# 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 IEEE Spectrum has organized a number of competitions on 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]

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## 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]

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## 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]

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## 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]

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## Fashion design

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.[11]

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## References

1. ^ Ellison, Elaine; Venters, Diana (1999), Mathematical Quilts: No Sewing Required, Key Curriculum, ISBN 1-55953-317-X.
2. ^ Henderson, David; Taimina, Daina (2001), "Crocheting the hyperbolic plane", Mathematical Intelligencer 23 (2): 17–28, doi:10.1007/BF03026623}.
3. ^ Osinga, Hinke M,; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold", Mathematical Intelligencer 26 (4): 25–37, doi:10.1007/BF02985416.
4. ^ belcastro, sarah-marie; Yackel, Carolyn (2009), "The seven-colored torus: mathematically interesting and nontrivial to construct", in Pegg, Ed, Jr.; Schoen, Alan H.; Rodgers, Tom, Homage to a Pied Puzzler, AK Peters, pp. 25–32.
5. ^ Bloxham, Andy (March 26, 2010), "Crocheting Adventures with Hyperbolic Planes wins oddest book title award", The Telegraph.
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. ^ Miller, J. C. P. (1970), "Periodic forests of stunted trees", Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences 266 (1172): 63–111, Bibcode:1970RSPTA.266...63M, doi:10.1098/rsta.1970.0003, JSTOR 73779
11. ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News.
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