Crocheting and Math

My last post, Quilting and Math, was discussed this week by Doug Peterson in This Week in Ontario Edublogs, and with Chey, Pav and Stephen on VoicEd Radio. They made connections to other types of needlework, and they inspired me to look at my own projects for more connections to mathematics.

I’ve been crocheting (aka “hooking”) since I was about twelve. It appealed to me in the same way that Bach and ballet appealed to me: structured, beautiful, and satisfying.


My first crocheting projects were “granny squares”, which were very popular in the 1970’s. They begin with a central ring, into which you stitch clusters of three double crochet stitches, separated by single chain stitches. Here’s an afghan that I made in university for a boyfriend, who broke up with me as I was working on it. I decided to use it as my bedspread in residence, and it has travelled with me since.

Granny Square Afghan

You can see, in this detailed image, how there are four clusters in the first round, eight in the second, twelve in the third, and so on. The corners can be one to three chains, depending on how tight you crochet, and how flat you need your fabric to lay.

Granny Square Detail

Here’s a baby afghan, made from one very large granny square:

Baby Granny Square

By combining more than three double crochets in a cluster it is possible to create variations on the granny square, as seen in this city block pattern:


You don’t have to make squares when you work from a central ring. You can add chains, and other stitches, and create shapes borrowed from botany:

Doily Detail


Some crochet projects begin with a foundation chain, and then proceed in rows. These rows can then be made to “zigzag”, through the addition of clusters of stitches at the “zig”, and then skipping stitches on the “zag”.

These afghans were stitched in continuous rows. The pink variegated afghan is sets of single crochets, and was made by my grandmother in the early 1970’s. The green stripes are half-double crochets, done in the back loop of the stitch to create a ribbed effect. The look of the “zigzag” is determined by the stitch height, with single crochet being the shortest, and double crochet the tallest. If you look closely you can see small triangular voids that are formed as the rows pivot.

You can also crochet in rows where you always begin at the same side, and cut the yarn at each end to create a fringe. In this case the pattern is based upon single crochet stitches, with double crochet stitches that extend down to previous rows to create the hearts. This technique layers stitches on top of those behind, creating a texture that is very unforgiving if you mis-count your stitches!

It’s also possible to create a mobius strip, by joining the foundation row of chains with a twist, and then crocheting a single spiraling row:

Mobius Strip Cowl


Working in the round is fun, and it even allows you to create three-dimensional works:

It’s fun to play with crochet in the round to create hats. Check out my son’s TikTok videos, where he explains how to create a wizard’s hat. Here’s Part 1:

I also like crocheting in layers, so that you get a different look on either side of the afghan:

The Math

Your building blocks are chains, single crochet, half-double crochet, and double crochet. The chains are wider than they are high, and create thin strands, or are the foundation into which you work your next stitches. Single crochet stitches are the closest to square, so you could imagine that you are adding small cubes. Half-double stitches are almost twice as high as they are wide. And double crochet stitches can stretch to three times higher than they are wide. These last two stitches are also “thicker” at the top, so several of them can be stitches into the same foundation stitch, and then curve around a corner, or create a cluster that begins to look like a trapezoid.

If you put chains between stitches you begin to get a lacy effect, and can create patterns of stitches and gaps. I have given away all of my filet crochet projects, so I don’t have any pictures to share. However, they can be designed in a similar way to the pixel images we create on computers, or on paper using grids. If you want to learn how to do this, check out the Spruce Crafts.

An example of Filet Crochet

Since crochet work involves only a single tool (hook) and a yarn, it’s a great technique for beginners. Preschoolers can learn to chain, and love making long strings. Older kids can easily learn row-based patterns, or simple granny squares. There are lots of tutorials on YouTube, and free patterns on Ravelry.

Data Representation

Because of its stitch structure, and the ability for several stitches to be made into a single foundation stitch, it’s a great way to illustrate concepts, and here are just a few examples from YouTube:

Math Concepts

In the Ontario Curriculum – Mathematics 2020 – Grades 1 – 8 there are many places where crochet might fit within Strand E – Spatial Sense:

“In this strand, students analyse the properties of shapes – the elements that define a shape and
make it unique – and use these properties to define, compare, and construct shapes and
objects, as well as to explore relationships among properties. Students begin with an intuition
about their surroundings and the objects in them, and learn to visualize objects from different
perspectives. Over time, students develop an increasingly sophisticated understanding of size,
shape, location, movement, and change, in both two and three dimensions. They understand
and choose appropriate units to estimate, measure, and compare attributes, and they use
appropriate tools to make measurements. They apply their understanding of the relationships
between shapes and measurement to develop formulas to calculate length, area, volume, and

In addition to the obvious spatial skills, students can also estimate yardage required for a project, calculate yardage in a ball of yarn based upon weight, and scale patterns to fit. I’m sure that you will find many other applications, if you embark on crochet in your classroom.

Fidget Toys

And if all else fails, a crochet hook and yarn is the perfect fidget toy in a classroom. It is quiet, you can crochet out of sight under the desk, and it can result in beautiful works of art.

I believe I could continue to write for days on this topic…. so I’ll pause now. If you think mathematically while you “hook”, please share in the comments below.

Quilting and Math

We’ve all heard about the connection between mathematics and music, and much of my life has been proof of this. I never thought of myself as much of a visual artist, but mathematics has been the basis of much of my enjoyment of cross-stitch, needlepoint, crochet, knitting and quilting.

During COVID, this interest blossomed. I began working with numerical sequences as well as exploration of the golden ratio. That resulted last spring in a quilt that features a logarithmic wave on one side, and sets of golden ratio “rectangles” on the reverse:

Golden Ratio Quilt
Logarithm Quilt

I designed the golden ratio side, and my son helped me with a table of logarithmic values in Excel, to make the best use of one “jelly roll” of print fabric to fit a Queen-size quilt. I tried out both “walking foot” machine quilting for the stripes and long curves on the logarithmic side, and “free motion quilting” for the spirals through the golden ratios. I love having a reversible quilt, and it’s kept me warm all winter with its wool batting.

My next challenge was to combine my daughter’s love of Fibonacci sequences with her social justice advocacy. I had two “jelly rolls” to work with, with 22 rainbow colours. And here’s the result:

Fibonacci Rainbow Quilt

This quilt was machine pieced and then hand-quilted. I could have chosen to machine quilt, since the quilting is very simple “stitch in the ditch”, but I needed the meditative process this spring as to balance out my long days online as Principal. As the weather became warmer it was more difficult to sit under the quilt, so it was July before I was able to bind and complete.

Yesterday I went looking for more challenges, but was hoping for something that wouldn’t take months to complete. I have enjoyed playing with “disappearing” patterns, but had not actually constructed any yet. This is a technique of piecing a simple square, and then cutting it into quarters or ninths, and sewing it together with the pieces rotated. So I tried out the “disappearing hourglass” pattern. You create it by sewing all the way around a pair of squares, cutting them on the diagonal, resewing them into an hourglass shape, and then cutting again into nine-patches.

What do you think?

These were both machine pieced and quilted, so they worked up quickly, and make a bright pillow for my sunroom. They each began with a 10″ square from a “layer cake”, so I have 40 more possible “disappearing” squares to construct. If I can find enough background fabric for the contrast to these wonderful Kaffe Fassett prints I might just make this my next “mathematical” quilt.