Paul Gailiunas

Newcastle UK

I have participated in every Bridges conference since 2000, and exhibited artwork since 2007, usually related to my conference presentation. I am interested in any visually interesting manifestation of mathematics, and have used a variety of media at various times: paper or card models, geometrical drawings, computer images, and I have used mathematically inspired designs in leather bookbindings. I exhibited basketry pieces using madweave in Coimbra (2011) and Enschede (2013), and a non-standard structure in Linz (2019). Recently I have experimented using hexagonal weave (kagome) to create closed surfaces. It is possible to create self-intersecting surfaces using hexagonal weave because the structure naturally includes holes.

Klein Basket
7 x 23 x 23 cm
Plastic strapping and trimmer line

This figure-8 immersion of the Klein bottle is more straightforward to make as a basket than the familiar version, although it is not without its own problems. In particular hexagonal weave is best made with flat strips, which will not bend in their own plane. I resolved this by using 2mm trimmer line (green) for the strands in one of the three directions of the triaxial fabric. It is quite stiff and helps to form the basket into a good shape. The ends have been joined for neatness but could have been left free without affecting the shape, which depends on bending forces. A single continuous strand (white strapping) completes the basket in both of the other directions, which is possible since the surface is one-sided.