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, http://www.math.cornell.edu/%7Edwh/papers/crochet/crochet.PDF }.
3. ^ 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 .
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, http://www.telegraph.co.uk/culture/books/bookprizes/7520047/Crocheting-Adventures-with-Hyperbolic-Planes-wins-oddest-book-title-award.html .
6. ^ 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 .
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, http://abcnews.go.com/Entertainment/wireStory?id=10017982 .

Further reading

• 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 

External links

• Mathematical quilts
• Mathematical knitting
• Mathematical weaving
• Mathematical craft projects

• 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)