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.