Knitwear Design and Applied Maths, part 2

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You can read part 1 of this series here.

Being a knitwear designer has taught me more about mathematics than my formal education. This isn’t an exaggeration: I mean this seriously and literally. 

I know that when I calculate, write and grade pattens, I need the numbers to convey the visual relationship that embodies the aesthetic of the design.  I work very intuitively, relying on my senses – but I am still learning how to reconcile my creative power with my level of mathematical proficiency. 

Maths is a netherworld of language learning that frustrates a number of knitwear and crochet designers.  I know what I want to say, I can draw it, I can show you how to do it, but because I am highly unlikely to meet every knitter who buys my patterns, I have had to learn how to speak in numbers.

Whilst writing this post, Googling in hopes of this predicament not being all in my weird little head, I came across these two sentences from mathematician Josh Lury:

The act of doing mathematics is not…about grinding through a process, but instead becomes a way of triangulating meaning from a context, a representation, and a symbolic description.

For many mathematicians, a problem remains unsolved until it is unlocked not by completing calculations, but by finding the visualisation or picture that reveals its structure.

https://blog.pearsoninternationalschools.com/reconsidering-maths-as-a-creative-discipline/

Knitwear designers need to create their own mathematical language

I couldn’t find out whether Josh Lury is a knitter, but he certainly sounds as if he could be one!  The notion of triangulation had never crossed my mind, but it describes perfectly what knitwear designers are trying to do.  Our work is far from easy: our context is the overall design (e.g., shawl, sweater); the representation is the stitch pattern; and the symbolic description is the knitting language we have learnt in the pursuit of our craft. 

Our (creative) problems are the designs we originate, the swatches we produce, and it is the image of these – especially the latter – that reveal the structure of how our design works mathematically.  We designers create patterns, but we also need to identify these patterns in a way that makes numerical sense; to define the principles that make the pattern repeat work.

THIS is applied maths and knitwear design in action.

Again, to do this well requires an understanding of maths methodologies that surpasses formal education – if not formal education as it is currently.  A knitwear designer has to understand and choose the most appropriate way of approaching their design mathematically.  

This makes the difference between a well-written pattern and a badly-written pattern: How articulate and concise are the instructions?  Identifying the number patterns and choosing the best methodology for a particular design has to do with so much more than getting the correct stitch counts throughout; it also relates to mental energy and comprehension for designer, tech editor, and knitter.

Knitwear design decisions = mathematical implications

To recontextualise and further exemplify: it is the order of construction for a sewn garment design, or the recipe for a dessert.  Regarding the former, why have you, as the designer and pattern cutter, chosen to hem in the middle of a project instead of at the end?  Why have you taken suppression as pleats instead of gathers, when both are suitable for design and fabric?  Why are the sleeves inserted flat instead of in the round?

For your sweet dish, you need to make a meringue for part of it – but how will you do it?  Will you choose the French or Italian method?  Why?  And how might your choice affect the composition and outcome of the recipe – and other people’s ability to follow it?

These discrete, unitary choices are especially important – and sometimes frustrating – for designers whose work often features details that set key conditions.  (Hello! 😊) The Alyssum sweater, my summer release for 2022, tested me like no other design has before. The mathematical principles of Alyssum’s shaping is the reason why it missed the planned spring schedule.  The stitches must align perfectly AND over a specific multiple, otherwise the design fails. 

And it’s so important to understand the how and the why. Without this comprehension, you won’t choose the most efficient way of working, and the knock-on effect will make editing and grading more laboured than you could’ve imagined.  Design conception and idea generation establish a mathematical relationship; design realisation and pattern grading demonstrate how this mathematical relationship works. 

After all, your garment can’t only work for the sample garment or root sizes; it needs to work for all the other sizes too. This process in itself is an exercise in applied maths and knitwear design.

Applied maths, sizing, and grading knitting patterns

I’ve saved sizing and grading until last for good reason, in case you were wondering about its conspicuous absence.  I couldn’t write a blog series about applied maths and knitwear design otherwise! Grading is last because the mathematical foundation set by the stitch pattern (design development) and anatomy (pattern drafting) informs the grading process. 

In Alyssum’s case, the complexities meant that I had to offer 6 dual sizes instead of 12 single sizes. The maths wouldn’t let me have it any other way.  The scale of the repeat and the fitting standards across the range couldn’t be satisfied within 12 sizes.  I realised this early on because training in pattern cutting = understanding how silhouettes relate to the body.

I cannot stress enough how much an understanding of how this works geometrically can benefit knitwear designers.  Drafting and creating toiles allows you to see spatial relationships and how the shapes of pattern pieces relate to the bodies wearing the garment. This includes how the ease and grading is distributed.  Dress forms can be adapted for various sizes and shapes to accommodate any research or testing. 

You don’t have to design garments in pieces to benefit from this.  For example, if you design top-down yoked sweaters, training in pattern cutting and draping will help you to understand how and why percentage systems fail, and exactly how your design needs to flexible across a sizing range.  Human bodies are full of curves and contours, so make allowances for them. Don’t knit and hope that the malleability of knit fabric will help you out.  Your pattern has to be well engineered.

We humans – especially knitters – are MADE for this type of maths.

Thankfully, the ability to do this is part of human nature.  Josh Lury again:

Patterns are irresistible to humans – our brains are highly sophisticated pattern-spotting machines!  As pupils see patterns emerging in calculations, their brains will automatically start to work mathematically by:

Predicting how the pattern will continue;

Looking for similarities and differences;

Looking for what remains constant, and what changes.

Their thinking will be greatly enhanced if they are supported in:

Checking if their predictions were right;

Adjusting their thinking where their predictions break down;

Considering the reasons for what causes the pattern.

It is important that pupils recognise the essential patterns but they can also gain a deeper understanding by taking them apart and putting them back together.

Josh Lury, A Creative Approach to Teaching Calculation (Bloomsbury, 2015)

To engineer is to innovate, and that’s what designers do, including knitwear designers.  Mathematics is there to help us, but we’re not always aware of how supportive and powerful it can be.  We just have to tune in to what makes our designs work, and why.  There’s truth in the numbers.

I go into more detail about my approach to applied maths and knitwear design with these short courses:

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