sarah-marie belcastro

Director of MathILy
Mathematical Staircase, Inc.
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 Blanket Square and Torus
28 x 43 x 6 cm
Knitted wool yarns (Dream in Color Classy)

The Petersen graph is the smallest snark and has genus one, meaning that it can be embedded in the torus, but not the plane, without edges crossing. The edges are properly four-colored, as an edge three-coloring is not possible. We show this embedding on an ordinary torus and also on a torus with a disc removed so that it can be instantiated as a blanket square. The Petersen graph is literally embedded in the ordinary torus via intarsia, whereas it is surface-crocheted as an embellishment on the toroidal blanket square.