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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 make use of the natural pixels of the weave, lending themselves to geometric designs.^[7]^[8]

Weaving

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

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]

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" (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.

External links

[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] stro, 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.

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+{{short description|Ideas from Mathematics have been used as inspiration for fiber arts}}
-[[Mathematics|Mathematical]] ideas have been used as inspiration for a number of [[fiber art]]s including [[quilt]] [[quilting|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]].
+[[File:Moebiusstripscarf.jpg|right|thumb|200px|A [[Möbius strip]] scarf made from crochet.]]
+Ideas from [[mathematics]] have been used as inspiration for [[fiber art]]s including [[quilt]] [[quilting|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 [[geometry|geometrical]]; other kinds of [[textile]] provide a ready means for the colorful [[mathematics and art|physical expression of mathematical concepts]].
 ==Quilting==
+{{main|quilt}}
-The [[IEEE Spectrum]] has organised a number of competitions on Quilt Block Design, and several books have been published on the subject. Notable quilt makers 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]], [[ellipse]], [[hyperbola]], [[parabola]], [[The Sacred Cut]], [[Leonardo da Vinci's Claw]], [[Koch curve]], [[Clifford torus]], [[Pascal's Pumpkin]], the [[Chartres Cathedral Labyrinth]], [[San Gaku]], [[Mascheroni cardioid]], the Music of the Genes, [[Pythagorean triple]]s, [[Spidron]]s, the six [[trigonometry|trigonometric]] [[function]]s, and the Peacock. The authors believe can be very effective as teaching tools in the classroom.  The quilt can be used as a visual springboard for the student and teacher to begin the lesson in an interesting way.
+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 section]]s, [[Leonardo da Vinci]]'s Claw, the [[Koch curve]], the [[Clifford torus]], [[San Gaku]], [[Lorenzo Mascheroni|Mascheroni]]'s [[cardioid]], [[Pythagorean triple]]s, [[spidron]]s, and the six [[trigonometric functions]].<ref>{{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}}.</ref>
 ==Knitting and crochet==
+[[Image:Cross stitch embroidery.jpg|thumb|[[Cross-stitch]] [[counted-thread embroidery]]]]
-Knitted mathematical objects include the [[Platonic solid]]s, [[Klein bottle]]s [[Boy's surface]] the [[Lorenz attractor|Lorenz manifold]], and the [[hyperbolic plane]].
+Knitted mathematical objects include the [[Platonic solid]]s, [[Klein bottle]]s and [[Boy's surface]].
+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]]
+ | 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
+ | 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
+ | url = https://www.telegraph.co.uk/culture/books/bookprizes/7520047/Crocheting-Adventures-with-Hyperbolic-Planes-wins-oddest-book-title-award.html}}.</ref>
-==Cross-stitch==
+==Embroidery==
-Many of the [[wallpaper pattern]]s and [[frieze group]]s have been used in cross-stitch.
+[[File:Florentin.png|thumb|upright|Two [[Bargello (needlework)|Bargello patterns]]]]
-== Weaving ==
+Embroidery techniques such as [[counted-thread embroidery]]<ref>Gillow, John, and Bryan Sentance. ''World Textiles'', Little, Brown, 1999.</ref> including [[cross-stitch]] and some [[canvas work]] methods such as [[Bargello (needlework)|Bargello]] make use of the natural [[pixel]]s of the weave, lending themselves to geometric designs.<ref>Snook, Barbara. ''Florentine Embroidery''. Scribner, Second edition 1967.</ref><ref>Williams, Elsa S. ''Bargello: Florentine Canvas Work''. Van Nostrand Reinhold, 1967.</ref>
-[[Ada Dietz]] (1882 &ndash; 1950) was an American [[weaving|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 [[polynomial]]s 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.
+==Weaving==
+<!--[[File:Polynomiography carpet.jpg|thumb|Polynomiography carpet]]-->
