Week 19 = Mathematical Knitting Day 6 = May 12, 2014
Well tonight I wanted to give you someone else's opinion and research. I picked 2 articles from completely different sources and put them here for you to read. I hope you learn something new just like I did.
Binary Bonsai. These trees were created as part of the Botanica Mathematica project to illustrate exponential growth, bifurcation and fractals. Credit: Designer and coordinator: Madeleine Shepherd and Julia Collins. Artists: AZLY, Kicki Frisch, Ingalilsusa, Carmen Moran and Madeleine Shepherd. When knitters want to make tubes without seams, they sometimes use circular knitting needles, in which two points are connected by a flexible wire. A few years ago sarah-marie belcastro tied her circular knitting needles in a knot to see what would happen. She knitted along the knotted needles and ended up with a knitted trefoil knot, the simplest knot you can tie. Belcastro, a mathematician as well as a skilled knitter, was delighted. Her research interests include graph theory and knot theory, and after creating her first knitted trefoil she continued her adventures in mathematical knitting, developing a technique for knitting more complicated knots and links. At the Joint Mathematics Meetings in Baltimore last month, belcastro, along with Mercer University mathematician Carolyn Yackel, organized a special session that brought together mathematics, mathematics education and fiber arts. The mathematician-crafters involved in the session explored a wide range of topics. Most presentations fell into two broad categories: mathematics in the service of arts, and arts in the service of mathematics. University of Victoria mathematician Veronika Irvine's bobbin lace piece, "Cyber Rose," is in the first category. Irvine used mathematics to develop an algorithm for creating novel lace patterns. On the other hand, Central Connecticut State University mathematician S. Louise Gould's "Cuboctahedron-Projective Plane Transformer" is in the second category. Gould's motivation for making the brightly colored, zippered figure was to better understand the projective plane, a hard-to-visualize mathematical surface, by getting her hands on this physical model. >> View a slide show of the exhibits. Some projects combined aspects of both categories. Malone University mathematician Kyle Calderhead's "Hexagonal Hilbert" is a visualization of a variant on the Hilbert curve, a space-filling curve that is built using an iterative, fractal process. So in some ways it is crochet in the service of math. But Calderhead had to develop a technique to interweave two crochet meshes to create the final project. Knowledge of the mathematics he wanted to illustrate helped him innovate in crochet. Likewise, belcastro's torus knots and links required her to figure out a way to entwine her knitting needles, sometimes several sets of them, to create the intricate figures. In addition to short talks, the session included a juried exhibition of mathematically inspired knit, crocheted, beaded and stitched creations. Yackel and belcastro organized the first session on mathematics and fiber arts at the 2005 Joint Mathematics Meetings. Mathematically inspired fiber artists have also participated in the annual Bridges mathematical art conference, with many knit, crocheted and quilted pieces appearing in Bridges art galleries. For more information on any of the pieces in the slide show, see the session Web site.
Knitting can be used to illustrate topology - the
study of mathematical properties preserved when an object is twisted, stretched
or otherwise "deformed"
For some people knitting is an
ancient art, one they saw their granny do and one, because it takes so much
time, that seems to have little relevance for the modern age.
But there are growing numbers of people reclaiming the craft and trying make
it evolve. Dr Sarah-Marie Belcastro uses knitting to explore the mathematical concepts
that she uses, encounters and thinks about every day. She is not alone. Many knitters try to reproduce mathematical concepts in wool to stretch their
skills. Some, such as Brits Pat Ashforth and Steve Plummer, use it as a teaching
aid. Why? Because, Dr Belcastro said, the thinking required to turn a mathematical
concept into a pattern, then into a finished knitted object forces a greater
understanding of that shape, idea or object. "Sometimes," she added, "turning a concept or object into a knitting pattern
is often a mathematics problem on its own." Take, for instance, the job of knitting a surface. As Dr Belcastro points
out, surfaces are continuous unbroken sheets. By contrast, knitting is discrete, being made up of individual stitches like
the pixels on a TV screen. "Converting a smooth curve into a knitted pattern is a math problem because
one has to figure out where exactly to place the discrete changes in curvature
so that the object as a whole has as close as possible to the desired smooth
curving," she said.
Each colour of this knitted shape represents a
different projective plane
Dr Belcastro got the idea to unite yarn and maths at college after having
knitted on and off since childhood. As a left-hander, knitting had always
involved more thinking, and frustration, than it did for right-handed people.
But it also made her adept at knitting without patterns. She now uses the skill to turn fiendishly complex mathematical concepts into
woolly objects. The most complicated object she has knitted might, to the uninitiated, look
like a squashed hat, but mathematicians would recognise it as the
"non-orientable surface of genus 5". It represented, said Dr Belcastro, the connected sum of five projective
planes. She has since worked on an even more complicated object but is reluctant, so
far, to give details.
Metallic knits
Someone else stretching knitting into a 21st Century mould is crafter and
maker Charmione Lloyd. She has kept the needles but dropped the yarn in favour
of wire. She uses very fine needles and narrow-gauge wire - 0.4mm thick to form rings,
and 0.5mm thick to make bracelets. The inspiration to use wire came about because she had seen another crafter
using recycled copper coaxial cable to form part of a corset. At the time Ms Lloyd had a big spool of fine wire sitting around at home and
decided to see what she could turn it into. "No-one else seems to have gone the same way," she told the BBC. Part of the reason for that, she said, is because wire is not as forgiving a
material as yarn or wool.
There are Stitch 'n' Bitch groups in Cambodia,
Austria, South Korea and dozens of other countries
"I can only do so many before my fingers start to ache," she said. "It's quite stiff and you have to work it quite a lot." Knitting is going through something of a renaissance, said Ms Lloyd, its
growing attraction is revealed by the success of local groups where knitters
regularly gather. What they get up to there is captured in the name of the meeting: Stitch 'n'
Bitch. At least, she said, that is what it used to be called. Some of the older
women who attend objected to the name and now it is just called Knit and Natter.
A title, she said, which doesn't have quite the same anti-establishment
ring.
Feminist fun
The Stitch 'n' Bitch name is still used by other groups all over the world,
from Israel to Thailand. The first was established by New Yorker Debbie Stoller. As a pastime, she believes, it is far more suited to the fractured nature of
modern life than a casual onlooker might suppose. She also thinks it deserves to be reclaimed because it has explicit feminist
credentials. It's not a view everyone shares, she said.
Charmione Lloyd's bracelets are made out of knitted
wire, fastened with a magnetic clasp
"If I had said I was into soccer, that would have been fine, but because it
is knitting people look down on it," she said. She believes knitting and other crafts should be reclaimed for exactly the
same reason that feminists in the 1960s and 70s rejected them - because of their
historical link to women. Those early feminists tried to forge a new identity by setting themselves
apart from such traditions. But, said Ms Stoller, this missed the point that knitting was a hard craft to
master and had played a social role. "It's something that women have traditionally done and I went on a mission to
take it back," she said. Many have joined her. There are now more than 1,300 Stitch 'n' Bitch groups
around the world, and many more that are as well established but have not taken
that modern name. For Ms Stoller, the most important part is that those people, men and women,
young and old, have turned to knitting and found what it can do for them. "In the same way that fishing is not just about getting something to eat,
knitting is not just about making something to wear," she said.
Knitting question of the day
Which article piques your interests more and why?
Article Knitting,
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