# sarah-marie belcastro

I am a mathematician who knits as well as a knitter who does mathematics. It has always seemed natural to me to combine mathematics and knitting, whether that results in knitting a model of a mathematical object or in using mathematics to design a garment. Indeed, over my mathematical life both of these types of combinations have occurred. Most of the mathematical models I have created are only of aesthetic value and have no real function; it is rare that I am able to adapt a mathematical object for use as a garment. (It is perhaps too much to hope that I could regularly combine artistry and function in addition to knitting and mathematics.)

The central property of the Borromean rings---that removing any component unlinks the remaining components---generalizes to the class of Brunnian links. Here are two different generalizations: more crossings within components, and more crossings between components.

Small Borromean rings are knitted in neutral colors because of their relative plainness. The other links are knitted in richer colors so as to emphasize their richer structure, and are functional garments (cowls). Each component of the pastel link is a two-loop unknot. The brighter cowl has three times as many intercomponent crossings as the Borromean rings. All linking is intrinsic, rather than introduced post-construction via grafting.

The central property of the Borromean rings---that removing any component unlinks the remaining components, which collectively form the unlink---generalizes to the class of Brunnian links. The Rainbow Brunnian Link Cowl has seven components rather than the three components of the Borromean rings. All linking is intrinsic, rather than introduced post-construction via grafting.

The Rainbow Brunnian Link Cowl is also a garment that can be worn two different ways, which are pictured alongside that cowl in the exhibit.