Sooner or later, all mathematician knitters try to knit mobius strips, and we are no exception. We know several good ways to knit mobius strips, some of which are well-known to knitters. We have invented two new homogeneous methods, both more complicated but more satisfactory than the traditional ones.
Of particular interest are strips with a homogeneous pattern of stitches throughout. More explicitly, we desire strips whose local appearance is the same everywhere on the strip. In particular, we try to avoid strips that possess seams. We will discuss these concepts later in the paper as they arise.
Below we discuss the various methods. We describe some explicit constructions for the reader already familiar with knitting [2] [3]. We ignore most of the physical issues such as tension and friction that determine the exact shape of stitches and fabrics.