The Home of Mathematical Knitting (sarah-marie's mathematical knitting pages)

I used to keep everything on one page, but then there were too many pictures...now there are none on this page.

New! 2009 AMS Special Session on Mathematics and Mathematics Education in Fiber Arts at the January 2009 Joint Mathematics Meetings in Washington, DC

AMS Special Session in Mathematics and Mathematics Education in Fiber Arts (at the January 2005 Joint Mathematics Meetings in Atlanta, GA)

Making Mathematics with Needlework: Carolyn and I have edited a book, based on the 2005 Special Session, for mathematicians, crafters, and mathematics educators. (Yes, that includes almost everyone. Follow the link for more details.)

sarah-marie's mathematical knitting:
Möbius bands (pattern included)
Projective Planes
Klein bottles (yes, my pattern is here, as well as some hat pictures)
Other Nonorientable Surfaces
Orientable surfaces
Hyperbolic plane (small chunks)
S₃ scarf
Mini-braids

Selected Mathematical Knitting Links
Selected Mathematical Other-Fiber-Arts Links
reference list of published articles on mathematics in fiber arts (not just knitting, but knitting's in there!)

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.

• 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 which 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). He 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.
• and of course there were many talks at the AMS Special Session in January 2005.

Not on this page: sarah-marie's home page

Selected external links: Mathematical Knitting

Staceyjoy Elkins' compact notation for texture patterns
Mark Shoulson's homemade topological shapes include various embeddings of nonorientable surfaces
Claire Irving's embeddings and immersions of the projective plane (look for a paper by Claire in the reference list; her work is shown on the cover of the journal as well.)
Nate Berglund's wacky projective-plane-on-a-hat and other nonorientable knitting
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.
Janet's Petersen Graph stitch pattern (subtle and brilliant)
Caitlin's very flexible random stripe generator
generate cellular automaton knitting patterns with perl (for more on cellular automaton knitting, check out Debbie New's awesome Unexpected Knitting)
Lisa Grossman's change-ringing socks (for more on the math, see here)
Pattern: Fibonacci sleeveless shirt
Lara Neel's Math4Knitters podcast/blog (where this website is mentioned, in Episode 12!)
Eleanor Kent hand knits mathematical images of the sort we mathematicians generally have to computer-generate.
Horst Schultz's tumbling blocks design (lots of other beautiful things on that site...)
Claire's tetrahedral dice bag
Rachel Bishop's Perfect Shuffle Scarves, which are cute. (Try to ignore her poor mathematical grammar and highly nonstandard terminology.)
Heather Taylor's article on knitting and mathematics in elementary school
Wooly Thoughts' afghans (of all their designs, the afghans involve the most math)
Fuzzy Galore's use of probability and Fibonacci numbers in knitting design
fictional mathematical knitting...
...and who can resist Cliff Stoll's Acme Klein Bottle?
Marie-Christine Mahé has another klein bottle hat, in Knitty.

I know there must be more out there: witness qB'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 which 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.)

Not just math, but other disciplines are covered at the very-cool thomasina's guide to geeky knitting and geeky knitting index.

Selected mathematical fiber arts (but not knitting, see above) external links:

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)
Sarah Mylchreest and Mark Newbold's Penrose Tiling quilt
Lisbeth G. Clemons' Penrose 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 which is also a GCD table
Lorrie Kim's quilt with Perl-generated blocks (generated in Perl by Mark Jason Dominus)
Irena Swanson's 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 which correspond to quilt pieces; those that don't suggest topstitching patterns)

Mathematical Crochet
Daina Taimina's home page and awesome geometry textbook page
Fluxx's logic statement
Ariel Barton's Seifert surface
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

Mathematical Needlepoint
William Mitchell's Pascal's Triangle
John Young's QR Code Pillow and a different QR Code chart by Janet M. Perry

Mathematical Bead Weaving
Gwen Fisher's more mathematical beaded beads gallery and beaded bead kits

Defies Categorization
Shiela Morgan's woven Klein Bottle and more (includes knitting and sewing)
Anabeth Dollins' pieced polyhedral balls and page about stuffed rhombic hexecontahedra