the maths of miyake

Yes, here is yet another Issey Miyake maths inspired collection!

I was really excited to learn of Miyake's Autumn/ Winter 2010/11 ready to wear collection, a collaboration between Issey Miyake's creative director Dai Fujiwara and William Thurston, Professor of mathematics and computer science at Cornell University. "We used the technology of mathematics to make art" said Fujiwara at the opening show in Paris this March.

Fujiwara and Thurston share an interest and enthusiasm in three dimensional design, so the  collection entitled '8 Geometry Link Models as a Metaphor of the Universe', based on the fundamental geometries of three dimensional spaces, was of mutually beneficial interest to the pair. This article from ABC news and this interview on You Tube by Parismodesen gives an interesting insight into the common interest that unites these two seemingly disparate professions. Thurston explained "We are both trying to grasp the world in three dimensions, under the surface, we struggle with the same issue."

Fujiwara created garments based on different elements of Thurston's principles, resulting in inwardly twisting, knotting and crossed draped fabrics.

These designs have been criticised for there over simplified form, and there is no doubt that they are only loosely based on mathematical principle and not a literal interpretation, but then they have been used as inspiration, rather than to communicate an idea.

As one of my main focuses for this research I am looking at the question can maths be beautiful? As a designer I find these interpretations of mathematical ideas aesthetically pleasing. Is that because beauty truly lies 'in the eye of the beholder', or is there actually a winning formula that the majority of us would agree as beautiful? I find this collection of particular interest as there are many similar mathematically knitted objects already out there on  websites, such as that of Sarah - Marie's: The Home of Mathematical Knitting.

Even if the 'perfect' pattern is defined for us by the laws of mathematical 'beauty' (that of proportion & symmetry etc), there will always be a very personal design decision made by the knitter as to choice of scale, tension, yarns and colour used, and it appears to me that it is these elements that determine as much aesthetic value as the pattern itself.

132 5 issey miyake

This autumn Issey Miyake launched his latest label, 132 5 Issey Miyake, an idea "born from a union between mathematics and clothes making".

The title of the collection explains the concept:

" Each of the numerals has a special significance. The numeral '1' refers to a single piece of cloth, while '3' refers to its three- dimensional shape. The following '2' comes from the fact that a 3D piece of material is folded into a two dimensional shape, and the '5' seperated by a single space refers to the time between when the folded forms are made and people actually put them on, giving birth to clothing. The numeral '5' also signifies our hope that this idea will have many other permutations".

The collection consists of ten basic two dimensional patterns. The look of the eventual garments is decided by the positioning of sharp, precise, permanently creased lines that the patterns are folded along. 

These patterns expand into skirts, shirts, dresses and with the help of some strategically placed invisible snaps, the wearer can change the shape of the garment into trousers and sleeved jackets.


This origami style collection was inspired by Jun Mitani, a Japenese computer scientist, who created a program to construct three dimensional geometrics from a single piece of paper. The project was led by Reality Lab, a Research and Development team formed by Miyake, his Textile Engineer Manubu Kikuchi, and Pattern Engineer Sachinko Yamamoto.


The Japenese fashion designer is famous for his technology driven clothing design, with a focus on sustainability, efficiency, ecology and accessibility to the wearer. This collection ticks all the boxes, with all of the fabrics made from recycled plastic bottles (refined PET polyester). These articles, one from Dezeen magazine, and the other from the Independant newspaper hold informative interviews with Miyake and contain much more detail behind the concept of the design.


I am really inspired by this collection, not only for it's obvious mathematical connections, but by the techniques used to create these designs. In my original project proposal I outlined my interest in examining the construction of shapes, looking at the way seams could be joined and moved to alter form, and examining how to create form from a single piece of fabric as Miyake has so beautifully illustrated. 


The permanent creases are obtained by heat pressing the two dimensional fabric. I am not sure how well this technique would work on knit, but it is certainly something I will bear in mind when experimenting with synthetic yarns. I am sure that there are many possibilities of using heat to alter form with synthetics. Perhaps engraving or scoring fold lines into a garment on the laser cutter is also a possibility.

the science of knitting

Today I have been concentrating my research on the relationships between maths, science & knitting. There are more links out there than you might initially think.

