# 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.

## 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 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]

## Cross-stitch

Many of the wallpaper patterns and frieze groups have been used in cross-stitch.[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 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.[8]

## References

1. ^ Ellison, Elaine; Venters, Diana (1999), Mathematical Quilts: No Sewing Required, Key Curriculum, ISBN 155953317X .
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. ^  .
6. ^ Dietz, Ada K. (1949), Algebraic Expressions in Handwoven Textiles, Louisville, Kentucky: The Little Loomhouse .
7. ^ 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 .
8. ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News .

• Belcastro, Sarah-Marie; 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

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