beautiful equations

Today I watched the BBC 4 programme Beautiful Equations. I loved it. If slightly off centre for my research, it certainly asked the question can maths be beautiful? and gave scientists opinions on the answer, delving back as far as Isaac Newton and ending with Stephen Hawkins view today.

This programme was brilliant for me as it was made by an artist and art critic Matthew Collings, so was asked from a similar perspective to mine, whilst being answered, for the viewers benefit, in fantastically simple laymens terms. Hooray! I actually feel as if I understand a bit about maths, and am a little clearer about where I am headed with my research. 

The conclusion of this programme is that equations are "masterpieces that explain the universe we live in".  It would seem that several of the scientists featured in this programme used the idea of mathematical beauty to guide their work. Both Dirac and Einstein believed that the laws that governed the universe would have an elegant beauty, or simplicity, and therefore so would the equation that described them. Therefore, the idea of mathematical beauty comes back to nature, to simplicity and to purity of ideas, and leads to the notion that by pursuing beauty you end up with truth. 

Unfortunately it is only available to watch on BBC iplayer for another few days, so if anyone wants to catch up download now!

knitting - a teaching aid for maths?

Today I was sent a link to a video that showed and discussed the use of knitting in the classroom as a teaching aid for maths. Below is a highlight of the video via You Tube. Click here for the full video on Teachers.tv

The use of knitting being used in schools to aid learning interests me greatly, especially as part of the aim of my creative project is to use knitting as a form of accessible and tactile numerical communication.

This teaching took place in Shaftesbury Primary School in London. The maths teacher had a passion for knitting, and recognised how the use of numeracy within the knitting process could make maths both more accessible and easier to understand for those pupils who may ordinarily struggle with numbers and give them a chance to shine.

Children who excelled in knitting were teamed with children who were good at maths, and they were given several different tasks to complete that tackled many different areas of mathematical learning, from a timed knitting 'race', which combined the use of measurement, time, prediction and recording of data, to the adding and subtraction of stitches to form a certain shape, to the understanding and calculation of costing a garment.

The teacher felt that the important part of learning through knitting was that it took numeracy out of books and brought it to life. It inspired the children, put maths into a context and gave them a tangible and visible result for their efforts.

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.

freddie robins

Today I have been looking at the Freddie Robins project "how to make a piece of work when you are too tired to make decisions" . Robins conceived the idea for this when her daughter was only a few months old, and due to lack of sleep and time constraints she devised a way of working that eliminated the decision making process from her machine knitted textile art.

She achieved this by using 3 dice to select predefined choices. One die was to select the colour of the yarns, one to give numbers for the stitches and rows, and one to decide the technique that was to be knitted.

The results are an interesting reflection of a serendipitous piece of work, and also of how many smaller elements can be assembled to create a larger piece.

Although different in many ways from what I am hoping to achieve, the idea of the project is an interesting one, and has strong links with the idea of random theory and probability, which is a possible way forward for my work.

Obviously, Robins has come from a very different starting point and so her aims and objectives are not the same as mine. Although Robins used the dice to determine a random pattern, she did make decisions that were preassigned to each number thrown and these decisions were altered as the process developed, in order to achieve 'more consistently successful results".

I am quite surprised to find how much I like the idea of the random nature of the designs, but not the designers interference in the process. This is something I think I will battle with in my own work. Relinquishing aesthetic control is difficult for a designer, especially when my main aim is to produce something that is both mathematically viable and an object of beauty.

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.

garter bar

Ok, so the 'make your own garter bar' instructions from a load of hair pins and a metre rule turned out to be a lot more fiddly than it sounded! Apart from which, the hair grips pictured were far too big for the needles on my machine. Reading up on it a bit more it turns out that manufacturers didn't used to produce garter bars for chunky machines. I'm assuming that this would be the only sensible conclusion why someone would want to try to manufacture their own in this way.

After this I phoned round the existing knitting machine manufacturers, knitting machine spares shops & looked at the Guild of Machine Knitters website to see if I could find any for sale. The resounding answer was no, they stopped making them a long time ago and they are very rare and I would be lucky to find one.

