Ideas from mathematics have been used as inspiration for 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.

## QuiltingEdit

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.^{[1]}

## Knitting and crochetEdit

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 crocheted tori have also been constructed depicting toroidal embeddings of the complete graph *K*_{7} 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]}

## EmbroideryEdit

Embroidery techniques such as counted-thread embroidery^{[6]} including cross-stitch and some canvas work methods such as Bargello make use of the natural pixels of the weave, lending themselves to geometric designs.^{[7]}^{[8]}

## WeavingEdit

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.^{[9]}

J. C. P. Miller (1970) used the Rule 90 cellular automaton to design tapestries depicting both trees and abstract patterns of triangles.^{[10]}

## SpinningEdit

Margaret Greig was a mathematician who articulated the mathematics of worsted spinning.^{[11]}

## Fashion designEdit

The silk scarves from DMCK Designs' 2013 collection are all based on Douglas McKenna's space-filling curve patterns.^{[12]} The designs are either generalized Peano curves, or based on a new space-filling construction technique.^{[13]}^{[14]}

The Issey Miyake Fall-Winter 2010–2011 ready-to-wear collection 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.^{[15]}

## See alsoEdit

## ReferencesEdit

**^**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" (PDF),*Mathematical Intelligencer*,**23**(2): 17–28, doi:10.1007/BF03026623, S2CID 120271314}.**^**Osinga, Hinke M.; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold",*Mathematical Intelligencer*,**26**(4): 25–37, doi:10.1007/BF02985416, S2CID 119728638.**^**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.**^**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*(PDF), Louisville, Kentucky: The Little Loomhouse, archived from the original (PDF) on 2016-02-22, retrieved 2007-09-27**^**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, S2CID 123330469**^**Catharine M. C. Haines (2001),*International Women in Science*, ABC-CLIO, p. 118, ISBN 9781576070901**^**"Space-Filling Curves". DMCK. Retrieved 15 May 2015.**^**McKenna, Douglas (24 July 2007). "The 7 Curve, Carpets, Quilts, and Other Asymmetric, Square-Filling, Threaded Tile Designs".*Bridges Donostia: Mathematics, Music, Art, Architecture, Culture*. The Bridges Organization. Retrieved 15 May 2015.**^**McKenna, Douglas (28 July 2008). "Designing Symmetric Peano Curve Tiling Patterns with Escher-esque Foreground/Background Ambiguity" (PDF).*Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture*. The Bridges Organization. Retrieved 15 May 2015.**^**Barchfield, Jenny (March 5, 2010),*Fashion and Advanced Mathematics Meet at Miyake*, ABC News.

## Further readingEdit

- belcastro, sarah-marie; Yackel, Carolyn, eds. (2007).
*Making Mathematics with Needlework: Ten Papers and Ten Projects*. A K Peters. ISBN 978-1-56881-331-8. - 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. hdl:10338.dmlcz/104026. JSTOR 2690105. - Taimina, Daina (2009).
*Crocheting Adventures with Hyperbolic Planes*. A K Peters. ISBN 978-1-56881-452-0.

## External linksEdit

- 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)