There are three things I wouldn’t want to do without. Music, Math, and Crochet. They each shape my world in distinct yet interconnected ways, blending artistry, rhythm, and logic into a seamless experience. Crochet may seem like a simple craft, but it’s deeply rooted in math—from geometric shapes to complex algorithms that guide every pattern and stitch. Music, too, shares this mathematical foundation; its structure, timing, and harmonies are driven by beats and intervals, creating emotional depth with calculated precision. And what crocheter hasn’t known the relaxing calm that overtakes you after you’ve “found your rhythm” when working on a project. For me, math is the thread that binds them all, revealing patterns and symmetries across each realm. So, that’s what we’re going to explore today…Mathematics and Crochet.
Geometry in Crochet: Shape and Structure
One of the most evident ways mathematics manifests in crochet is through geometry. The basic building blocks of crochet—the stitches—come together to form various geometric shapes. For example, crocheting in the round can produce circles or polygons, while working in rows creates rectangular or square shapes. More complex patterns might incorporate triangles, pentagons, pineapples (which we’ll explore in another post) or even hyperbolic planes.
Many crocheters use geometry intuitively without realizing it. When you increase or decrease stitches, you’re manipulating angles and curves to change the shape of your project. For instance, adding stitches at the correct intervals in a round will create a flat circle, while fewer increases will produce a bowl-like structure. Conversely, too many increases will cause the fabric to ruffle or flare out—a principle used intentionally in decorative crochet like ruffled edges. (For those of you wanting to watch a Math Nerd nerd out on crocheting circles, check this out!)
The Fibonacci Sequence and Crochet Patterns
The Fibonacci sequence—a series of numbers where each number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13, etc.)—appears frequently in nature, from the arrangement of leaves on a stem to the spiral of a seashell. This sequence has also found its way into crochet.
In patterns such as the spiral motif, Fibonacci’s influence can be seen. Crafters often use the sequence to determine the number of stitches in each round, creating a natural-looking spiral. Sometimes refereed to as the Golden Rectangle or the Golden Ratio (the ratio of the length of a rectangle’s longer side to the length of its shorter side is equal to the golden ratio, or 1.618) makers of all sorts throughout history have used it to create things considered pleasing to the eye. By following Fibonacci numbers, a spiral expands at a consistent rate, mimicking the growth patterns found in nature.
Symmetry and Fractals in Crochet
Symmetry is a fundamental concept in both mathematics and crochet. Many crochet patterns rely on the repetition of motifs in symmetrical layouts, whether it’s a granny square blanket or a doily with radial symmetry. This balance and repetition create harmony in the finished product, much like the symmetry found in nature.
Fractals, self-similar patterns that repeat at different scales, also appear in crochet. A classic example of fractals is the Sierpinski triangle, a shape made up of smaller triangles that repeat infinitely. While it’s impossible to crochet an infinite fractal, many crafters have created impressive representations of fractals through repeating triangle or square motifs in their work. Visit VirtualMathMuseum.org to see how the Sierpinski Triangle pictured below is a continuous curve, or a piece of yarn tied end to end.
Algebra and Algorithms: The Foundation of Patterns
Crochet patterns are essentially algorithms—a series of instructions that, when followed, produce a specific outcome. Understanding patterns requires logical thinking, sequencing, and sometimes algebraic principles. For example, when creating complex designs like lace, crocheters must understand how different stitch combinations (such as chains, double crochets, and picots) will work together to create the desired effect.
Moreover, crocheting with motifs or modules, where the same element is repeated and joined together (think creations containing serval Granny Squares or a blanket made by Corner to Corner Crochet), is like solving a problem with modular arithmetic. You’re essentially working with a system where repetition and arrangement determine the outcome, much like how algorithms solve problems through step-by-step processes.
(and last, but by no means least…)
Hyperbolic Crochet: Bringing Curved Geometry to Life
This fascinating topic will have a post all its own! While you wait, you can check out some objects created by students from the Math Department of the University of Wisconsin - Madison
Conclusion: The Beauty of Numbers in Crochet
At first glance, crochet may seem worlds apart from math. But as you dive deeper into the stitches, shapes, and patterns, you find a beautiful intersection of the two. Crocheters, whether they realize it or not, have always applied mathematical principles in their work. From calculating stitch counts to creating symmetrical designs, math has played an essential role in turning a simple skein of yarn into a work of art.
So, the next time you pick up your hook, remember—you’re not just creating something beautiful. You’re also engaging with the art of numbers and combining creativity with the precision of mathematics to bring intricate designs to life.
This is yet another way that crochet is more than just a hobby; it’s an exploration of mathematical principles, whether through the geometry of shapes, the logic of patterns, or the aesthetics of natural growth. Embracing these connections between crochet and math can open up new creative possibilities, enhancing both the craft and the way we think about and see the world around us.
Wow! it all makes sense now.
5 years of School choir, a Statistics Graduate and practitioner of complex crocheter. thank you for putting this together. What a revelation of life :)