Susan Goldstine

Associate Professor of Mathematics
St. Mary's College of Maryland
St. Mary's City, MD

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 stem from an extended research project with computer scientist and artist Ellie Baker. As detailed in our recent book, Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist, we meet the challenge of designing coherent patterns on a toroidal spiral of beads by making periodic designs in the plane with special constraints that allow them to wrap seamlessly around the torus.

Hyperbolic Constellation
Hyperbolic Constellation
3" x 5" x 5"
Glass beads, crochet cotton thread

Hyperbolic Constellation is inspired by Daina Taimina's innovative technique for crocheting hyperbolic surfaces. Her breakthrough is that if you crochet with an increase (made by stitching twice into the same stitch) every n stitches for a fixed number n, the result has constant negative curvature. I have always been curious about how these increases are arranged.

While many artists have woven hyperbolic surfaces with beads, I have yet to see other examples of hyperbolic bead crochet, which moves more organically. In this pseudospherical beaded surface, the gold beads (every 6th bead on the thread) mark the locations of the crochet increases. The initial round contains 6 beads, while the outer edge contains 6 x 64 = 384 beads.

Map Coloring Jewelry Set
Map Coloring Jewelry Set
12" x 8" x 8"
Glass beads, gold-filled beads, thread, ear wires

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.