2012 Joint Mathematics Meetings

Susan Goldstine and Ellie Baker

Artists

Susan Goldstine

Professor of Mathematics

St. Mary's College of Maryland

St. Mary's City, Maryland, USA

sgoldstine@smcm.edu

http://faculty.smcm.edu/sgoldstine/gallery/mathart.html

Statement

Bead crochet bracelets have an allure that is hard to resist. For the wearer, adorned by the firm but pliable packing of beads into a sleek, snake-like skin, the appeal is both visual and tactile. For the crafter, the technique is meditatively repetitive and the bead color and texture choices endless. But for the mathematically minded, the greatest allure is in creating bracelet patterns. Behind the deceptively simple and uniform arrangement of beads is a subtle geometry that produces compelling design challenges and fascinating mathematical structures. We have been collaborating over several years on bead crochet design methods and on a variety of design questions that intrigue us. This project represents one of our forays.

Artworks

Image for entry 'close-up: P3 and P6'

close-up: P3 and P6

Image for entry 'close-up: P1 and P2'

close-up: P1 and P2

Image for entry 'Crystallographic Bracelet Series'

Crystallographic Bracelet Series

20" X 20"

glass, sterling, and semi-precious stone beads, thread, inkjet prints on paper

2011

Successful bead crochet bracelet patterns are best considered as infinite plane tilings, with the tiles composed of contiguous beads that obey certain placement rules dictated by the circumference of the beaded rope and the structure of the crochet. Since each of these planar bead tilings has a finite fundamental region, it is natural to ask which of the seventeen plane crystallographic groups arise from bead crochet bracelet designs. We have shown that bead crochet precludes all patterns with order four rotations (p4, p4g, p4m), as well as the group p31m, and that it limits two other groups (p6m and p3m1) to patterns with fundamental regions smaller than a single bead. This piece proves by example that the remaining eleven groups (p1, p2, p3, p6, pg, pgg, pmg, pm, cmm, cm, pmm) are all realizable in bead crochet.