Mathematical Design for Knotted Textiles

• Nithikul Nimkulrat
• Tuomas Nurmi
Living reference work entry

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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

2. 2.TurkuFinland

Section editors and affiliations

• Bharath Sriraman
• 1
• Kyeong-Hwa Lee
• 2
1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA
2. 2.Department of Mathematics Education, College of EducationSeoul National UniversitySeoulSouth Korea