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.

Makeri Mosaic
27 x 21 cm
Merino/cotton yarn, wooden dowels

An outgrowth of current research by the artist and Carolyn Yackel, this mosaic-knitted scroll shows all seven frieze symmetries. Mosaic knitting, a popular type of two-color knitting, imposes unusual constraints on color placement that limit the types of symmetry attainable in the form. All of the frieze groups are compatible with these constraints.

In older forms of two-color knitting, extended runs of a single color create long yarn floats across the back of the fabric, making the wrong side unruly and prone to snagging and the right side hard to keep neat and even. The mosaic technique makes this piece entirely free of floats.

The hand-dyed yarn comes from the yarn maker's shop, Makeri 14 in Stockholm.

Float Free, Bumblebee
35 x 26 cm
Merino/alpaca yarn, wooden dowels

Float Free, Bumblebee shows the two-color frieze groups attainable in mosaic knitting. In this case, the restrictions inherent in this form of color work make some of these symmetries incompatible with mosaic knitting.

There are seventeen two-color frieze groups, which are the possible symmetries of a strip pattern that has at least one color-swapping symmetry, However, our research proves three of them to be impossible in mosaic knitting, and nine more to be impossible to knit horizontally. These nine appear side-by-side at the bottom of the scroll, and the remaining five run across the top. The only floats on the wrong side of the fabric are at the edges of the fourteen designs.

This piece was knit by hand on 1.75 mm needles.