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.
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]
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 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]
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]
Margaret Greig was a mathematician who articulated the mathematics of worsted spinning. [11]
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]
Crochet is a process of creating textiles by using a crochet hook to interlock loops of yarn, thread, or strands of other materials. The name is derived from the French term croc, which means 'hook'. Hooks can be made from a variety of materials, such as metal, wood, bamboo, bone or even plastic. The key difference between crochet and knitting, beyond the implements used for their production, is that each stitch in crochet is completed before the next one is begun, while knitting keeps many stitches open at a time. Some variant forms of crochet, such as Tunisian crochet and broomstick lace, do keep multiple crochet stitches open at a time.
In geometry, a pseudosphere is a surface with constant negative Gaussian curvature.
In mathematics, a curve is an object similar to a line, but that does not have to be straight.
In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together.
In mathematics, hyperbolic geometry is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
Ralph William Gosper Jr., known as Bill Gosper, is an American mathematician and programmer. Along with Richard Greenblatt, he may be considered to have founded the hacker community, and he holds a place of pride in the Lisp community. The Gosper curve and the Gosper's algorithm are named after him.
Bargello is a type of needlepoint embroidery consisting of upright flat stitches laid in a mathematical pattern to create motifs. The name originates from a series of chairs found in the Bargello palace in Florence, which have a "flame stitch" pattern.
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.
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.
Textile design, also known as textile geometry, is the creative and technical process by which thread or yarn fibers are interlaced to form a piece of cloth or fabric, which is subsequently printed upon or otherwise adorned. Textile design is further broken down into three major disciplines: printed textile design, woven textile design, and mixed media textile design. Each uses different methods to produce a fabric for variable uses and markets. Textile design as an industry is involved in other disciplines such as fashion, interior design, and fine arts.
The manufacture of textiles is one of the oldest of human technologies. To make textiles, the first requirement is a source of fiber from which a yarn can be made, primarily by spinning. The yarn is processed by knitting or weaving, which turns it into cloth. The machine used for weaving is the loom. For decoration, the process of colouring yarn or the finished material is dyeing. For more information of the various steps, see textile manufacturing.
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.
The Hat and Fragrance Textile Gallery is an exhibit space at Shelburne Museum in Shelburne, Vermont which houses quilts, hatboxes, and various other textiles. The name "Hat and Fragrance" refers both to Electra Havemeyer Webb's collection of hatboxes and to the fragrant, herbal sachets used to preserve textiles. In 1954, Shelburne Museum was the first museum to exhibit quilts as works of art; prior to this exhibition quilts were only shown as accessories in historic houses.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Mathematics is a broad subject that is commonly divided in many areas that may be defined by their objects of study, by the used methods, or by both. For example, analytic number theory is a subarea of number theory devoted to the use of methods of analysis for the study of natural numbers.
In mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision rules in a sense are generalizations of regular geometric fractals. Instead of repeating exactly the same design over and over, they have slight variations in each stage, allowing a richer structure while maintaining the elegant style of fractals. Subdivision rules have been used in architecture, biology, and computer science, as well as in the study of hyperbolic manifolds. Substitution tilings are a well-studied type of subdivision rule.
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.
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.
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.
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.
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