The Home of Mathematical Knitting

Conferences and Books  sarahmarie's mathematical knitting 
talks on mathematical
knitting
(and a link to a course on mathematics and fiber arts) 
Reference List of published
articles on mathematics in fiber arts
(not just knitting, but knitting's in there!) 
Selected Mathematical Knitting
Links 
Selected Mathematical OtherFiberArts Links 
Also: Rachel's Cool Increase is a match for k2tog; two knit stitches flow out of one with no bumps.
Carolyn Yackel and sarahmarie belcastro coorganized three mathematics conference sessions, each of which included a sequence of talks and a mathematical fiber arts exhibit. We have coedited two books on mathematics and fiber arts written for crafters, mathematicians, and mathematics educators.
New! 2014 AMS Special Session in Mathematics and Mathematics Education in Fiber Arts, to take place at the Joint Mathematics Meetings in Baltimore, MD, January 2014.
Making Mathematics with Needlework is based on the based on the 2005 AMS Special Session in Mathematics and Mathematics Education in Fiber Arts (at the January 2005 Joint Mathematics Meetings in Atlanta, GA). A customizable pattern for the hyperbolic baby pants from Making Mathematics with Needlework is available for free at the Wolfram Demonstrations Project.
Crafting by Concepts is partially based on the 2009 AMS Special Session on Mathematics and Mathematics Education in Fiber Arts (at the January 2009 Joint Mathematics Meetings in Washington, DC).
Collections of objects  Individual objects  Functional mathematical patterns 
Möbius bands (recipe included)  Y x I twist: core 1, core 2, completion  Y x I twist cowl 
Klein bottles (recipe included)  Negatively Curved Möbius Bands: 1st, 2nd  sublimation socks (8 x 12) (7 x 10) (6 x 8) 
Other Nonorientable Surfaces  Fancy K6 embedded on a Möbius Band  Rachel's cool socks 
Orientable surfaces  Big K7 embedded on a torus  massively modular socks 
Projective Planes  three torus knots: (5,3), (3,2), RH (3,2)  simple fingerfree mitts 
Hyperbolic planes and pseudospheres (recipe included)  trefoil / triquetra  helix striped spiral bedsocks and nightcap 
Knots and braids  S_{3} scarf  
8colored pants = 2holed torus  
orthogonal doubleholed torus 
exhibits of sarahmarie's work:
YxI: Core and Cowl, Mathematical Art Exhibition (Juried), 2013 Joint Mathematics Meetings
Spring Forest (5,3) and Nonorientable Surfaces of Low Genus, ATMCS5 Art Exhibition (Juried), Algebraic Topology: Methods, Computation and Science, International Centre for Mathematics Sciences, Edinburgh, UK, July 2–6, 2012.
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 8colored Hyperbolic Pants (Map on the Surface of a TwoHoled Torus Requiring 8 Colors), Sticks, Hooks, and the Mobius: Knit and Crochet Goes Cerebral, Lafayette College Art Gallery, January 8–February 5, 2012.
Negatively curved Mobius Band and K_7 embedded on a torus, Mathematical Art Exhibit (Juried), 2012 Joint Mathematics Meetings
A mirror pair of (3,2) torus knots embedded on tori, Exhibition of Mathematical Art (Juried), 2010 Joint Mathematics Meetings
Six of my pieces were included in Yarn Theory, curated by Martha Lewis. PS122 Gallery, New York City, Apr. 25–May 17, 2009.
Nonuniform Nonorientable Nonsurfaces, Mathematical Fiber Arts Exhibit (Juried), 2009 Joint Mathematics Meetings
Connected sum of four projective planes, Exhibition of Mathematical Art (Juried), 2008 Joint Mathematics Meetings
Dual SevenColored Tori, SIGMAAARTS Juried Art Exhibit, Mathfest 2007. images here (.pdf from the MAA, see p.14)
Dual SevenColored Tori, Gathering 4 Gardner 7 Exhibit, March 2006. images here (scroll down page)
media mentions of sarahmarie's work:
Mathematical
Knitting, by Cory Doctorow, boingboing.net, February
15, 2013
Knitting
reinvented: Mathematics, feminism and metal by Mark
Ward, BBC News Technology, August 20, 2012
Interview by Lara Neel in Show
110 of the Math4Knitters
podcast
All Things Considered piece
by
Ari Daniel Shapiro, January 10, 2012 (photos
on his blog)
Math DongA (Korean highschool magazine) October 2010, p. 21.