This only made me want one more....I am desperate to experiment with this technique. I resorted to e-bay, where there were a couple (mostly by international sellers). I decided to splash out on a full boxed set with instructions. It should be arriving in the next few days! Now I only have to learn how to use it.

shima versus silvereed - the battle of the machines

I have been thinking a lot recently about which techniques and machinery I want to use in my creative project, and thought I'd better start writing it down in order to make some sense of it.

There seems to be so many possibilities that it baffles me deciding in which direction to go. The lack of decision on a final product ultimately makes it difficult to decide what equipment to use.

At Uni we have domestic Silvereed knitting machines and Dubied Industrial machines. There is of course, the option of finding someone to lend me their Shima for a few days.....?

I have turned over the question of the Shima Seiki in my mind for some time now, and think that I have finally resolved my dilemma about the pros and cons of using one.

Having had the amazing oppurtunity of doing my BA at a University that gave me the experience of designing and processing work on this machinery, I feel that I can confidently say that this is not the correct route for me to go down with this MA, or most certainly not at this stage and time.
There are several reasons for this. Firstly, one of my main aims for doing my Masters is to develop a working practice/ sustainable business from whatever product I develop. Using a Shima is neither physically or financially practical for me. Having spoken to the Director of Textile Studies at my old University, and a Senior knit lecturer at Kingston the practicalities of designing and using a machine at another university are limiting.
I made enquiries at Shima Seiki UK about the possibility of owning the software programme, designing at home and then 'bureauing' out to a company to knit the designs, as there is in other textile disciplines. I was told that the software is not sold seperate to the machinery and if it was would cost about £26,000! So that answers that question! Also, as brilliant as this equipment is, it does not lend itself well to several of the techniques that I am keen to take forward...for example, the knitted pockets are achievable on the Shima, but it is an impossibility to stop the machine and open the bed in order to place things inside, as I have done on the Dubied.

So on to the Dubied. I have a love hate relationship with these machines. These days it is more love than hate as I have become more confident and familiar with their sensitive quirks! I definately want to make use of these machines as they can achieve beautiful quality knits, and work both finer and chunkier than the domestic machines available. They have a double needlebed which allows me to work on just the front, or just the back of the knitting and to close the beds and knit across both, allowing greater versatility in my work. However, they don't allow me to hold stitches easily, which is something I really need to be able to do in order to create 3D effects.

After completing Year 1 of my degree course at the University of Derby, progressing to working on a Dubied in Year 2 and then onto using the Shima in my third year, I had dismissed the idea of ever working on a domestic knitting machine ever again. That was until I visited Knit-1 in August, and whilst there brushing up my skills on an industrial machine knitting course, I was wowed by the work that was being produced on the humble domestic machine. I think I had been put off by all my first year dropped stitches and clumsy attempts at fairisle using horrid coloured acrylic yarn that I never pushed the boundaries beyond the 1980's home knit conotations and realised the full potential of the machine.

Ironically enough most of my research and experimentation into constructing three dimensional knitted fabrics begins with partial knitting or short rowing, a technique most easily achieved on the domestic machine through the use of the Russell levers /Holding button. This allows me to hold some of the stitches, whilst knitting on others, exactly as you would in hand knitting when stitches would be held by moving them to a seperate needle or stitch holder.

The other advantage to the domestic machine is that you can add the ribber attachment to create a doublebed machine. This is not quite as smooth as the dubied, but something that opens up possibilities of having two needlebeds and the holding button on one machine.

The other technique I am interested in experimenting with is turning the knitting on the machine. When you knit on a machine there is garter stitch one side and stocking stitch the other. By the use of a garter bar you can pull all the stitches off the machine, turn them around and (hopefully!) put the knitting back onto the correct needles to resume knitting. Therefore creating stripes of alternate stitches.
I found this brilliantly innovative site which shows me how to make my own garter bar out of a metre rule and some hair clips....watch this space for the results.

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.

rearranging formulae: unwrapping books

Back in April I went to see this exhibition at the O3 Gallery in Oxford.

