Monday, August 6, 2007

Graduation torus

This was a bit of a quick project since it had a pretty short deadline(and wasn't too complicated), so it's only getting one post.
It's for a maths-studying friend who is completing his PhD soon(his viva is this thursday). So I made him a torus wearing a little mortarboard. We don't actually wear mortarboards at our graduations here at the university of Edinburgh, but hey.
There's some maths geekery behind this too, the torus is a manifold, which means that if you look at it in small enough pieces, it looks just like flat space. It's also a Lie group, but that's a little harder to explain. The cool thing about manifolds is you can do calculus on them, which you do by approximating them by planes one point at a time. So the mortarboard part is supposed to be the tangent plane at a point. The 'tassels' are supposed to represent a basis of this tangent space, which is to say they give the directions you can move along the surface. For Lie groups the tangent space is particularly useful because in some sense you only need to look at one of them rather than having one for each point.

Knitwise, I think the only tricky part was making the board. It has a piece of cardboard inside to make it nice and flat. I'd hoped to make this removable so it could be easily replaced if it got bent, but in the end the stocking stitch made the opening hang open too much, so I had to sew it closed. There might have been a nicer way to do this with tassels and eyelets.

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