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Mathematics and fiber arts

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Mathematics and fiber arts

A Möbius strip scarf made from crochet.

Mathematical ideas have been used as inspiration for a number of fiber arts including quilt making, knitting, cross-stitch, crochet, embroidery and weaving. A wide range of mathematical concepts have been used as inspiration including topology, graph theory, number theory and algebra. Some techniques such as counted-thread embroidery are naturally geometrical; other kinds of textile provide a ready means for the colorful physical expression of mathematical concepts.

Quilting

The quilt block design, and several books have been published on the subject. Notable quiltmakers include Diana Venters and Elaine Ellison, who have written a book on the subject Mathematical Quilts: No Sewing Required. Examples of mathematical ideas used in the book as the basis of a quilt include the golden rectangle, conic sections, Leonardo da Vinci's Claw, the Koch curve, the Clifford torus, San Gaku, Mascheroni's cardioid, Pythagorean triples, spidrons, and the six trigonometric functions.[1]

Knitting and crochet

Knitted mathematical objects include the Platonic solids, Klein bottles and Boy's surface. The Lorenz manifold and the hyperbolic plane have been crafted using crochet.[2][3] Knitted and crocheted tori have also been constructed depicting toroidal embeddings of the complete graph K7 and of the Heawood graph.[4] The crocheting of hyperbolic planes has been popularized by the Institute For Figuring; a book by Daina Taimina on the subject, Crocheting Adventures with Hyperbolic Planes, won the 2009 Bookseller/Diagram Prize for Oddest Title of the Year.[5]

Embroidery

Embroidery techniques such as counted-thread embroidery[6] including cross-stitch and some canvas work methods such as Bargello (needlework) make use of the natural pixels of the weave, lending themselves to geometric designs.[7][8]

Weaving

Ada Dietz (1882 – 1950) was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines weaving patterns based on the expansion of multivariate polynomials.[9]

J. C. P. Miller (1970) used the Rule 90 cellular automaton to design tapestries depicting both trees and abstract patterns of triangles.[10]

Spinning

Margaret Greig was a mathematician who articulated the mathematics of worsted spinning.[11]

Fashion design

The silk scarves from DMCK Designs' 2013 collection[12] are all based on space-filling curve patterns that Doug McKenna has devised or discovered. The designs are either generalized Peano curves, or based on a new space-filling construction technique. Both techniques are described in short papers available in the Bridges Math and Art conference proceedings (2007 and 2008).[13]

The Issey Miyake Fall-Winter 2010–2011 ready-to-wear collection featured designs from a collaboration between fashion designer Dai Fujiwara and mathematician William Thurston. The designs were inspired by Thurston's geometrization conjecture, the statement that every 3-manifold can be decomposed into pieces with one of eight different uniform geometries, a proof of which had been sketched in 2003 by Grigori Perelman as part of his proof of the Poincaré conjecture.[14]

References

  1. ^ Ellison, Elaine; Venters, Diana (1999), Mathematical Quilts: No Sewing Required, Key Curriculum,  .
  2. ^ Henderson, David;  }.
  3. ^ Osinga, Hinke M,; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold", Mathematical Intelligencer 26 (4): 25–37,  .
  4. ^ belcastro, sarah-marie; Yackel, Carolyn (2009), "The seven-colored torus: mathematically interesting and nontrivial to construct", in  .
  5. ^ Bloxham, Andy (March 26, 2010), "Crocheting Adventures with Hyperbolic Planes wins oddest book title award",  .
  6. ^ Gillow, John, and Bryan Sentance. World Textiles, Little, Brown, 1999.
  7. ^ Snook, Barbara. Florentine Embroidery. Scribner, Second edition 1967.
  8. ^ Williams, Elsa S. Bargello: Florentine Canvas Work. Van Nostrand Reinhold, 1967.
  9. ^ Dietz, Ada K. (1949), Algebraic Expressions in Handwoven Textiles, Louisville, Kentucky: The Little Loomhouse 
  10. ^  
  11. ^ Catharine M. C. Haines (2001), International Women in Science, ABC-CLIO, p. 118,  
  12. ^ DMCK Designs
  13. ^ Bridges Math and Art
  14. ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake,  .

Further reading

External links

  • Mathematical quilts
  • Mathematical knitting
  • Mathematical weaving
  • Mathematical craft projects
  • Wooly Thoughts Creations: Maths Puzzles & Toys
  • Penrose tiling quilt
  • Crocheting the Hyperbolic Plane: An Interview with David Henderson and Daina Taimina
  • AMS Special Session on Mathematics and Mathematics Education in Fiber Arts (2005)
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