Mathematics and fiber arts

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A Mobius strip scarf made from crochet. Moebiusstripscarf.jpg
A Möbius strip scarf made from crochet.

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.

Contents

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

Cross-stitch counted-thread embroidery Cross stitch embroidery.jpg
Cross-stitch counted-thread embroidery

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 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]

Embroidery

Two Bargello patterns Florentin.png
Two Bargello patterns

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

Related Research Articles

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Daina Taimiņa is a Latvian mathematician, retired adjunct associate professor of mathematics at Cornell University, known for developing a way of modeling hyperbolic geometry with crocheted objects.

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<span class="mw-page-title-main">Ada Dietz</span>

Ada K. Dietz was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines a novel method for generating weaving patterns based on algebraic patterns. Her method employs the expansion of multivariate polynomials to devise a weaving scheme. Dietz' work is still well-regarded today, by both weavers and mathematicians. Along with the references listed below, Griswold (2001) cites several additional articles on her work.

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<span class="mw-page-title-main">David W. Henderson</span> American mathematician (1923-2018)

David Wilson Henderson was a Professor Emeritus of Mathematics in the Department of Mathematics at Cornell University. His work ranges from the study of topology, algebraic geometry, history of mathematics and exploratory mathematics for teaching prospective mathematics teachers. His papers in the philosophy of mathematics place him with the intuitionist school of philosophy of mathematics. His practical geometry, which he put to work and discovered in his carpentry work, gives a perspective of geometry as the understanding of the infinite spaces through local properties. Euclidean geometry is seen in his work as extendable to the spherical and hyperbolic spaces starting with the study and reformulation of the 5th postulate.

<i>Crocheting Adventures with Hyperbolic Planes</i>

Crocheting Adventures with Hyperbolic Planes is a book on crochet and hyperbolic geometry by Daina Taimiņa. It was published in 2009 by A K Peters, with a 2018 second edition by CRC Press.

<i>Making Mathematics with Needlework</i>

Making Mathematics with Needlework: Ten Papers and Ten Projects is an edited volume on mathematics and fiber arts. It was edited by Sarah-Marie Belcastro and Carolyn Yackel, and published in 2008 by A K Peters, based on a meeting held in 2005 in Atlanta by the American Mathematical Society.

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Carolyn Yackel is an American mathematician who has been Professor of Mathematics at Mercer University in Macon, Georgia since 2001. From 1998 to 2001 she was Max Zorn Visiting Assistant Professor of Mathematics at Indiana University.

References

  1. Ellison, Elaine; Venters, Diana (1999). Mathematical Quilts: No Sewing Required. Key Curriculum. ISBN   1-55953-317-X..
  2. Henderson, David; Taimina, Daina (2001), "Crocheting the hyperbolic plane" (PDF), Mathematical Intelligencer , 23 (2): 17–28, doi:10.1007/BF03026623, S2CID   120271314 }.
  3. Osinga, Hinke M.; Krauskopf, Bernd (2004), "Crocheting the Lorenz manifold" (PDF), Mathematical Intelligencer, 26 (4): 25–37, doi:10.1007/BF02985416, S2CID   119728638 .
  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 (eds.), 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 .
  6. Gillow, John, and Bryan Sentance. World Textiles, Little, Brown, 1999.
  7. Snook, Barbara. Florentine Embroidery. Scribner, Second edition 1967.
  8. Williams, Elsa S. Bargello: Florentine Canvas Work. Van Nostrand Reinhold, 1967.
  9. 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
  10. 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
  11. Catharine M. C. Haines (2001), International Women in Science , ABC-CLIO, p.  118, ISBN   9781576070901
  12. "Space-Filling Curves". DMCK. Retrieved 15 May 2015.
  13. 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.
  14. McKenna, Douglas (26 Nov 2023). "Designing Symmetric Peano Curve Tiling Patterns with Escher-esque Foreground/Background Ambiguity". Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture. The Bridges Organization. Retrieved 26 Nov 2023.
  15. Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News .

Further reading