I'm drawn to crafting objects whose construction requires puzzle-solving, such as this three-way reversible toroidal scarf. In pursuit of design goals, I often stumble across fun puzzles and wind up not only with an interesting object, but also with a deeper understanding of some bit of mathematics. My experiences as a maker/crafter/artist/puzzler are also reflected in the book I coauthored with Susan Goldstine, “Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist.”
The mathematical ideas incorporated into the design of this scarf were developed in collaboration with Daniel Baker and Charles Wampler, and the theory behind it is described in our Bridges 2020 paper "Infinitely Invertible Infinity."
This "infinity" scarf inverts three ways, each displaying a different custom printed fabric illustrating the linked structure of the scarf itself. The linkage is composed of three cloth tori whose geometry is carefully chosen to be shape invariant on inversion. When any one torus in the link is inverted, the other two remain linked and nested inside it. A double-slotted inversion slit (shown lower right) allows the wearer to choose which of the two hidden surfaces to expose next. The fabric motifs depict three different arrangements of this specific link and were hand drawn and organized as repeating patterns using the app iOrnament.