Mathematics and fiber arts
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. Some techniques such as counted-thread embroidery are naturally geometrical; other kinds of textile provide a ready means for the colorful physical expression of mathematical concepts.
The IEEE Spectrum has organized a number of competitions on quilt block design, and several books have been published on the subject. Notable quiltmakers 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.
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. Knitted and crocheted tori have also been constructed depicting toroidal embeddings of the complete graph K7 and of the Heawood graph. 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.
Embroidery techniques such as counted-thread embroidery including cross-stitch and some canvas work methods such as Bargello (needlework) make use of the natural pixels of the weave, lending themselves to geometric designs.
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.
The silk scarves from DMCK Designs' 2013 collection are all based on space-filling curve patterns that Doug McKenna has devised or discovered. The designs are either generalized Peano curves, or based on a new space-filling construction technique. Both techniques are described in short papers available in the Bridges Math and Art conference proceedings (2007 and 2008).
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.
- Ellison, Elaine; Venters, Diana (1999), Mathematical Quilts: No Sewing Required, Key Curriculum, ISBN 1-55953-317-X.
- Henderson, David; Taimina, Daina (2001), Crocheting the hyperbolic plane, Mathematical Intelligencer 23 (2): 17–28, doi:10.1007/BF03026623}.
- Osinga, Hinke M,; Krauskopf, Bernd (2004), Crocheting the Lorenz manifold, Mathematical Intelligencer 26 (4): 25–37, doi:10.1007/BF02985416.
- 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.
- Bloxham, Andy (March 26, 2010), Crocheting Adventures with Hyperbolic Planes wins oddest book title award, The Telegraph.
- Gillow, John, and Bryan Sentance. World Textiles, Little, Brown, 1999.
- Snook, Barbara. Florentine Embroidery. Scribner, Second edition 1967.
- Williams, Elsa S. Bargello: Florentine Canvas Work. Van Nostrand Reinhold, 1967.
- Dietz, Ada K. (1949), Algebraic Expressions in Handwoven Textiles, Louisville, Kentucky: The Little Loomhouse
- 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
- DMCK Designs
- Bridges Math and ArtTemplate:Better ref needed
- 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 1-56881-331-7
- 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 1-56881-452-6
- Mathematical quilts
- Mathematical knitting
- Mathematical weaving
- Mathematical craft projects
- Wooly Thoughts Creations: Maths Puzzles & Toys
- 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)