+[[Ada Dietz]] (1882 &ndash; 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>
+{{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>
+==Spinning==
+[[Margaret Greig]] was a mathematician who articulated the mathematics of [[worsted spinning]].<ref>{{citation |title=International Women in Science |author=Catharine M. C. Haines |publisher=ABC-CLIO |year=2001 |isbn=9781576070901 |page=[https://archive.org/details/internationalwom00hain/page/118 118] |url-access=registration |url=https://archive.org/details/internationalwom00hain/page/118 }}</ref>
+==Fashion design==
+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>
+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>
+==See also==
+* [[Mathematics and art]]
 ==References==
-*{{cite book |last= Ellison |first= Elaine |coauthors= Venters, Diana |title= Mathematical Quilts: No Sewing Required |year= 1999 |publisher= Key Curriculum  |isbn= 155953317X}}
+{{reflist|28em}}
-*{{Citation
-  | last =Henderson
+==Further reading==
-  | first =David
+*{{cite book |editor1=belcastro, sarah-marie<!--intentionally not caps--> |editor2=[[Carolyn Yackel|Yackel, Carolyn]] |title=Making Mathematics with Needlework: Ten Papers and Ten Projects |title-link= Making Mathematics with Needlework |year=2007 |publisher=A K Peters |isbn=978-1-56881-331-8}}
-  | author-link =
+*{{cite journal |doi=10.2307/2690105 |author1=Grünbaum, Branko |author-link1=Branko Grünbaum |author2=Shephard, Geoffrey C. |title=Satins and Twills: An Introduction to the Geometry of Fabrics |date=May 1980 |journal=Mathematics Magazine |volume=53 |issue=3 |pages=139–161 |jstor=2690105|hdl=10338.dmlcz/104026 |hdl-access=free }}
-  | last2 =Taimina
+*{{cite book |author=Taimina, Daina |author-link=Daina Taimina|title=Crocheting Adventures with Hyperbolic Planes |year=2009 |publisher=A K Peters |isbn=978-1-56881-452-0}}
-  | first2 =Daina
-  | author2-link =
-  | title =Crocheting the hyperbolic plane
-  | journal =Math. Intelligencer
-  | volume =23
-  | issue =2
-  | pages =17&ndash;28
-  | date =
-  | year =2001
-  | url =http://www.math.cornell.edu/%7Edwh/papers/crochet/crochet.PDF
-  | doi =
-  | id =  }}
-*{{Citation
-  | last =Osinga
-  | first =Hinke M,
-  | author-link =
-  | last2 =Krauskopf
-  | first2 =Bernd
-  | author2-link =
-  | title =Crocheting the Lorenz manifold
-  | journal =Math. Intelligencer
-  | volume =26
-  | issue =4
-  | pages =25&ndash;37
-  | date =
-  | year =2004
-  | url =http://www.enm.bris.ac.uk/anm/preprints/2004r03.html
-  | doi =
-  | id =  }}
-*{{cite book
- | author = Dietz, Ada K.
- | title = Algebraic Expressions in Handwoven Textiles
- | year = 1949
- | publisher = The Little Loomhouse
- | location = Louisville, Kentucky
- | url = http://www.cs.arizona.edu/patterns/weaving/monographs/dak_alge.pdf}}
 ==External links==
-*[http://www.mathematicalquilts.com/ Mathematical Quilts] home page.
+*[http://www.mathematicalquilts.com/ Mathematical quilts]
+*[http://www.toroidalsnark.net/mathknit.html Mathematical knitting]
-*Two [[Penrose tiling]] quilts: [http://dogfeathers.com/quilt/penrose.html] [http://www.math.mcgill.ca/rags/PenroseQuilt.html]
+*[http://www.allfiberarts.com/cs/math.htm Mathematical weaving]
-*[http://www.quiltsandseams.com/index_files%5CQuilt%20Block%20Contest%20Winners.htm IEEE Spectrum's fifth Quilt Block Design Contest winners]
+*[http://www.k2g2.org/links:math_craft_projects Mathematical craft projects]
+*[http://www.woollythoughts.com/mathspuzzles.html Wooly Thoughts Creations: Maths Puzzles & Toys]
+*[http://dogfeathers.com/quilt/penrose.html Penrose tiling quilt]
 *[http://www.cabinetmagazine.org/issues/16/crocheting.php Crocheting the Hyperbolic Plane: An Interview with David Henderson and Daina Taimina]
-*[http://www.toroidalsnark.net/mkss.html AMS Special Session on Mathematics and Mathematics Education in Fiber Arts]
+*[http://www.toroidalsnark.net/mkss.html  AMS Special Session on Mathematics and Mathematics Education in Fiber Arts] (2005)
+{{Mathematical art}}
+{{Textile arts}}
 [[Category:Mathematics and culture]]
-[[Category:Quilting]]
+[[Category:Textile arts]]
+[[Category:Recreational mathematics]]
+[[Category:Mathematics and art]]

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