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Handbook of the Mathematics of the Arts and Sciences pp 1–28Cite as

Mathematical Design for Knotted Textiles

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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.

Keywords

  • Design
  • Knot diagram
  • Knot theory
  • Knotted textiles
  • Rhombille tiling
  • Wang tiles

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Author information

Authors and Affiliations

  1. OCAD University, Toronto, Canada

    Nithikul Nimkulrat

  2. Turku, Finland

    Tuomas Nurmi

Authors
  1. Nithikul Nimkulrat
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  2. Tuomas Nurmi
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Corresponding author

Correspondence to Nithikul Nimkulrat .

Editor information

Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Dr. Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

  2. Department of Mathematics Education, College of Education, Seoul National University, Seoul, South Korea

    Kyeong-Hwa Lee

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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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

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