“Mathematics and fiber arts”的意思、由来-开放百科全书

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 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

Embroidery techniques such as counted-thread embroidery^[6] 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.^[7]^[8]

Weaving

Spinning

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 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.^[15]

References

1. ^{{cite book | last1=Ellison | first1=Elaine | last2=Venters | first2=Diana | isbn=1-55953-317-X | publisher=Key Curriculum | title=Mathematical Quilts: No Sewing Required | year=1999}}.
2. ^{{citation | last1 = Henderson | first1 = David | last2 = Taimina | first2 = Daina | author2-link = Daina Taimina | doi = 10.1007/BF03026623 | issue = 2 | journal = Mathematical Intelligencer | pages = 17–28 | title = Crocheting the hyperbolic plane | url = http://www.math.cornell.edu/%7Edwh/papers/crochet/crochet.PDF | volume = 23 | year = 2001}}}.
3. ^{{citation | last1 = Osinga | first1 = Hinke M. | author1-link = Hinke Osinga | last2 = Krauskopf | first2 = Bernd | doi = 10.1007/BF02985416 | issue = 4 | journal = Mathematical Intelligencer | pages = 25–37 | title = Crocheting the Lorenz manifold | url = http://www.enm.bris.ac.uk/anm/preprints/2004r03.html | volume = 26 | year = 2004}}.
4. ^{{citation|first1=sarah-marie|last1=belcastro|first2=Carolyn|last2=Yackel|contribution=The seven-colored torus: mathematically interesting and nontrivial to construct|pages=25–32|title=Homage to a Pied Puzzler|editor1-first=Ed, Jr.|editor1-last=Pegg|editor1-link=Ed Pegg, Jr.|editor2-first=Alan H.|editor2-last=Schoen|editor3-first=Tom|editor3-last=Rodgers|publisher=AK Peters|year=2009}}.
5. ^{{citation | last = Bloxham | first = Andy | date = March 26, 2010 | journal = The Telegraph | title = Crocheting Adventures with Hyperbolic Planes wins oddest book title award | url = https://www.telegraph.co.uk/culture/books/bookprizes/7520047/Crocheting-Adventures-with-Hyperbolic-Planes-wins-oddest-book-title-award.html}}.
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. ^{{citation | last = Dietz | first = Ada K. | location = Louisville, Kentucky | publisher = The Little Loomhouse | title = Algebraic Expressions in Handwoven Textiles | url = http://www.cs.arizona.edu/patterns/weaving/monographs/dak_alge.pdf | year = 1949}}
10. ^{{citation|first=J. C. P.|last=Miller|authorlink=J. C. P. Miller|title=Periodic forests of stunted trees |journal=Philosophical Transactions of the Royal Society of London |series=Series A, Mathematical and Physical Sciences |volume=266| issue=1172| year=1970 |pages=63–111 |doi=10.1098/rsta.1970.0003 |bibcode=1970RSPTA.266...63M |jstor=73779}}
11. ^{{citation |title=International Women in Science |author=Catharine M. C. Haines |publisher=ABC-CLIO |year=2001 |isbn=9781576070901 |page=118}}
12. ^{{cite web|title=Space-Filling Curves|url=https://dmck.us/the-company/space-filling-curves/|publisher=DMCK|accessdate=15 May 2015}}
13. ^{{cite web | author=McKenna, Douglas |title=The 7 Curve, Carpets, Quilts, and Other Asymmetric, Square-Filling, Threaded Tile Designs |work=Bridges Donostia: Mathematics, Music, Art, Architecture, Culture |url=http://www.bridgesmathart.org/2007/2007-program.html |publisher=The Bridges Organization | date=24 July 2007 |accessdate=15 May 2015}}
14. ^{{cite web |last1=McKenna |first1=Douglas |title=Designing Symmetric Peano Curve Tiling Patterns with Escher-esque Foreground/Background Ambiguity |work=Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture |url=http://www.bridgesmathart.org/2008/Schedule_V9-1.pdf |publisher=The Bridges Organization |accessdate=15 May 2015|date=28 July 2008}}
15. ^{{cite | last = Barchfield | first = Jenny | date = March 5, 2010 | publisher = ABC News | title = Fashion and Advanced Mathematics Meet at Miyake | url = http://abcnews.go.com/Entertainment/wireStory?id=10017982}}.