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==Fashion design==
==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]].<ref>{{citation
The [[Issey Miyake]] Fall-Winter 2010&ndash;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]].<ref>{{citation
| last = Barchfield | first = Jenny
| last = Barchfield | first = Jenny
| date = March 5, 2010
| date = March 5, 2010

Revision as of 22:04, 18 August 2010

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.

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]

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.[7]

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" (PDF), Math. Intelligencer, 23 (2): 17–28, doi:10.1007/BF03026623}.
  3. ^ Osinga, Hinke M,; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold", Math. Intelligencer, 26 (4): 25–37, doi:10.1007/BF02985416{{citation}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link).
  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 (eds.), Homage to a Pied Puzzler, AK Peters, pp. 25–32{{citation}}: CS1 maint: multiple names: editors list (link).
  5. ^ Bloxham, Andy (March 26, 2010), "Crocheting Adventures with Hyperbolic Planes wins oddest book title award", The Telegraph.
  6. ^ Dietz, Ada K. (1949), Algebraic Expressions in Handwoven Textiles (PDF), Louisville, Kentucky: The Little Loomhouse.
  7. ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News.

Further reading

  • belcastro, sarah-marie; Carolyn, Yackel, eds. (2007), Making Mathematics with Needlework: Ten Papers and Ten Projects, A K Peters, ISBN 1568813317
  • Taimina, Daina (2009), Crocheting Adventures with Hyperbolic Planes, A K Peters, ISBN 1568814526
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