Mathematics and fiber arts
Ideas from Mathematics have been used as inspiration for fiber arts
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 .
Quilting
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 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 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]
Embroidery
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]
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 . [9]
J. C. P. Miller ( 1970 ) used the Rule 90 cellular automaton to design tapestries depicting both trees and abstract patterns of triangles. [10]
Spinning
Margaret Greig was a mathematician who articulated the mathematics of worsted spinning . [11]
Fashion design
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 also
References
- ↑ 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 reading
- 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 links
- 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)
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