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 upcoming 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.

Eight-Color 8
Eight-Color 8
4.25 in x 1.25 in x 0.25 in
Glass beads, sterling silver bead, cotton crochet thread

The analog of the Four-Color Theorem for the two-holed torus is the Eight-Color Theorem: Every map on a two-holed torus can be colored with eight colors so that no two adjacent countries are the same color, and there are maps that require eight different colors. This beaded pendant shows a map with eight countries, each of which touches all of the others, an impossible feat on a surface with genus less than two. The ornamental silver bead is a purely aesthetic accent that exploits an unavoidable asymmetry in the eight interlocking spirals around the middle of the 8.

The pendant was crocheted in a single piece with 797 beads and then joined with two circular seams, one on each side of the thicker central section.