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Mathematics and fiber arts

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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.

Quilting

The IEEE Spectrum has organised a number of competitions on Quilt Block Design, and several books have been published on the subject. Notable quilt makers 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.

Knitting and crochet

Knitted mathematical objects include the Platonic solids, Klein bottles, Boy's surface, the Lorenz manifold, and the hyperbolic plane.

Cross-stitch

Many of the wallpaper patterns and frieze groups have been used in cross-stitch.

Weaving

Ada Dietz (1882 – 1950) was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines a novel method for generating weaving patterns based on algebraic patterns. Her method employs the expansion of multivariate polynomials to devise a weaving scheme. Dietz' work is still well-regarded today, by both weavers and mathematicians. Along with the references listed below, Griswold (2001) cites several additional articles on her work.

References

  • Ellison, Elaine (1999). Mathematical Quilts: No Sewing Required. Key Curriculum. ISBN 155953317X. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
  • Henderson, David; Taimina, Daina (2001), "Crocheting the hyperbolic plane" (PDF), Math. Intelligencer, 23 (2): 17–28
  • Osinga, Hinke M,; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold", Math. Intelligencer, 26 (4): 25–37{{citation}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  • Dietz, Ada K. (1949). Algebraic Expressions in Handwoven Textiles (PDF). Louisville, Kentucky: The Little Loomhouse.
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