In last week’s post, I went into a lot of detail about how to crochet a flat circle. I touched on the Pi circle method, which led to me experimenting with it so I could go into a bit more depth about how it works.

It’s a really interesting alternative approach to the traditional ‘even increase’ circle method.

In this post I share an explanation of how it works and how I got on with it.

The Pi Shawl

The Pi circle method was designed by Elizabeth Zimmerman, an icon in the history of knitting, to help knitters make and design semi-circular shawls.

In this method you only work an increase round every time the stitch count doubles. I’ll explain this in more detail below, but this difference gives you more freedom with the kinds of stitch patterns you can use.

It means that you have fewer rows on which you need to think about working your increases into the stitch pattern.

There is also a lot less counting, meaning that pi shaws are often relaxing projects to work.

What you need understand about circles in a pi shawl / pi circle

I went into some detail about the geometry of a circle, in the context of crochet in my ‘how to crochet a flat circle’ post, so I won’t repeat that now. Although I have added some simple definitions at the end of this post for reference.

The main thing you need to understand when it comes to a pi circle is this:

As the diameter of a circle doubles, so does the circumference.

This is the mathematical rule on which the pi shawl is based.

In crochet terms, every time you double the number of rounds, you should double the number of stitches

The important stitch measure here is the height as this dictates the diameter of the circle.

How to crochet a Pi circle

Pi circles are worked centre out.

With a Pi increase method, you only work an increase round where it would double the stitch count. The rounds in between have no increases.

These instructions should work both for a full circle and for a semi-circle if you’re creating a shawl.

For the purposes of this article, I’m going to assume that you know the traditional method of crocheting a flat circle using regular equal increases. It’s useful to know this so you can compare the two methods.

I find it easiest to look at the pi circle as worked in sections, where each section has double the number of rounds as the previous section.

Each section starts with an increase round, where you double the stitch count by working 2 stitches into each stitch around (or as the stitch pattern dictates).

The diagram below illustrates how the depth of the sections double in the Pi circle. Each pink circle represents an increase round and the start of a new section.

The numbers given in the diagram are only to illustrate the point. When working a pi shawl, you may see either radius or diameter used in the calculations.

With the pi circle, the rules about the number of stitches you start with apply the same way they would with a circle using even increases.

Below I will walk you through an example. I had never used this method before, so I’m sharing the results of my experiments here!

Worked example

Lets say you’re working a circular motif in single crochet and you start your first round with 6 single crochet (sc) using US terms.

Using the traditional method, you would increase by 6 stitches each round, so your stitch count for the first 10 rounds would look like this: 6, 12, 18, 24, 30, 36, 42, 48, 60, 66

With the Pi method you double your stitch count on the increase round (working 2 stitches into each stitch all round), so your stitch count would look like this

Basic Pi Circle Pattern:

Round 1: 6 sts

Round 2: Double st count – 12 stitches

Round 3: No increase – 12 sts

Round 4: Increase – 24 sts

Round 5: No increase – 24 sts

Round 6: No increase – 24 sts

Round 7: No increase – 24 sts

Round 8: Double st count – 48 sts

Round 9: No increase – 48 sts

Round 10: No increase – 48 sts

As you see, the number of non increase rounds between each increase round gets larger as your circle gets bigger.

Looking at it in sections (as referred to in circle diagram above), the rounds would be distributed as follows:

Section A = Round 1 (1 round / 6 sts)

Section B = Rounds 2-3 (2 rounds / 12 sts)

Section C = Rounds 4-7 (4 rounds / 24 sts)

Section D = Rounds 8 – 15 (8 rounds / 48 sts)

Below shows a swatch I made using the pattern above.

Each increase round is worked in blue so that it stands out.

I have continued to work the pattern up to 96 stitches, working about half the non-increase rounds after the last increase. (Then I ran out of the stash yarn I was using!)

Here’s what I found when working this example.

What to expect when crocheting Pi Circles

Before you get to the next increase round you will find your circle starts to curl and bend in. Sometimes mine curled quite a lot, but it straightened out impressively once I worked the increase round.

After an increase, the pattern may be a bit wavy (excess fabric) for a round or two, Again, it flattens out.

You will need to block your work when using the pi circle.

I gave mine a light steam press under a tea towel. Not the most pro way to block something but I was just swatching so I wasn’t being too precious!

Here’s what it looked like before blocking.

Also, please ignore the dodgy colour changes – I was trying out a new colour change technique at the same time which didn’t quite work!!

Slapdash techniques aside, I was quite impressed with how this method worked. But I still had questions…

Does the pi circle method work with all crochet stitches?

The Pi circle examples I found were almost all related to knitting. Based on my limited understanding of knitting, it tends to create relatively short stitches compared to the taller crochet stitches.

I wanted to see if the method worked with any crochet stitch, so I made another swatch the way I might approach a pi shawl.

In this one, I upped my hook size a bit (4.5mm and DK yarn) and planned to work a semi-circle using US double crochet (dc).

Typically when working a circle with double crochet, I would start with 12 sts in the first round. So it follows that to work a semi circle, I’d start with 6, which is what I did.

I followed the pi circle method as described above and this is what it looked like:

Again, the blue yarn is used for the increase rows.

What I learned from my pi shawl swatch

Working with a larger hook meant I found I got less curling than when I did working single crochet with a 4mm (using dk yarn).

I gave the swatch a quick press with a cold iron, but did not really block it.

I haven’t worked as many rounds with this one (just up to the first round of 96 sts) but felt it worked pretty well.

However, my semi-circle shape is a bit off, so were I trying to make a precise semi-circle, I would be disappointed.

I think that when making semi-circles you probably need to up your starting stitch count to more than half the number of stitches you would use to make a circle.

My maths brain intuits that this is because the tension that exists in a complete circle means that it holds it’s shape better. With a semi circle, there is nothing to pull the edges outwards – the tension is all in the centre, pulling the edges in.

Blocking might sort out the shape here, but were I to design a shawl using this method, I would most likely increase the starting stitch count to around 8 or 9.

The other thing I notice with this semi-semi-circle is that the edges are not straight. And not just in a turning chain bump way.

The edging seems to shift inwards through the non increase / work even rounds. Or maybe, the increase rounds just poke out a bit more?

This might also be straightened out by adding more stitches but were I making this a shawl, I would need to add a boarder along the ‘straight’ edge to sort this out!

Crochet pi shawls – my verdict

Over all, I think this method has a huge amount of potential. It is a really interesting approach to crocheting circular projects, whether they are shawls or motifs or something else.

I also think that combining the pi circle and the even increase circle approaches would be possible and make for some interesting designs.

My head is buzzing with ideas on how I could play with these ideas.

This is why I love trying new techniques!

If you want to get stuck straight into a pi shawl, why not try the Cherry Pi shawl design from the Crochet Project which uses this method.

I hope you’ve found this useful and are feeling inspired by circles, rather than running round in them!!

Hap-pi Hooking

Dx

Terms and definitions relating to circles:

Diameter = the width across the circle if you cut it in half

Radius = half the diameter / the length from the centre of the circle to the edge

Circumference = the length around the circle. To calculate the circumference you just multiply the diameter by pi.

Pi = 3.14. What’s useful to know about Pi for this context is that it is the ratio of the diameter to the circumference of any circle. It is the same regardless of the size.