I have always had diverse interests, double majoring in mathematics and English. Several manuscripts on which I have worked during my tenure at A K Peters have fostered an interest in connections between mathematics and art, including needlework. I am particularly interested in the diverse possibilities of crochet, which I learned after working on Daina Taimina's book, Crocheting Adventures with Hyperbolic Planes. I was inspired by the technique of creating crocheted models of hyperbolic planes. Once I had made one for myself, I was able to believe non-Euclidean properties that I had previously accepted but not truly believed at heart. Both the Möbius band and hyperbolic geometry are somewhat unintuitive mathematical constructs, which makes them particularly appealing as artistic subjects.
This model is a hyperbolic Möbius band. The starting “spine” consists of 20 chain stitches, and the outer single edge has over 1600 single crochet stitches. The negative curvature of the surface allows the width of the band to be much greater than if the curvature were zero. The surface can move freely through the “hole” in the center. The bead work highlights the nonorientability of the surface. In isolated sections, it looks as if the beads are on two sides of the band; but if one traces the line of beads, one will return to the chosen starting point having traced all of the beads. The same amount of yarn is used for the red and the pink, to display the exponential growth of the surface. (There is a greater amount of white yarn, to have a constant final row for aesthetic purposes.) The color scheme arose from the fact that, at an earlier construction stage, the silhouette of the model resembles a heart.