 Mathematics and fiber arts

Mathematical ideas have been used as inspiration for a number of fiber arts including quilt making, knitting, crossstitch, crochet, embroidery and weaving. A wide range of mathematical concepts have been used as inspiration including topology, graph theory, number theory and algebra.
Contents
Quilting
The IEEE Spectrum has organized 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.^{[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 crochetted tori have also been constructed depicting toroidal embeddings of the complete graph K_{7} 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]}
Crossstitch
Many of the wallpaper patterns and frieze groups have been used in crossstitch.^{[citation needed]}
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.^{[6]}
J. C. P. Miller (1970) used the Rule 90 cellular automaton to design tapestries depicting both trees and abstract patterns of triangles.^{[7]}
Fashion design
The Issey Miyake FallWinter 2010–2011 readytowear 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 3manifold 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.^{[8]}
References
 ^ Ellison, Elaine; Venters, Diana (1999), Mathematical Quilts: No Sewing Required, Key Curriculum, ISBN 155953317X.
 ^ Henderson, David; Taimina, Daina (2001), "Crocheting the hyperbolic plane", Mathematical Intelligencer 23 (2): 17–28, doi:10.1007/BF03026623, http://www.math.cornell.edu/%7Edwh/papers/crochet/crochet.PDF}.
 ^ Osinga, Hinke M,; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold", Mathematical Intelligencer 26 (4): 25–37, doi:10.1007/BF02985416, http://www.enm.bris.ac.uk/anm/preprints/2004r03.html.
 ^ belcastro, sarahmarie; Yackel, Carolyn (2009), "The sevencolored 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.
 ^ Bloxham, Andy (March 26, 2010), "Crocheting Adventures with Hyperbolic Planes wins oddest book title award", The Telegraph, http://www.telegraph.co.uk/culture/books/bookprizes/7520047/CrochetingAdventureswithHyperbolicPlaneswinsoddestbooktitleaward.html.
 ^ Dietz, Ada K. (1949), Algebraic Expressions in Handwoven Textiles, Louisville, Kentucky: The Little Loomhouse, http://www.cs.arizona.edu/patterns/weaving/monographs/dak_alge.pdf.
 ^ 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.
 ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News, http://abcnews.go.com/Entertainment/wireStory?id=10017982.
Further reading
 Belcastro, SarahMarie; Carolyn, Yackel, eds. (2007), Making Mathematics with Needlework: Ten Papers and Ten Projects, A K Peters, ISBN 1568813317
 Grünbaum, Branko; Shephard, Geoffrey C. (May 1980), "Satins and Twills: An Introduction to the Geometry of Fabrics", Mathematics Magazine 53 (3): 139–161, doi:10.2307/2690105, JSTOR 2690105
 Taimina, Daina (2009), Crocheting Adventures with Hyperbolic Planes, A K Peters, ISBN 1568814526
External links
 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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