Mathematics and fiber arts#Knitting and crochet

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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.{{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}}.

Image:Cross stitch embroidery.jpg 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.{{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 }}}.{{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 }}. Knitted and crocheted tori have also been constructed depicting toroidal embeddings of the complete graph K₇ and of the Heawood graph.{{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}}. 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.{{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}}.

File:Florentin.png]]

Embroidery techniques such as counted-thread embroideryGillow, John, and Bryan Sentance. World Textiles, Little, Brown, 1999. 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.Snook, Barbara. Florentine Embroidery. Scribner, Second edition 1967.Williams, Elsa S. Bargello: Florentine Canvas Work. Van Nostrand Reinhold, 1967.

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.{{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 }}

{{harvs|first=J. C. P.|last=Miller|authorlink=J. C. P. Miller|year=1970|txt}} used the Rule 90 cellular automaton to design tapestries depicting both trees and abstract patterns of triangles.{{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}}

Margaret Greig was a mathematician who articulated the mathematics of worsted spinning.{{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 }}

The silk scarves from DMCK Designs' 2013 collection are all based on Douglas McKenna's space-filling curve patterns.{{cite web|title=Space-Filling Curves|url=https://dmck.us/the-company/space-filling-curves/|publisher=DMCK|access-date=15 May 2015}} The designs are either generalized Peano curves, or based on a new space-filling construction technique.{{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}}{{cite conference |last1=McKenna |first1=Douglas |contribution=Designing Symmetric Peano Curve Tiling Patterns with Escher-esque Foreground/Background Ambiguity |title=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|pages=123–130 |isbn=978-0-9665201-9-4 }}

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.{{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}}.

• Mathematics and art

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• {{cite book |editor1=belcastro, sarah-marie |editor2=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}}
• {{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 }}
• {{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}}

• [http://www.mathematicalquilts.com/ Mathematical quilts]
• [http://www.toroidalsnark.net/mathknit.html Mathematical knitting]
• [http://www.allfiberarts.com/cs/math.htm Mathematical weaving]
• [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] (2005)

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