The Science of Stitches: Exploring the Math & Geometry Behind Knitting & Crocheting

Are you one of those people who believe maths is as useless as wearing a hat to protect yourself from hail? If yes, we are about to prove you wrong!

Contrary to popular belief, maths and geometry are deeply integrated into even the smallest aspects of our daily lives. Take knitting, for example. Have you ever considered how you are able to make these beautiful symmetrical patterns and shapes through nothing more than a little yarn and two knitting needles? It is all thanks to the geometrical applications of mathematical equations.

Get ready to have your mind blown because, in this blog, we take a deep look at the relationship between knitting, geometry, and math. Additionally, we will analyse how you can create mind-blowing knitting patterns with nothing but math and some yarns. So, let’s get this crochet party started!

The Relationship Between Knitting and Math

According to many studies, knitting and math are linked indefinitely through a number of ways:

  • When you knit with yarn, a non-elastic substance, you will end up with an elastic fabric. This is due to the knot theory.
  • Many geometrical shapes tend to be created by the linkage of lines drawn at particular angles, tied together with different fixed points, much like a knitted article where strings are tied together with different angles, fixed at a knot to hold it in place. This is why making geometrical shapes using crochet is so easy.
  • Another great observation made by scientists and mathematicians working on this is that you can also alter the durability and integrity of a knitted fabric by using different knitting patterns.

Top Math Knitting Patterns You Can Try

Since maths and geometry can be easily expressed and explained through crochet and knitting, many scientists have taken to crocheting various geometrical shapes and patterns. Let us take a look at some of these:

1.    Cyclic Groups

Cyclic groups are a phenomenon in maths that distinguishes a subset of integers using their repeating properties. To put it simply, certain groups generated by the same elements and following a specific path only to return to the starting point can be defined as cyclic groups. In geometry, these groups would be represented by a flower or star-like figure.

This shape can easily be translated onto a crochet medium through the magic of geometry. In order to do so, however, each line in this geometric figure needs to be knitted as a cylinder while keeping the connecting points interlinked to each other.

Ken Levasseur, a University of Massachusetts maths professor, used a similarly generated shape from a Knitting Nancy program to demonstrate the various cyclic groups interlinked to each other through channels within the tubes and repeated patterns. This method of teaching makes complex mathematical equations and phenomenon easy to understand and digest.

2.    Hyperbolic Plane

Hyperbolic planes may be shapes with a noticeable curvature at every possible angle, but these shapes are actually planes. The curvatures are a result of its counterintuitive and complex geometry. It is commonly known as a surface that is expanded by space and curves away from itself at every point of tension.

These geometric shapes are commonly used to make frills or elaborate designs that draw your attention. Such shapes are hard to translate to any form other than crochet, as paper and other unconventional materials aren’t durable enough to maintain their shape in a hyperbolic state.

Even though there is no known analytical formula for such a shape, crocheting allows you to control every point of tension and, therefore, the curvature of the fabric. This shape can be knitted into existence by starting to crochet in a circular motion only to increase the tension in every other stitch to give it that curvature.

3.   Klien Bottle

A Klein bottle is quite an interesting mathematical shape that has no inside or outside; instead, its surface continues on indefinitely till you reach the starting point again. Such shapes can be cut in half and made into a Möbius band, which we will discuss later on in this blog.

Although not naturally occurring, this shape is imperative to understanding the seamless continuity in a set of elements or integers. When knitting in such a way, you need to understand that there is no difference in yarn or texture that would distinguish the two sides of this shape. Of course, you can knit a design by interchanging various colours to represent the Möbius bands within the Klien bottle.

To knit a Klien bottle, you should consider the shape to be made up of cylinders. Knit a cylinder, pass one end of the crocheted shape through its side, and fix it in place with a few stitches.

4.    Multiplication

When we go towards more basic mathematics, children often find multiplication quite hard to understand. Such a concept can easily be explained through the aid of knitting as a visual aid. Human beings tend to gravitate towards visuals, and using crochet to explain otherwise difficult-to-grasp phenomena can help students understand the most complex mathematical and geometrical theories.

According to Pat Ashforth and Steve Plummer, – British maths teachers who used a knitted chart with varying colours to help their students learn how to multiply – students found it easy to visualise ideas that were previously unclear to them. This way, students also get the chance to recognise the occurrence of colour patterns in the crocheted fabric and identify data sets.

5.    Lorenz Manifold

A Lorenz manifold is a geometrical representation of seven equations that mathematically denote the transfer of thermal energy in an atmosphere. Obviously, such a shape does not exist in nature and cannot be seen, but creating a knitted version of it could aid people in understanding the complexities of such a unique phenomenon.

Hinke Osinga and Bernd Krauskopf, professors at the University of Bristol, used a knitted version of this shape to explain chaotic weather systems. According to the theory, even chaos, as a destructive force, gravitates towards organisation.

Crocheting a Lorenz Manifold works on the same principle of knitting a hyperbolic plane. Use coloured stitched markers since the pattern is a little more complex than the usual shapes on this list. Make sure to follow a proper blueprint and keep alternating the skein colours to highlight the contrast in the system.

6.    Numerical Progression

A numerical progression refers to the concept of a set of numbers occurring one after the other with a common difference between them. This type of progression is also termed arithmetic progression and can be used to simplify complex geometrical graphs into a simple, easy-to-digest, three-dimensional structure.

A good example of this is a recent trend that a knitting enthusiast with the TikTok handle @itsbreellis followed, where she crocheted a temperature blanket for the entire year 2023. Many people on the r/knitting subreddit were seen to follow suit and showcased their complete blanket at the start of the new year. This type of numerical progression is linear and has around 24 hours of common difference in between.

7.    Möbius Band

A Möbius band, much like its amalgamated form, is a shape with a continuous side and no inside or outside. Its shape is achieved by closing a single strip by introducing a little half-twist. This type of shape is less complex than the Klien Bottle but works on the same principle. When you follow one side of a Möbius strip or band with your finger, you will continue to move across it all the way over and return to the starting point without ever having to change sides.

Theoretically, the Möbius band represents infinite space. Of course, to understand it, you may need to make it much more digestible and simpler. This is where using a knitted version of the Möbius band comes in.

When you knit a long strip, twist it into a slight curve, and stitch together the ends of it, the Möbius band will take form. This is perhaps the simplest crochet geometry pattern on this list, but it is also the most commonly represented in pop culture, media, and science museums.

Where Can You Get The Supplies To Make Your Crochet Geometry Patterns?

To get the finest quality knitting supplies in Australia, you don’t need to look further than Grumpy Ginger Yarn Co. Providing the highest quality yarn and crocheting tools; we introduce you to an entirely new world of colour and creative freedom. Unlock your true knitting potential with the best in the market!

To Wrap Up

It is quite clear that the relationship between knitting, geometry, and math is not coincidental. In fact, you can even go as far as to say that knitting and mathematical phenomena go hand in hand. The reason why there is so much interlinking between these concepts is that math is a numbers game, and when you crochet a pattern, you are essentially playing that game on a more three-dimensional plane than your regular two-dimensional paper one.

To get the best crochet supplies, you can trust Grumpy Ginger Yarn Co. to deliver them. So, if you have the skills of crocheting, it may be time to bring out your knitting needles in your math class to understand complex concepts.