Susan Goldstine

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

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.

The Double-Knitting Groups
40 x 40 cm
Silk/merino yarn

The Double-Knitting Groups exhibits all of the wallpaper symmetry types possible in double knitting. For a harmonious overall design, I grouped the nine structures into three pattern families: scrolls, hearts, and vines. Roughly speaking, the symmetry groups get more complex from top left to bottom right: the upper left pattern has only translations, the three adjacent to it have only translations and one other type of plane symmetry (clockwise: reflections, rotations, and glide reflections), and the remaining patterns have at least three symmetry types.

This work is based on my scarf design, Crystalline, whose pattern is published in the Deep Fall 2016 issue of Knitty. The square wall hanging was knit by hand on 1.75 mm needles.