When knitters want to make tubes without seams, they sometimes use circular knitting needles, in which two points are connected by a flexible wire. A few years ago sarah-marie belcastro tied her circular knitting needles in a knot to see what would happen. She knitted along the knotted needles and ended up with a knitted trefoil knot, the simplest knot you can tie. Belcastro, a mathematician as well as a skilled knitter, was delighted. Her research interests include graph theory and knot theory, and after creating her first knitted trefoil she continued her adventures in mathematical knitting, developing a technique for knitting more complicated knots and links.
At the Joint Mathematics Meetings in Baltimore last month, belcastro, along with Mercer University mathematician Carolyn Yackel, organized a special session that brought together mathematics, mathematics education and fiber arts. The mathematician-crafters involved in the session explored a wide range of topics. Most presentations fell into two broad categories: mathematics in the service of arts, and arts in the service of mathematics. University of Victoria mathematician Veronika Irvine's bobbin lace piece, "Cyber Rose," is in the first category. Irvine used mathematics to develop an algorithm for creating novel lace patterns. On the other hand, Central Connecticut State University mathematician S. Louise Gould's "Cuboctahedron-Projective Plane Transformer" is in the second category. Gould's motivation for making the brightly colored, zippered figure was to better understand the projective plane, a hard-to-visualize mathematical surface, by getting her hands on this physical model.
Some projects combined aspects of both categories. Malone University mathematician Kyle Calderhead's "Hexagonal Hilbert" is a visualization of a variant on the Hilbert curve, a space-filling curve that is built using an iterative, fractal process. So in some ways it is crochet in the service of math. But Calderhead had to develop a technique to interweave two crochet meshes to create the final project. Knowledge of the mathematics he wanted to illustrate helped him innovate in crochet. Likewise, belcastro's torus knots and links required her to figure out a way to entwine her knitting needles, sometimes several sets of them, to create the intricate figures.
In addition to short talks, the session included a juried exhibition of mathematically inspired knit, crocheted, beaded and stitched creations. Yackel and belcastro organized the first session on mathematics and fiber arts at the 2005 Joint Mathematics Meetings. Mathematically inspired fiber artists have also participated in the annual Bridges mathematical art conference, with many knit, crocheted and quilted pieces appearing in Bridges art galleries. For more information on any of the pieces in the slide show, see the session Web site.