This is a temporary page (until we find it a better home) for the Needlework Cocurricular (or is it a crafts cocurric?) for Spring '05. For now, it's being used to store links of interest....

Formal Publications

• Daina Taimina and David Henderson, "Crocheting the Hyperbolic Plane", Mathematical Intelligencer, Vol. 23, No. 2, pp. 17-28, Spring 2001.

• Daniel C. Isaksen and Alabama P. Petrovsky, "Moebius Knitting", Bridges: Mathematical Connections in Art, Music, and Science, ed. R. Sarhangi, 1999, 67--76.

  • Includes a stitch of their invention.

• Hinke Osinga and Bernd Krauskopf, "Crocheting the Lorenz Manifold", Briston Centre for Applied Nonlinear Mathematics Preprint. (and a photo)

• Judith J. McDonald and J. Harley Weston, Friezing at Washington State University, Mathematical Notes, Washington State University, Vol. 46, No. 2, June 2003.

  • The website at Frieze designs in indigenous art by the same authors gives a very readable discussion of similar territory.

* See also the Ethnomathematics Digital Library, where I found some of the above and the below

• Bier, C. (2001). Mathematical aspects of Oriental carpets (Special issue of Symmetry: Culture and Science). Symmetry in Ethnomathematics, 12(1-2), 67-77. Budapest, Hungary: International Symmetry Foundation.

• Mayan Geometry: a geometry of mosaics en espanol

• Ethnomathematics unit developed by Katherine Patterson

• == Web Pages == === Knitting and Crochet ===

I grouped these together because many sites include both and often patterns can be translated back and forth.

• sarah-marie's mathematical knitting pages includes these links:

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

  • Mobius bands (includes instructions and an embedding of K6)

  • Projective Planes (pics and instructions)
  • Klein bottles (pics and instructions)
  • Hyperbolic plane (pics and allusion to instruction; knitted; see crochet instructions in the Taimina and Henderson paper)
  • S3 scarf (pics, but instructions are obvious from pic)
  • Mini-braids (pics)
  • Selected Mathematical Knitting Links

• Claire Irving did a master's thesis on Embeddings and Immersions of Real Projective Spaces and has the knitting to show for it.

  • "My sphere-with-crosscap, Steiner's Roman Surface and Boy's Surface (versions of the real projective plane) are shown ... together with my knitted Klein Bottle." (pics)

  • Includes instructions

• eleanor kent textile arts Fractal knitting (on planar squares; pics only)

• Fuzzy Galore articles (w/instructions, pics, and math) on

  • a probabilistic cable sweater

  • fibonacci socks

  • Ada Deitz polynomial knitting patterns

• Design your own Mobius scarf included because it has such a different look to it -- it's far and away the prettiest one I've seen, though less math-y.

• Homemade Topological Shapes These tend to have lots of seams.

  • Moebius strip
  • Klein Bottle
  • Real Projective Plane

• math for craft design is pretty nontechnical, but includes

  • a (knitted) Fibonacci afghan
  • a Mobius scarf (actually three different knit patterns and a crochet pattern)

  • also converting between knitting and crochet

• Woolly Thoughts Afghans === Embroidery and Needlepoint ===

• Pascal's Triangle in needlepoint (pics and explanation) === Quilting ===

• Quilting links

  • Math Quiltspics include geometry | perspective | topology | irrational numbers | feathered star | fractals | tessellations and tiling including Escher

  • Penrose Tiling (pic, math, links)

  • The Mathematics Quilt (pics)

  • Various Enterprises For Exploring Mathematics Through Quilts

  • Mathematical Quilts book and poster

  • Quilt Square Math

  === Knots ===
• Knots
  • I haven't looked much for this topic. I know it's a big area waiting for exploration.

    • I would bet that you could apply principles from knitting and crochet to netting, which is more knotwork than needlework -- though web resources for netting are sparse. A Klein net might be interesting, though. -Katie

  • The KnotPlot Site an OpenGL program and lots of good info

  === Symmetry, Tesselation ===

(Obviously lots more out there)

• Symmetry and Pattern, The Art of Oriental Carpets === Miscellaneous ===

• Ethnomathematics A huge collection of resources on a much broader topics, but includes many links of interest.

• Pulse Microsystems The world's #1 Embroidery Software.

  • This is serious industrial embroidery.

  • How many companies would even want to say that they have "... the largest pool of programming, mathematics and embroidery expertise in the industry."

• Acme Klein Bottles Glass, but worth reading anyway.

Conferences

• AMS Special Session in Mathematics and Mathematics Education in Fiber Arts

  • To be held Friday, January 7, 2005, 1:00 p.m.-5:50

  • I want to go!!!

  • The page has pictures of what will be exhibited
  • There are also links to the abstracts (here with my annotations from the abstracts)

       1:00 - 1:20: sarah-marie belcastro An Overview of Mathematics in Fiber Arts, with an Attempt to Answer an Age-Old Question.  (Topology of knitting stitches)
       1:30 - 1:50: Mary Shepard Symmetries in Cross-Stitch.
       2:00 - 2:20: Josh Holden The graph theory of Blackworkembroidery.  (Graph theory)
       2:30 - 2:50: Daina Taimina Experiencing and Learning Hyperbolic Geometry from Crocheted Models.  [also see paper above]
       3:00 - 3:10: Amy Szczepanski Quilts in the Classroom. (Geometry, Moebius Quilt)
       3:15 - 3:25: Susan Goldstine Fortunatus's Purse  (Real Projective Plane)
       3:30 - 3:55: EXHIBIT
       4:00 - 4:10: Jake Wildstrom The Sierpinski Variations: Self-Similar Crochet. (Cellular automata)
       4:15 - 4:25: Sharon Frechette Cable patterns in Aran knitting, and braid groups.
       4:30 - 4:50: Lana Holden Picking up Stitches.  (Diophantine equations; math to solve knitting problems)
       5:00 - 5:20: Dan Isaksen Braid groups and knitting.  (Topology of knitting)
       5:30 - 5:50: Carolyn Yackel Realizing Algebraic Structures Through Knitting.
    Mid-Session (3:30 - 4) we will host the Mathematical Fiber Arts Exhibit. 

Literary allusions

• Fortunatus's Purse (from Lewis Carroll, Sylvie and Bruno) -- the story that inspired Susan Goldstine's talk in the Math session above.

Politics

Men Who Knit:

• http://www.menknit.net especially http://www.menknit.net/history.html

• Clinton W. Trowbridge "When Knitting Was A Manly Art" Christian Science Monitor December 05, 1997.