Klein Bottle Hat, in 1000 Fabulous Knit Hats by Annie
Modesitt, p.
133.
Creabeta: Rechtlijnig, Mobiussjahl (.pdf),
natuurweenschap
& techniek, jaargang 78, nummer 3, maart 2010, pp. 5455.
The Bizarre and Brilliant World of Knitted Science, Discover
Magazine Online Gallery by Eliza Strickland, September 2009.
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).
New
Math by Liz Worth, broken pencil blog, September 1,
2007.
Knitting a Mobius Band by Elise Gibson, Smith Alumnae
Quarterly, Spring 2007.
Mathematical Knitting
by Sarah E. White for about.com, Jan. 24, 2007
Knitting
Network by Ivars Peterson in MathTrek, Science News
Online, Jan. 27, 2007; Vol. 171, No. 4.
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.
Not on this page: sarahmarie's home page
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.
A class on math and fiber arts: Jill Zarestky's seminar at TAMU.
Selected external links: Mathematical Knitting
Jeny Carden Staiman's doubleknitted
Möbiusbandintotorus experiment
Jana's Escher patterns: koi1,
koi2,
birds/rays/turtles
cushions, birds/rays/turtles
blanket, birds/rays/turtles
symmetry, fish
tessellation, fish
tessellation geometry.
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)
Nate Berglund's wacky projectiveplaneonahat
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 halfstitch 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)
Sarah Hauschka's knitted
tessellation (it's 6 x 8 feet!)
Woolly Thoughts
contains a variety of objects and patterns with mathematics
ranging from elementary to advanced.
Knitting pattern generators:
generate
cellular
automaton knitting patterns with perl (for more on cellular
automaton knitting, check out Debbie New's awesome Unexpected
Knitting)
Brent Annable's perfect
(yes!
it is!) sphere and selfintersecting
doubleknitting and rotating ring
of tetrahedra (youtube link)
Camille Fox's cellular automata tea cozies (Rule 30
and Rule
110)
Lisa Grossman's changeringing
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
(of the old incarnation of the podcast)! and again in Episode
33!(.mp3; text here))
Eleanor Kent hand knits
mathematical images of the sort we mathematicians generally
have to computergenerate.
Norah Gaughan's Celestine
Sondra Eklund's prime
factorization
sweater
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
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?
MarieChristine Mahé has another
klein bottle hat, in Knitty.
You can find more mathematical knitting projects if you are a ravelry member by flipping through my favorites.
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 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 verycool 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)
Tanya Scharaschkin's Penrose Quilt
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 pagescheck out pages 2, 4, 5 in particular.
Lorrie Kim's quilt that
is also a GCD table (and commentary)
Lorrie Kim's quilt
with Perlgenerated blocks (generated in Perl
by Mark Jason Dominus)
Lorrie Kim's e
quilt
Irena Swanson's quilts
Travis's visit
to a quilt show
PDF of slides for Jason Cantarella's talk
on Lsystems in quilt design (some Lsystems 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
Sorrel Forbes's irrational
ribbons
Fluxx's logic
statement
Ariel Barton's Seifert
surface
Matthew Wright's Seifert
surfaces and Alexander Horned Sphere
Patrick Rodriguez's Crochet Sphere
Pattern Generator
Florine Meijer's Seifert
surface, double
torus, cube
with
holes, weird
hyperbolic
structure, and 345
Janet's selforthogonal 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 gallery
Defies Categorization
Anabeth Dollins' pieced
polyhedral
balls and page about stuffed
rhombic
hexecontahedra