(sarah-marie's mathematical knitting pages and mathematical fiber arts pages)
Also: Rachel's Cool Increase is a match
for k2tog; two knit stitches flow out of one with no bumps.
Conference Sessions and Books
Carolyn Yackel and sarah-marie belcastro co-organized three
mathematics conference sessions, each of which included a sequence
of talks and a mathematical fiber arts exhibit. We have co-edited
two books on mathematics and fiber arts written for crafters,
mathematicians, and mathematics educators.
AMS Special Sessions in Mathematics and Mathematics Education in
Fiber Arts:
A customizable pattern
for the hyperbolic baby pants from Making Mathematics with
Needlework is available for free at the Wolfram
Demonstrations
Project.
Negatively curved Mobius bands, Virtual and Physical
Shape Exhibition (Juried), Shape
Modeling International, College Station, TX, May 22--25,
2012.
Dusk or Dawn (K_6 on Mobius band) and 8-colored Hyperbolic
Pants (Map on the Surface of a Two-Holed Torus Requiring 8
Colors), Sticks,
Hooks,
and the Mobius: Knit and Crochet Goes Cerebral, Lafayette
College Art Gallery, January 8--February 5, 2012.
Knitting
by Numbers, Lucinda Mathews, Plus Magazine, Issue 51,
June 2009 (runner up in the general public category of the Plus
new writers award 2009).
Crafting Geometry (.pdf from O'Reilly Media) by Arwen
O'Reilly, CRAFT: magazine, Vol. 01, pp. 46--49.
Crafty
Geometry (.pdf from fiberfolio) by Erica Klarreich,
Science News, Dec. 23, 2006; Vol. 170, No. 26/27, p. 411.
talks on mathematical knitting
You know, just in case you want to invite someone to speak on
mathematics and knitting...and if you've been to or given a talk
not listed here, please let me know
so I can add it.
Mary Harris, Spring 2011, Some Mathematics Within? (YouTube
recording of much of the talk, in four parts) Mary reviews
some of her educational projects that expose the mathematical
thinking embedded in practical knitting (and sewing and weaving
and...) that is done around the world.
Hugh Griffiths, Spring 2010, Geometric Knitting II .
(slides)
This describes how to knit Seifert surfaces, generate cellular
automata lace, and make a particular universal cover scarf.
Hugh Griffiths, Fall 2007, Geometric Knitting. (slides)
Hugh describes how to use differential geometry to use the
metric on an embedded surface to produce a knitting pattern.
Amy Szczepanski, Spring 2006, Knitting Geometric Shapes:
How do you knit a circle? Amy talks about how gauge and
appropriate increasing combine to design a proper circle, and
applies her methodology to discover and fix a mathematical flaw
in Elizabeth Zimmerman's Pi Shawl.
Amanda Redlich, Spring 2006, Knitting Knerdery. (abstract)
Her survey for non-knitters included coordinatizing knitting,
non-rectangular grids, different mobius strip constructions, and
some mathematics that arises from knitting (knot theory,
curvature/shaping, Turing machines).
Nate Berglund, Spring 2006, Knitting as a means of
Visualizing One-Sided Surfaces. (slides)
His audience is mathematicians (beginning grad student level).
Nate explains how knitting can model immersions of surfaces, and
shows how he designed his knitted Boy's Surface using a
polyhedral model of the immersion.
Dan Isaksen's Möbius Knitting paper. I disagree with the conclusions of this
paper, because (a) the special stitch introduced is not as
symmetric as claimed (it still has a half-stitch glide reflection)
and (b) plain seed/moss stitch is just as symmetric, but much
simpler. But Dan is cool anyway, because he can use cohomology to
do arithmetic.
By convention, change ringing only lists the first half of the permutations in a sequence, and ringers then reverse the first half to get the second half. The script doesn't incorporate this, so the user must enter the whole place notation sequence to get the entire chart.
Lara Neel's Math4Knitters podcast/blog (where this website is mentioned, in Episode 12
(of the old incarnation of the podcast)! and again in Episode
33!(.mp3; text here))
I know there must be more out there: witness qB (Rachel
Rawlins)'s comment
from 1.12.2004 on a Making Light
blog entry. "Damn! and I thought I was the only person to explore
maths in knitting. One particular favourite was to start with the
alphabet in morse code (x and blank), write an appropriate word or
series of initials as the base and then run Xor or other similar
function in a spreadsheet. Binary numbers would also do, I
suppose. Then you have a unique pattern which can form the basis
for work in either colour or texture."
(There are tons of technical textile sites and professional
journals that deal with the engineering issues involved in the
knitting industry. While there is plenty of mathematics involved,
it all deals with the physical properties of yarn instead of
examining the mathematics of knitting itself.)
Selected links: Mathematical Fiber Arts (but
not knitting)
I haven't been able to make an exhaustive list of cool stuff on
the web relating to mathematical fiber arts other than knitting,
because, well, I don't know much about the other fiber arts,
mostly. So I'm not quite sure how to effectively search. Thus,
like just about everything else on my pages... if you know of
something I've missed, please tell me.