Science and maths books were donated by Oxford University Press, selected by Robert Fox (Emeritus Professor of the History of Science) and then given to participating artists.
In keeping with the logic and order associated with these disciplines, the books were wrapped, allocated a number at random and then distributed to the artists in numerical/ alphabetical order.

Here are some of the artists responses to the books they were given:

I love these images. It was fantastic to find an exhibition that related so directly to my area of research with such a diverse range of artists participating. Once again I could see elements of my own work within several of these pieces.

My design

The use of mirror reflection, light and transparency in these objects relates back to my observations of Blanka Sperkova's work, and once again highlights a direction in which I would like to take my own.

The other part of this exhibition I really liked was the accompanying booklet that was essential to viewing and understanding the work on display. It held a chart, set out like a periodic table, which corresponded each number, book and art work to each other. I like the fact that the viewer was given an key to unlock the mystery of this show.

This exhibition was held as part of the Oxford Science Festival, which runs every year so I will be looking out for more events here in 2011.

blanka sperkova

Blanka Sperkova is a jewellery designer who is probably best known for her organic wire sculptures.

She has perfected her unique way of working, a form of finger knitting inspired by traditional wire and lace making techniques from her Slovakian homeland.

Whilst neither a fashion designer nor a machine knitter, I came across Sperkova's sculptures in my search for three dimensional knits, and was fascinated by the degree of freedom of manipulation her chosen media allows. I am still uncertain in which direction my work is going...fashion or interiors? It is helpful to see this designers work and contemplate this.

She creates internal forms, experimenting with lighting and film to animate the sculptures, so that the shadows cast become more expressive than the original object.

"My objects take shape from within themselves; they anticipate themselves. There is matter, then form. Or there is form, then matter."

The use of light and shadow fits well with the latter two pieces of work shown on my first blog. I have used laser cut coloured acetate to form a pattern, but it only really works when it is backlit, then a whole new dimension is added.

Sperkova's designs led me to look further into knitting with wire, and specifically machine knitting with wire. I consulted 'Textile Techniques in Metal' by Arline Fisch.

It would appear that the biggest problem when knitting wire on a knitting machine is tension control. It is also advisable to cast on in yarn to begin with, then knit 1 row with yarn & metal together, before dropping the yarn and knitting solely with wire.

Materials that knit well are: fine silver wire, fine brass wire and copper insulation & electrical wire.

Tubular knitting with a knitting dolly or sock machine also appears to be a successful pursuit.

liz collins

Liz Collins is an American designer and artist who combines machine knitting with techniques of fabric manipulation to create wearable art pieces.

Whilst studying for her degree she came across the idea of 'knit grafting', a technique of hanging fabric from the latch needles during the process of machine knitting. This technique has allowed her to layer and fuse varying fabrics into her designs, creating sculptural forms over a tightly knitted bodice.

"It was a form of alchemy - turning simple cones of yarn into three dimensional, multilayered, and wearable pieces in a very short time frame."

The idea of constructing a multilayered and multi textured fabric is an interesting one. Like Sandra Backlund, Collins also says that the fabric itself is of 'perpetual ongoing inspiration' to her.

I like the way that Collins manipulates form whilst the knitting is still on the machine, building the garment and the fabric simultaneously.

One of my points of research is to look at the different ways in which I could construct shapes, other than by altering the surface of the fabric. I am interested in the way seams could be joined and moved to alter form, creating shapes from a single piece of fabric and examining contouring, shaping and placement within this theme. The technique of 'fabric grafting' is not unknown to me, and is a definite point of interest when thinking of alternative ways to join seams.

Collins is also known for working with experimental materials, something else I am keen to research on this MA. She is quite strategic in her methods, taking advantage of the natural stretch in the knitting, working with complimentary and contrasting fabrics to create shape, volume and silhouette.

Looking at this designers work has made me think a lot about the types of yarns I am using, and the possibilities and differences I could create within a technique by using high or low twist yarns, or by using a combination of natural and manmade fibres to experiment with shrinkage or expansion in the natural elements when heated or washed.