The Mathematics of Crochet

Summary

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 ...