Knitted Surfaces

Today I was procrastinating on the interwebs, and I came across a variety of super-cool mathematical knitting resources. Most of these involve the knitting of various orientable and non-orientable surfaces.

Möbius bands are fairly ubiquitous these days, with varying degrees of mathematical precision and authenticity (I would contend that a möbius band with intrinsic twist is superior to one that is knitted as a rectangle and then stitched together). I haven't made one yet, but I'm interested ...

Orientable surfaces are pretty easy to knit (at least in theory - I'm sure that if I actually try to do it I'll discover differently), but many non-orientable surfaces (f.eks. the Klein bottle and RP^2) do not live in R^3. This makes knitting them rather difficult, since "immersing" them into our world involves singularities. Maybe this will be the subject of next year's CMS talk ...

Here are a few resources I found:

1. Dr. Miles Reid, a British mathematician, put together this series of articles on knitted surfaces when he was a grad student (I think). It's pretty technical - not recommended for non-mathematicians.
2. The Home of Mathematical Knitting is a much more accessible list of resources maintained by Dr. Sarah-Marie Belcastro.