# Susan Goldstine

## Artists

## Statement

For me, the most exciting part of mathematics is communicating it to others. I am especially interested in models that make mathematical concepts tactile or visual. This passion has led me to many artistic projects in the course of my work as a math professor and to some unexpected and delightful collaborations. My bead crochet artworks are outgrowths of an extended research project with computer scientist and artist Ellie Baker, outlined in our recent book, Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist. I am fascinated both by the challenge of producing regular patterns on bead crochet surfaces and by explorations of what geometric forms are achievable in bead crochet.

## Artworks

While every map on a plane can be colored with four colors so that no two adjacent countries are the same color, maps on other surfaces may require more colors. This jewelry set displays maps requiring the maximum number of colors for three surfaces.
The bracelet, bead crochet with a bead-woven closure, is a double torus in eight colors, each of which touches all the others. The gold bead in the center of the pink and blue spiral is strictly ornamental. The pendant is a bead-crochet torus with seven colors, and all of the color contacts are visible from the front side. The bead-woven earrings are each four-color maps in the plane. With over 5300 beads in total, the entire set is wearable topology at its finest.

The frieze groups describe the various symmetries of two-dimensional patterns that repeat in a single direction, like decorative borders in many traditional artworks. This bead crochet disk with 6471 beads shows patterns for each of the seven frieze groups. Although the strips bend around the circle, warping the planar symmetries, each strip consists of three rounds of beads with the same number of beads in each round, and so its design is equivalent to a straight-strip design with unwarped translations, reflections, rotations and/or glide reflections. I am indebted to Brigitte Servatius, whose charming paper The Geometry of Folding Paper Dolls led me to consider an artwork incorporating frieze patterns.