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The [[Lorenz attractor|Lorenz manifold]] and the [[Hyperbolic manifold|hyperbolic plane]] have been crafted using crochet.<ref>{{citation | last1 = Henderson | first1 = David | last2 = Taimina | first2 = Daina | author2-link = Daina Taimina | doi = 10.1007/BF03026623 | issue = 2 | journal = [[Mathematical Intelligencer]] |
The [[Lorenz attractor|Lorenz manifold]] and the [[Hyperbolic manifold|hyperbolic plane]] have been crafted using crochet.<ref>{{citation | last1 = Henderson | first1 = David | last2 = Taimina | first2 = Daina | author2-link = Daina Taimina | doi = 10.1007/BF03026623 | issue = 2 | journal = [[Mathematical Intelligencer]] |
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| pages = 17–28 | title = Crocheting the hyperbolic plane | url = http://www.math.cornell.edu/%7Edwh/papers/crochet/crochet.PDF | volume = 23 | year = 2001| s2cid = 120271314 }}}.</ref><ref>{{citation | last1 = Osinga | first1 = Hinke M. | author1-link = Hinke Osinga |
| pages = 17–28 | title = Crocheting the hyperbolic plane | url = http://www.math.cornell.edu/%7Edwh/papers/crochet/crochet.PDF | volume = 23 | year = 2001| s2cid = 120271314 }}}.</ref><ref>{{citation | last1 = Osinga | first1 = Hinke M. | author1-link = Hinke Osinga |
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| last2 = Krauskopf | first2 = Bernd | doi = 10.1007/BF02985416 | issue = 4 | journal = Mathematical Intelligencer | pages = 25–37 | title = Crocheting the Lorenz manifold | url = |
| last2 = Krauskopf | first2 = Bernd | doi = 10.1007/BF02985416 | issue = 4 | journal = Mathematical Intelligencer | pages = 25–37 | title = Crocheting the Lorenz manifold | url = https://research-information.bris.ac.uk/files/163834512/2004r03.pdf | volume = 26 | year = 2004| s2cid = 119728638 }}.</ref> Knitted and crocheted [[torus|tori]] have also been constructed depicting [[toroidal graph|toroidal embeddings]] of the [[complete graph]] ''K''<sub>7</sub> and of the [[Heawood graph]].<ref>{{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}}.</ref> 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]].<ref>{{citation | last = Bloxham | first = Andy | date = March 26, 2010 | journal = [[The Daily Telegraph|The Telegraph]] | title = Crocheting Adventures with Hyperbolic Planes wins oddest book title award |
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| url = https://www.telegraph.co.uk/culture/books/bookprizes/7520047/Crocheting-Adventures-with-Hyperbolic-Planes-wins-oddest-book-title-award.html}}.</ref> |
| url = https://www.telegraph.co.uk/culture/books/bookprizes/7520047/Crocheting-Adventures-with-Hyperbolic-Planes-wins-oddest-book-title-award.html}}.</ref> |
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==Weaving== |
==Weaving== |
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<!--[[File:Polynomiography carpet.jpg|thumb|Polynomiography carpet]]--> |
<!--[[File:Polynomiography carpet.jpg|thumb|Polynomiography carpet]]--> |
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[[Ada Dietz]] (1882 – |
[[Ada Dietz]] (1882 – 1981) was an American [[weaving|weaver]] best known for her 1949 monograph ''Algebraic Expressions in Handwoven Textiles'', which defines weaving patterns based on the expansion of multivariate [[polynomial]]s.<ref>{{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 | access-date = 2007-09-27 | archive-url = https://web.archive.org/web/20160222003421/http://www.cs.arizona.edu/patterns/weaving/monographs/dak_alge.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> |
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{{harvs|first=J. C. P.|last=Miller|authorlink=J. C. P. Miller|year=1970|txt}} used the [[Rule 90]] [[cellular automaton]] to design [[tapestry|tapestries]] depicting both trees and abstract patterns of triangles.<ref>{{citation|first=J. C. P.|last=Miller|author-link=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|s2cid=123330469}}</ref> |
{{harvs|first=J. C. P.|last=Miller|authorlink=J. C. P. Miller|year=1970|txt}} used the [[Rule 90]] [[cellular automaton]] to design [[tapestry|tapestries]] depicting both trees and abstract patterns of triangles.<ref>{{citation|first=J. C. P.|last=Miller|author-link=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|s2cid=123330469}}</ref> |
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==Fashion design== |
==Fashion design== |
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The silk scarves from DMCK Designs' 2013 collection are all based on Douglas McKenna's [[space-filling curve]] patterns.<ref>{{cite web|title=Space-Filling Curves|url=https://dmck.us/the-company/space-filling-curves/|publisher=DMCK|access-date=15 May 2015}}</ref> The designs are either generalized Peano curves, or based on a new space-filling construction technique.<ref>{{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 |access-date=15 May 2015}}</ref><ref>{{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= |
The silk scarves from DMCK Designs' 2013 collection are all based on Douglas McKenna's [[space-filling curve]] patterns.<ref>{{cite web|title=Space-Filling Curves|url=https://dmck.us/the-company/space-filling-curves/|publisher=DMCK|access-date=15 May 2015}}</ref> The designs are either generalized Peano curves, or based on a new space-filling construction technique.<ref>{{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 |access-date=15 May 2015}}</ref><ref>{{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=https://archive.bridgesmathart.org/2008/bridges2008-123.html#gsc.tab=0 |publisher=The Bridges Organization |access-date=26 Nov 2023|date=26 Nov 2023}}</ref> |
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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]].<ref>{{citation | last = Barchfield | first = Jenny | date = March 5, 2010 | publisher = [[ABC News]] | title = Fashion and Advanced Mathematics Meet at Miyake | url = https://abcnews.go.com/Entertainment/wireStory?id=10017982}}.</ref> |
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]].<ref>{{citation | last = Barchfield | first = Jenny | date = March 5, 2010 | publisher = [[ABC News (United States)|ABC News]] | title = Fashion and Advanced Mathematics Meet at Miyake | url = https://abcnews.go.com/Entertainment/wireStory?id=10017982}}.</ref> |
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==See also== |
==See also== |
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Latest revision as of 15:55, 3 July 2024
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
[edit]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
[edit]
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
[edit]
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
[edit]Ada Dietz (1882 – 1981) 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
[edit]Margaret Greig was a mathematician who articulated the mathematics of worsted spinning.[11]
Fashion design
[edit]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
[edit]References
[edit]- ^ 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" (PDF), 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 (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.
- ^ Barchfield, Jenny (March 5, 2010), Fashion and Advanced Mathematics Meet at Miyake, ABC News.
Further reading
[edit]- 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
[edit]- 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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