Mathematical textiles: the use of knot theory to inform the design of knotted textiles

This paper reports on an ongoing practice-led research project examining the relationship between mathematical knot theory and knotted textiles, i.e., how mathematics may be used to characterize knotted textiles and how mathematics learners and textile designers can mutually benefit from this relationship. The research questions include: (1) whether craft and mathematical knots share comparable characteristics; (2) whether knot theory can examine the mathematical properties of knotted textile structures; and (3) how knot theory can facilitate the conceptualization, design and production of three-dimensional textiles. This paper focuses on the first phase of the research process, which commences with the mathematical characterization process which enables three-dimensional knotted textiles previously created by the author to be considered, e.g., what a knot is, how it is formed, what makes two knots equivalent, what composite knots (two or more knots together) are, what effect the spaces between and within knots have, what influence material characteristics (elastic, flexible, or rigid) have on knots, etc.