up to sarah-marie belcastro's home page

The Home of Mathematical Knitting

(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.


sarah-marie's mathematical knitting

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
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
S3 scarf
orthogonal double-holed torus

Graphs and Maps Embedded on Surfaces
( pages)

Petersen torus
Petersen-Embellished Toroidal Blanket Square
Petersen-Embellished Non-orientable Blanket Square
the smallest snark polyhedrally embedded on a klein bottle
toroidal snarks: smallest, third-smallest, fourth-smallest
Fancy K6 embedded on a Möbius Band
Big K7 embedded on a torus
8-colored pants = 2-holed torus

exhibits of sarah-marie's work:
publicly available media mentions of sarah-marie's work:

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 taught a seminar when she was at TAMU.

A January-term course: Sara Jensen's class at Carthage College and an article she wrote about it

Selected links: Mathematical Knitting

You can find more mathematical knitting projects and patterns if you are a 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.)

Selected links: 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
Hanne Kekkonen's surfaces and Seifert surfaces
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
Heather Lewis's Non-Euclidean Granny
Lana Holden's space-filling curve and Sierpinski fractal
Andrea Heald's Bn scarf
Moira Chas's hexagonal torus tiling
Susan Goldstine's Serpentine Symmetries (scroll down) and bead-crocheted jewelry and hyperbolic surface
Heidi Burgiel's Hyperbolic {3,7} Afghan
Kyle Calderhead's H-fractal blanket
Andrea Heald's Collatz cornsnake and Penrose doily and snood
Gabriele Meyer's many many many many crocheted hyperbolic surfaces
Ron Asherov's crocheted spirals

Selected links: Mathematical Fiber Arts (but not knitting or crochet)

I haven't been able to make an exhaustive list of cool stuff on the web relating to mathematical fiber arts other than knitting, and to a lesser extent crochet, 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
Andreia Hall's D4 rosette 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
Madison Howard, Angela Vichitbandha, and Kate Ponto's Octahedral tiling of the Poincare Disk quilt
Heather Dye's catenary quilt
Louise Gould's (ir)reptiles
Nina Paley and Theodore Gray's quiltimations and pi quilts and fibonacci sequins quilt
Travis's visit to a quilt show
Andreia Hall and Prudencia Leite's Voronoi diagram quilts
Andreia Hall's rep-tiles quilt
Jane Adler's pentagonal tessellation quilt
Sabetta Matsumoto's Klein quartic quilt
Natalie Hobson's rainbow Pythagoras tree fractal quilt
Taneli Luotoniemi's hyperbolic surfaces
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 Embroidery
Craig Kaplan's triaxial aida cross stitch
Wing Mui's simple symmetric square sampler
Larry Riddle's space-filling curves and dragon curves and dragon curve tilings and dragon curve lace and pythagorean tree and more fractals
Maggi Harriss's tiled cushions
Debbie Borkovitz's S4 temari ball
Kiyoko Urata's icosahedral temari balls
William Mitchell's Pascal's Triangle
Lisa Shier and Doug Dunham's hyperbolic Fish Pattern (5,3)

Mathematical Bead Weaving and Other Weaving
Gwen Fisher's gallery
Mary Klotz's triaxial weaving
Lana Holden's Fibonacci word fractal
Sally Eyring's ASCII weaving
Donna Contractor's Cantor dust weaving
Natalie Priebe Frank's self-similar tiling mobile
Joke van Biesen's Lorenz attractor (scroll down)
Marina Toeters and Loe Feijs's cellular automata houndstooth

Veronika Irvine's bobbin lace embedded surface, periodic bobbin lace, and reflection symmetry bobbin lace
Mónica y Andrés Manceñido's tatted platonic solids
Ellie Baker's seven-colored torus scarves and first and second invertible infinity scarves
Ayelet Lindenstrauss Larsen's Mobius color wheel
Louise Gould's It's All Squares: The Truncoctahedral 45 multiplied snub cube
Joni Marie Davis's Voronoi/Delaunay sphere
Anabeth Dollins' pieced polyhedral balls and page about stuffed rhombic hexecontahedra
Louise Mabbs's fabric borromean rings sculptures
Eunsuk Hur's modular scarves

up to sarah-marie belcastro's home page