# 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 inspiration for this work is Example 1.29 in Allen Hatcher's Algebraic Topology. It involves the Cartesian product of an equilateral Y with an interval, where one end has been rotated by 2 pi/3 before identifying the ends. The result is a nonmanifold generalization of a Mobius band. The boundary of the core is wired so that the three fins of the Y are visible.

Each piece was constructed from the central circle outwards using a single strand of yarn, using seed stitch so as to obscure the location of the central circle. The major design challenge was creating a knitting cast-on that would produce three interlaced sets of free stitches (instead of the usual one or two sets).

After making the core, I realized it looked like a skinny cowl. Therefore I altered the dimensions to create a winter accessory garment. The knitting pattern for this garment includes two sizes (wrapping once and wrapping twice around the neck) and two textures (seed stitch and ribbing).