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 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.)
These are knotted Klein bottles---specifically, each is a figure-8 knotted figure-8 embedding of the Klein bottle. One was constructed by knitting a figure-8 (self-intersecting) tube and wrapping it into a figure-8 knot before grafting the tube into a Klein bottle, so it is an intrinsic figure-8 embedding and an extrinsic figure-8 knot. The other was constructed by knitting a figure-8 knotted Moebius band and grafting the boundaries into a figure-8 embedding of the Klein bottle, so it is an intrinsic figure-8 knot with an extrinsic figure-8 embedding. (Can you tell which is which?) That is, this pair of objects was made so that one could say that each is an intrinsic and extrinsic figure-8, but in different ways!