Also: Rachel's Cool Increase is a match for k2tog; two knit stitches flow out of one with no bumps.
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.
A customizable pattern for the hyperbolic baby pants from Making Mathematics with Needlework is available for free at the Wolfram Demonstrations Project.
Article: Adventures in Mathematical Knitting. American Scientist, 101(2), March--April 2013, 124–133.
Types of objects
Möbius bands (recipe
included)
Projective Planes
Klein bottles (recipe included)
Other Nonorientable Surfaces
Orientable surfaces
Hyperbolic surfaces (recipe included)
Knots, links, and braids
Functional mathematical knitting patterns available on
Y x I twist cowl
Y x I skinny scarves
Sublimation Socks (8 x 12) (7 x 10) (6
x 8)
Borromean rings cowl
Least Common Scarf
Metacarpals
Rachel's cool socks
massively modular socks
simple finger-free mitts
Individual objects' pages
all publicly-accessible ravelry projects on one page
Brunnian links: Borromean rings, more crossings, more complicated components, lots more components
torus links: (4,2) link, (5,3) knot, (6,4) link, (8,6) link, (15,6) link
Y x I twist: core 1, core 2, completion
Negatively Curved Möbius Bands: 1st, 2nd
S_{3} scarf
orthogonal double-holed torus
Graphs and Maps Embedded on Surfaces
( pages)
Petersen-Embellished Non-orientable Blanket Square
the smallest snark polyhedrally embedded on a klein bottle
toroidal snarks: smallest (in process), third-smallest, fourth-smallest
Fancy K6 embedded on a Möbius Band
Big K7 embedded on a torus
8-colored pants = 2-holed torus
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.
A class on math and fiber arts: Jill Zarestky's seminar at TAMU.
You can find more mathematical knitting projects if you are a ravelry member by flipping through my favorites.
Not just math, but other disciplines are covered at the very-cool thomasina's guide to geeky knitting and geeky knitting index.
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.)
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.
Mathematical Quilting
Rebecca Chaky's Flow Snake
Sarah Mylchreest and Mark Newbold's A Piece of
Hyperspace (another execution here)
Tanya Scharaschkin's Penrose Quilt
Sarah Mylchreest and Mark Newbold's Penrose Tiling
quilt
Lisbeth G. Clemons' Penrose
Quilt
Chawne Kimber / Ethan Berkove's origami quilt
Karen Meagher's quilts
Anabeth Dollins' mathematics quilt and quilted proof of the Pythagorean Theorem (gorgeous!)
Gwen Fisher's quilted
Cayley tables
Elaine Ellison's mathematical
quilts pages---check out pages 2, 4, 5 in particular.
Lorrie Kim's quilt that
is also a GCD table (and commentary)
Lorrie Kim's quilt
with Perl-generated blocks (generated in Perl
by Mark Jason Dominus)
Lorrie Kim's e
quilt
Irena Swanson's quilts
Heather Dye's catenary quilt
Nina Paley and Theodore Gray's quiltimations and pi quilts
Travis's visit
to a quilt show
PDF of slides for Jason Cantarella's talk
on L-systems in quilt design (some L-systems create tilings
that correspond to quilt pieces; those that don't suggest
topstitching patterns)
Mathematical Crochet
Daina Taimina's home page
and photo blog and and text blog
Hinke Osinga's crocheted Lorenz manifold
Sorrel Forbes's irrational
ribbons
Ariel Barton's Seifert
surface
Matthew Wright's Seifert
surfaces and Alexander Horned Sphere
Emily Premise-Conclusion's ideal crocheted sphere
Florine Meijer's Seifert surface, double
torus, cube
with
holes, weird
hyperbolic
structure, and 3-4-5
Janet's self-orthogonal latin square of order
10
Lana Holden's space-filling curve
Moira Chas's hexagonal torus tiling
Susan Goldstine's bead-crocheted jewelry and hyperbolic surface
Heidi Burgiel's Hyperbolic {3,7} Afghan
Andrea Heald's Collatz cornsnake and Penrose doily and snood
Gabriele Meyer's many crocheted hyperbolic surfaces
Ron Asherov's crocheted spirals
Mathematical Needlepoint
Wing Mui's simple symmetric square sampler
Larry Riddle's space-filling curves and dragon curves and dragon curve tilings
Maggi Harriss's tiled cushions
William Mitchell's Pascal's
Triangle
Mathematical Bead Weaving and Other Weaving
Gwen Fisher's gallery
Mary Klotz's triaxial weaving
Sally Eyring's ASCII weaving
Donna Contractor's Cantor dust weaving
Other
Veronika Irvine's periodic bobbin lace and reflection symmetry bobbin lace
Ellie Baker's invertible infinity scarf
Ayelet Lindenstrauss Larsen's Mobius color wheel
Louise Gould's multiplied snub cube
Anabeth Dollins' pieced
polyhedral
balls and page about stuffed
rhombic hexecontahedra