2019 Joint Mathematics Meetings

# Susan Goldstine

## Artists

## Statement

There are two things I have done for as long as I can remember: explore mathematics, and create things with my hands. In my professional academic life, these impulses have merged into my specialization in mathematics and the arts. I am particularly devoted to exploring handcrafts, especially those in the fiber arts traditionally viewed as feminine. The interplay between mathematics and fiber arts is endlessly fascinating, both in the ways that mathematics allows for a deeper understanding of knitting, crochet, weaving, and so forth, and in the ways that these crafts can illuminate complex concepts in mathematics.

## Artworks

The Fundamental Frieze Scroll series follows in the footsteps of earlier pendants depicting the seven frieze groups in knitted lace. In those works, each of the seven designs occupies the same amount of space, regardless of complexity. Here, each frieze design is generated by the same fundamental region, a rectangular pattern with no internal symmetries. Each design uses only enough copies of this rectangle to generate three translations of its primitive cell.
In Fundamental Frieze Scroll I, the fundamental region design is a lace rendition of a Truchet tile, a rectangle divided along a diagonal into light and dark triangles. Truchet tiles appear in many recent mathematical artworks, including Carolyn Yackel's lace knitting.

Glass beads incorporated during the hand-knitting process highlight the symmetries in the Fundamental Frieze Scroll series. White beads mark reflection axes, yellow beads mark glide reflection axes, and blue beads mark centers of rotation. The red beads along the edges of the designs mark their translational symmetries, with the minimal duplication needed to preserve reflections, glide reflections and rotations.
The fundamental region in Fundamental Frieze Scroll II is an embellishment of the Truchet motif that produces more elaborate lace panels than those in the first scroll.