The name that crops up most when researching this category is that of Daina Taimina, a mathematician who teaches at Cornell University in New York. She made a significant scientific breakthrough by inventing what is now known as 'hyperbolic crochet'. By using a handicraft technique she produced a surface model of a hyperbolic plane, something that until that time had only been understood as an abstract concept. This article in The Times explains it much better than I ever could!

Hyperbolic crochet

The fashion & knitwear designer Sandy Black has a different link with the subject. She studied pure and applied mathematics at University College London, where she also bought her first knitting machine and began to combine her two favourite subject matters together.

This article demonstrates Black's theories linking maths and knitting.

Sandy Black is now Professor of Fashion and Textile Design & Technology at the London College of Fashion University of the Arts London. She is also Director of the Centre for Fashion Science, an institute focusing on research into:

• Considerate design
• Direct 3D design and manufacture
• Digital Studio: Direct 3D design and manufacture/ blending the real and the virtual
• Seamfree production in knitting, welding and rapid prototyping technologies
• Mass customisation for fashion and footwear
• Multifunctional textiles and fashion
• Living Colour
• Cosmetic Science

There is some fascinating sustainable designing going on here. Check out the Wonderland projects dissolvable dresses! The idea behind this is to develop a plastic that usefully degrades once it's use has expired. In this instance the dress dissolves into a gel that can be used to grow plants.

The subject of architectural knit is also pretty exciting. There seems to be a surge of development towards knitted performance fabrics. CITA, the Centre for Information Technology & Architecture in Denmark has developed some fantastic 'working' textiles such as this blend of Kevlar, polyeurethane and carbon fibre which has been knitted into a composite material for building structures.

Another collaborative project undertaken by this company is that of CNC knitting and CAD Architectural software, resulting in the design of Listener, a smart material that reacts, via sensors woven into the construction of the fabric, to the human touch.

I came across the above two developments from a blog called Fashioning Technology by Syuzi Pakhchyan. It contains posts that explain how to combine craft & technology to make electronic working and wearable art pieces.

Along similar lines, I came across this article in Knitting Industry News, which showcased the development of the Cullus fabric which has sound absorbent properties.

Cullus is a flat knitted material. It can be hung as flat panels or manipulated into three dimensional objects. It is interesting to observe that the sound absorbency qualities are the same, regardless of the form taken by the material.

As well as these very technical, industry developed fabrics, there is also a lot of interest in science and maths related knitting going on in the domestic circle.

When searching on Wikepedia the link to Mathematics and fiber arts brings up many sites where ordinary people have knitted objects based on mathematical or scientific theory.

A good example of this would be the DNA scarf, commissioned by Dr. Thomas Montville a Professor at Rutgers University, New Jersey from one of his students, June Oshiro.

This article has an interview with Oshiro, now a microbiologist in Food Science, describing how she was inspired to describe a double helix in yarn whilst persuing her PhD research.

I have found many other objects of interest created by domestic knitters to illustrate or answer some of these mathematical questions. This website has some interesting patterns and ideas, from the klein bottle hat to the Fibbonacci sleeveless shirt, but from a design perspective, most lack aesthetics.

Overall, it would appear that there is a definate interest from scientists about the value of craft techniques, especially knitting & crochet, and a reciprocal interest from artisans to collaborate on projects.

I came across a blog by Andrew Maynard, Director of the Risk Science Center at the University of Michegan School of Public Health. It's called 2020 Science and one post in particular, knitting science,  discusses why there is this growing interest between knitting, science and mathematics.

"Knitting patterns as code for complex three dimensional structures - it's an idea that makes perfect sense when you think about it. After all, DNA uses sequences of four molecules to code for complex protein structures, so why not use deceptively simple "knit one purl one"- type sequences to construct complex shapes."

This blog has many relevant links to my subject and confirms to me that there are parallels between these areas that have begun to be explored by others, but I feel really excited that there is still plenty for me to investigate.

science museum(s)

As inpiration for my research topic I visited both the History of Science Museum in Oxford, and the London Science Musuem. I only had a short amount of time in each, and took hundreds of photos to make up for this. Another visit is definately due.

