Shawl Geometry: Right Triangle
This is the fourth post in a series about different shawl shapes and how to knit them. All the posts in the series can be found right here.
Right Triangle from the top down
If you take a square and cut it in half diagonally, you’ll be left with two right triangles. So, working half of the shaping for a Square Knit in the Round, will give you a Right Triangle shawl.
The Right Triangle is shaped using a pair of increases (or decreases) down the center spine, and a single increase (or decreases) along either edge, all worked every other row.
Knitting Instructions
CO 7sts.
{4 border sts + 2 sections + 1 spine}
R1: k2, yo, k1, yo, pm, k1, pm, yo, k1, yo, k2.
R2: purl across.
R3: k2, yo, k to marker, yo, sm, k1, sm, yo, k to last 2sts, yo, k2.
R4: purl across.
Rep R3&4 to desired dimensions.
Bind off loosely.
Right Triangle from the bottom up
Just like the Square Knit in the Round, can be worked from the center out and the hem in, this Right Triangle can be worked from the top down or the bottom up. This makes sense since a triangle is half a square.
Calculating your cast on
Determine your final gauge, and desired depth down the center spine.
[Desired depth] / 2 = [Z]
[Z] x [1.4142] = [magic number]
[Magic number] x [row gauge] = [# 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] / [2 shawl sections] = [# of sts in one section aka Y]
Knitting Instructions
CO [# of sts to CO].
R1: ssk, kY minus four, k2tog, pm, ssk, kY minus four, k2tog.
R2: purl across.
R3: ssk, k to 2sts before marker, k2tog, sm, ssk, k to last 2sts, k2tog. R4: purl across.
Rep R3&4 to 4sts.
Bind off loosely.
Both of these methods create shawls that are half squares and right triangles. Some people find these a little bit hard to wear in that they slide off the shoulders and are therefore a little bit fiddly. So over the next two weeks we’ll talk about two variations that I think are a little easier to wear, a Shallower Triangle and a Right Triangle with “Wings.”
These are simply the basics, backwards and forwards. These basics can then be manipulated and expanded upon and played with to create a myriad of other shawl shapes. However, these shapes are incredibly powerful on their own, add patterns & textures, lace, cables, knits/purls, color work, anything you can think of.
The previous post: Octagon Circle
The next post: Shallower Triangle
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
