# sarah-marie belcastro

Director / Research Associate

MathILy / Smith College

Holyoke, Massachusetts, USA

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 or other practical use. (It is perhaps too much to hope that I could regularly combine artistry and function in addition to knitting and mathematics.)

Petersen-Embellished Non-orientable Blanket Square

32 x 32 x 2 cm

knitting with surface crochet

2015

This piece arose from an interdisciplinary challenge to represent one's research as a blanket square. As a topological graph theorist, I study graphs embedded on surfaces. One can remove a disk from any surface and stretch/manipulate the resulting boundary into an "exterior" square, so in theory any embedded graph could become a blanket square. However, to be of use in a blanket the finished square must not be unwieldily thick or rife with gaping holes; thus, the surface must have low genus. I chose to work with the projective plane, and to embed the Petersen graph. Because this surface is nonorientable, there is no "front," and so the finished square can be viewed equally from either side.