Abstract
This chapter examines the relationship between mathematics and textile knot practice, i.e., how mathematics may be adopted to characterize knotted textiles and to generate new knot designs. Two key mathematical concepts discussed are knot theory and tiling theory. First, knot theory and its connected mathematical concept, braid theory, are used to examine the mathematical properties of knotted textile structures and explore possibilities of facilitating the conceptualization, design, and production of knotted textiles. Through the application of knot diagrams, several novel two-tone knotted patterns and a new material structure can be created. Second, mathematical tiling methods, in particular the Wang tiling and the Rhombille tiling, are applied to further explore the design possibilities of new textile knot structures. Based on tiling notations generated, several two- and three-dimensional structures are created. The relationship between textile knot practice and mathematics illuminates an objective and detailed way of designing knotted textiles and communicating their creative processes. Mathematical diagrams and notations not only reveal the nature of craft knots but also stimulate new ideas, which may not have occurred otherwise.
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References
Adams C (1994) The knot book: an elementary introduction to the mathematical theory of knots. W H Freeman, New York
Ashley CW (1944) The Ashley book of knots. Faber and Faber, London
Devlin K (1998) The language of mathematics: making the invisible visible. W H Freeman, New York
Devlin K (1999) Mathematics: the new golden age. Columbia University Press, New York
van de Griend P (1996) A history of topological knot theory. In: Turner JC, van de Griend P (eds) History and science of knots. World Scientific, Singapore, pp 205–260
Grünbaum B, Shephard GC (1987) Tilings and patterns. W H Freeman, New York
Harris M (1988) Common threads: mathematics and textiles. Math Sch 17(4):24–28
Harris M (1997) Common threads: women, mathematics and work. Trentham Books, Stoke-on-Trent
Issey Miyake Inc (2018) 132 5. Issey Miyake. http://www.isseymiyake.com/en/brands/132_5.html. Accessed 20 July 2008
Jablanand S, Sazdanovic R (2007) LinKnot: knot theory by computer, vol 21. World Scientific, Singapore
Kaplan CS (2009) Introductory tiling theory for computer graphics. Morgan & Claypool, San Rafael
Lagae A, Dutre P (2006) An alternative for Wang tiles: colored edges versus colored corners. ACM Trans Graph 25(4):1442–1459
Lee MEM, Ockendon H (2005) A continuum model for entangled fibres. Eur J Appl Math 16:145–160
Mann C (2004) Heesch’s tiling problem. Am Math Mon 111(6):509–517
Meluzzi D, Smith DE, Arya G (2010) Biophysics of knotting. Annu Rev Biophys 39:349–366
Nimkulrat N (2009) Paperness: expressive material in textile art from an artist’s viewpoint. University of Art and Design Helsinki, Helsinki
Nimkulrat N, Matthews J (2016) Novel textile knot designs through mathematical knot diagrams. In: Torrence E, Torrence B, Séquin C, McKenna D, Fenyvesi K, Sarhangi R (eds) Proceedings of Bridges 2016: mathematics, music, art, architecture, education, culture. Tessellations, Phoenix, pp 477–480
Nurmi T (2016) From checkerboard to cloverfield: using Wang tiles in seamless non-periodic patterns. In: Torrence E, Torrence B, Séquin C, McKenna D, Fenyvesi K, Sarhangi R (eds) Proceedings of Bridges 2016: mathematics, music, art, architecture, education, culture. Tessellations, Phoenix, pp 159–166
Osinga HM, Krauskopf B (2004) Crocheting the Lorenz manifold. Math Intell 26(4):25–37
Osinga HM, Krauskopf B (2014) How to crochet a space-filling pancake: the math, the art and what next. In: Greenfield G, Hart GW, Sarhangi R (eds) Bridges 2014: mathematics, music, art, architecture, culture. Tessellations, Phoenix, pp 19–26
Sennett R (2008) The craftsman. Yale University Press, New Haven
Sossinsky A (2002) Knots: mathematics with a twist. Harvard University Press, Cambridge, MA
Taimina D (2009) Crocheting adventures with hyperbolic planes. AK Peters, Wellesley
Woodhouse T, Brand A (1920) Textile mathematics: part I. Blackie & Son, London
Woodhouse T, Brand A (1921) Textile mathematics: part 2. Blackie & Son, London
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Nimkulrat, N., Nurmi, T. (2019). Mathematical Design for Knotted Textiles. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_39-1
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DOI: https://doi.org/10.1007/978-3-319-70658-0_39-1
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