square Knit in the Round
