# The mathematics of crochet

I remember thinking at school when will I ever in my “real life” use maths.  Well much to my utter surprise I’ve come to the stark realisation that there is a link between mathematics and crochet.  Yes its true…  In fact, crochet patterns have an underlying mathematical structure — the pattern created by the regular presence or omission of stitches is the very essence of this art form. The similarities to Base2 math, with its series of 0s and 1s, are obvious. That is to say, a present stitch is like a “1”, and a missing stitch is like a “0”.  Crochet has been used to illustrate shapes in hyperbolic space that are difficult to reproduce using other media or are difficult to understand when viewed two-dimensionally.

It is believed that the partnership between math and craft dates back to the invention of geometry where the repetitive patterns seen in ancient baskets and weavings first hinted at a mathematical subtext to the world at large.

Alan Turing, the theorist and computer scientist, was often seen knitting Möbius strips (a surface with one continuous side formed by joining the ends of a rectangle after twisting one end through 180°.) and other geometric shapes during his lunch break.  The Mobius strip in crochet terms is nothing other than the infinity scarf. Below is a beautiful example of an infinity scarf designed by our talented friend Anneke Wiese.  The pattern is available here.

Mathematics and hyperbolic crochet

Hyperbolic Crochet is the name given to applying a mathematical principle to crochet patterns.

A hyperbolic plane expands exponentially from any point on its surface, always curving away from itself. You can easily crochet a hyperbolic surface by increasing at a constant rate throughout the piece.   From a crochet perspective this is clearly depicted in the pattern called Barb’s Koigu Ruffle scarf.

For hundreds of years mathematicians tried to show that anything like hyperbolic space was impossible, until finally, in the nineteenth century, they accepted the “existence” of this form of geometry. Still many believed it wasn’t possible to model the structure materially. They were thus surprised to learn in 1997 that Dr. Daina Taimina had done just that using the traditional art of crochet.

Lilian Boloney is a textile artist who uses crocheting to explore the geometry of hyperbolic figures. There is an elegant simplicity to the off-white cotton thread she used to crochet the sculpture “Boy’s surface”. This allows the viewer to explore the complex topology of the figure without the distraction of patterns or color. Lilian not only has a clear understanding of her Mathematical subject, but she transposes their beauty into graceful objects. “Instead of models of Hyperbolic figures I see them crocheted portraits” says Lilian.

Hyperbolic growth in nature gives rise to the ruffled shapes of coral, kelp, and sea anemone.  The Institute for Figuring created the concept of the Coral Reef with hyperbolic crochet and have been developing this concept since 2005.

Chaotic Crochet

Dr. Hinke Osinga and Professor Bernd Krauskopf (Engineering Mathematics, University of Bristol) have turned the famous Lorenz equations into a beautiful real-life object, by crocheting computer-generated instructions of the Lorenz manifold: all crochet stitches together define the surface of initial conditions that under influence of the vector field generated by the Lorenz equations end up at the origin; all other initial conditions go to the butterfly attractor that has chaotic dynamics.  The overall shape of the surface is created by little local changes: adding or removing points at each step.

Dr Osinga has been able to crochet since she was seven years old , so she noticed that this is exactly the same way that crochet instructions work – by specifying a “surface” (more usually a poncho or baby’s blanket!) in rows, with the number of stitches increasing or decreasing. From there it was a simple step to turn the algorithm into a crochet pattern, and to start to create a real-life Lorenz manifold.

Fractal Crochet

Dictionary.com defines a fractal as: A geometric pattern that is repeated (iterated) at ever smaller (or larger) scales to produce (self similar) irregular shapes and surfaces that cannot be represented by classical (Euclidian) geometry. Fractals are used especially in computer modeling of irregular patterns and structures found in nature.

Scientists and mathematicians have discovered how to use fractals to numerically describe coastlines, the shape of trees, our vascular system and much more.  Fractal crochet is absolutely beautiful in its form and you can buy a fractal crochet pattern on Ravelry

I hope you found this post as insightful and fascinating as I did.  I like to think that there is intelligence behind crochet in more ways than one.  What I am sure of though is that Crochet is most certainly my second language.  I cannot say the same for mathematics!

May your creativity multiply twofold this week!

Yarn blessings

## 6 thoughts on “The mathematics of crochet”

1. I love looking at crochet in math. I’ve done a few different posts about it including a roundup of crochet fractals. So neat seeing what can be done in crochet that can’t be done in other crafts!

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1. Jean says:

Where can I get some of these patterns? Hopefully in USA directions…not UK. Thanks Jean

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This post is wonderful. But it appears that Barb’s Koigu Ruffle Scarf is knitted and the Ravelry link says the same. Do you know of a crocheted pattern for this? I’ll keep looking as well, since I prefer to crochet.

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3. Loved this post, but I agree Barb’s Koigu Ruffle scarf is knitted. Crochet purists and all… I have seen some of these projects on Pinterest and Ravelry but it’s wonderful to see them all together with your informative narrative. Thanks.

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