Mathematics and fiber arts: Difference between revisions
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==Quilting== |
==Quilting== |
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The [[IEEE Spectrum]] has |
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 section]]s, [[Leonardo da Vinci]]'s Claw, the [[Koch curve]], the [[Clifford torus]], [[San Gaku]], [[Lorenzo Mascheroni|Mascheroni]]'s [[cardioid]], [[Pythagorean triple]]s, [[spidron]]s, and the six [[trigonometric functions]].<ref>{{citation |
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==Fashion design== |
==Fashion design== |
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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 |
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 |
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| date = March 5, 2010 |
| date = March 5, 2010 |
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Revision as of 03:20, 9 April 2010
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] 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.[4]
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.[5]
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.[6]
References
- ^ Ellison, Elaine; Venters, Diana (1999), Mathematical Quilts: No Sewing Required, Key Curriculum, ISBN 155953317X.
- ^ Henderson, David; Taimina, Daina (2001), "Crocheting the hyperbolic plane" (PDF), Math. Intelligencer, 23 (2): 17–28, doi:10.1007/BF03026623}.
- ^ 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). - ^ Bloxham, Andy (March 26, 2010), "Crocheting Adventures with Hyperbolic Planes wins oddest book title award", The Telegraph.
- ^ Dietz, Ada K. (1949), Algebraic Expressions in Handwoven Textiles (PDF), Louisville, Kentucky: The Little Loomhouse.
- ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News.
Further reading
- belcastro, sarah-marie and Carolyn Yackel (eds.), ed. (2007). Making Mathematics with Needlework: Ten Papers and Ten Projects. A K Peters. ISBN 1568813317.
{{cite book}}:|editor=has generic name (help) - 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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