Exploring mathematical concepts of topology through knitting technology

I like to think of knitting as a type of soft engineering. Consider the form of the humble sock: constructed from a continuous thread (yarn) as a seamless tube with an elegantly engineered bend that creates no waste material. Knitwear combines fashion, textiles, mathematics, craft, and design, and has a particular affinity with 3D production ‘in the round’. Knitwear is unique in that both the fabric and the 3D form can easily be created simultaneously – a process well known to the earliest hand knitters, and eventually mimicked by machine techniques. Knitwear design is a hybrid between textiles and fashion, incorporating both stretch and drape, and requiring its own methods of shape calculation and technical knowledge.

My background spans both mathematics and knitwear design, as before entering academia I ran my own internationally successful designer knitwear label Sandy Black Original Knits. Knitted fabric, with its inherent malleability and symmetries based on the formation of the knitted loop, lends itself to potential transformations that correlate with mathematical concepts of surface geometry and topology. This practice-based research explores the potential for non-conventional structures in knitted artefacts related to the body, inspired by the topological concepts of single-surfaced objects such as the well-known Moebius strip and the Klein bottle. The research also examines the knitwear development process and technical communication between designers and technical experts, an area of research that can impact the industry more widely.

Mobius Strip png
Moebius strip by Jennifer Smith, CC BY-SA 3.0.

In the context of fashion using woven fabrics, the creation of 3D forms from 2D cloth is realised by one of two methods: utilising precision 2D pattern drafting techniques, or by draping fabric on the 3D form, then reverse engineering to a 2D pattern. Knitwear, however, can be created either by assembling 2D pieces or by direct 3D construction processes. Three-dimesional knitted artefacts (such as gloves) can be made using the simplest knitting needles or the most advanced industrial knitting technology. Creating fashion builds upon tacit knowledge of fabric handle and drape; creating with knitted construction additionally requires knowledge related to the interplay of yarns, gauge and stitch structure.

The exceptional programmability of contemporary industrial flat knitting machinery, utilising the proprietary software developed by the leading machine builders (notably Stoll in Germany and Shima Seiki in Japan) allows for infinite possibilities, but neither commercial knitwear designers nor creative fashion designers have the knowledge or resources to fully explore this potential. As a result a gap has arisen between the capability of the machinery and the industry’s ability to fully develop it in fashion and clothing, and this is where exploratory design and research is needed, exemplified by the extraordinary one-piece knitted sports shoes recently developed by both Nike and Adidas.

This fellowship builds on existing research links with Auckland University of Technology (AUT), New Zealand to explore new research collaborations in knitted and smart textiles, and is based in the Textile Design Lab, one of four specialist research centres in AUT’s CoLab. The fellowship will also enable me to explore possibilities for new collaborative research with other universities such as RMIT in Melbourne.

Professor Sandy Black
London College of Fashion , University of the Arts London