In particular I liked the 'Strange Surfaces' exhibition in the Mathematics section of the Science Museum. This included mathematical surface models made of cardboard and string. These are an example of descriptive geometry and have been used to illustrate geometric ideas in mathematics since the 1840's.

'A mathematical surface model is one that follows a mathematical formula or definition, or illustrates a mathematical concept'.

In particular I liked these cardboard sliceforms by John Sharp. They made me think of different ways of cutting and joining and contructing shapes. I suppose there are lots of possibilities in the area of three dimensional knit design to cover and wrap a supporting framework in knitting. This is an area I have thought about before and rejected. Part of my interest in this area is in developing and manipulating the fabric on the machine and not afterwards. It has reaffirmed the idea that I definately want to construct from within the fabric, and then construct a product from that fabric.

The mathematical instruments were inspiration in themselves.

Everything about these instruments is pleasing to me. The symmetry, repetitive patterning and grid divisions as design inspiration. Also, something about the similarity to the knitting machine bed makes me think of patterning & counting as I work.

A sketchbook sample based on these ideas

Once again the use of glass and light in the form of prisms and telescopes (and this cylindroid) had me thinking of relection and refraction.

As you would expect there were also hundreds of other brilliant and inspiring three dimensional objects on display. Here are a few more:

All of these shapes and colours and structures have energised my 3D aspirations, and given me a bit of clarity of how I am going to combine my inspirational science & maths subject matter with knitting.

london design week

In September I visited Tent London & 100% Design as part of London Design Week. My aims were to gauge the target market for 3D textile design (particularly knit), check out the competition and gain inspiration & direction for my Masters creative project.


Not holding out much hope on the knitting front I was amazed that the first thing that greeted me at the Truman Brewery entrance into Tent was the 'Giant Knitting Nancy' by Superblue Design.

More of a community project than a piece of textile art, this giant 3D structure combines creative participation with a growing seating and play area. Still food for thought on a grand scale for 3D knit design.


There were some amazing interiors products on display at both trade shows, but probably the two I felt were most relevant to me were that of Penelope Jordan (Tent) and Siwen Huang (100% Design).


Penelope Jordan creates textile art pieces. Her work combines colour, structure and three dimensional design through placing and folding "a variety of textiles in a controlled repetitive order".

Although my work has a very different aesthetic from Penelope Jordan's, I feel there is a similarity in both the ethos and the outcome. She too is interested in traditional craft skills and the making process, but brings a contemporary twist through her designs and use of materials.


Siwen Huang is a textile designer with a range fabrics that she describes as 'textile futures'. She specialises in collecting and redirecting light for pattern creation.


"I used reflective and flexible materials to create three dimensional optical surfaces, by laser cutting and hand finishing techniques. The finished pieces distort and redirect light as it hits the surface creating illusory and ambiguous surfaces."

It seems as though there is a very clear pattern emerging within the designers and exhibitions I am inspired by.  That of combining traditional and modern textile techniques, the repetitive order of designs and the creative use of light and shadow to form part of the design.


As far as my aims to gauge the target market went, it appears that there is a lot of interest in creating three dimensional textural surfaces, everything from fabrics to wallpapers to textile art. 
There were industrially knitted performance fabrics on show at 100% Design,  but no three dimensional innovative knitted fabrics for either fashion or interiors.

e-diary

I am a student studying at Bath Spa University for an MA Design: Textiles. This blog will show the online development of my research and progression of my creative work throughout the course. I am a knitter, and am fascinated by constructed and constructing textiles.

My aim is to create an aesthetically pleasing design based on three dimensional mathematical principles. I have always felt that writing a knitting pattern is akin to writing a formula that allows me to calculate a unique equation, or in this case, creation. Can knitting be scientific? Can maths be beautiful? By blurring the lines between the 'domestic' and the 'academic' I intend to create a formula that satisfies everyone, communicating unfamiliar ideas through accessible design.

Here are some recent samples I have been working on: