'D' orbital

Hi folks!

A quick project to talk about today - last week I had a strange urge to knit an atomic orbital. The story goes that according to quantum mechanics, electrons live in atoms not as particular points, but as probability distributions. The standard way to represent these distributions is to draw surfaces enclosing 'most' of the probability. (I'm a little shaky on how this works exactly)
Surprisingly, the geometry of these surfaces can be quite interesting, particularly as the energy increases.
I decided to make the 3dz^2 orbital, which is my personal favourite - it's complicated enough to be very recognisable, while being simple enough to make some sense. I should say thanks too, to the Scientific Knitters group over at Ravelry for helping me figure out the shape.
I should say too that one of the components of this particular orbital is a ring, so this counts as another torus toy.


So here it is! I decided to knit the ring and the cones in different colours just to make it look colourful and nice, but apparently this has some physically relevance too - I'm told there is some kind of phase difference between the wave functions in the two parts. I don't really understand, but it's a nice coincidence.
I decided too to make the ring detachable, in the hope that this would make it more play-with-able, but this has the downside that the ring can't be tight enough around the waist to stay in place by itself. I guess I could make a second version in which the ring is smaller and sewn on to make it more realistic. But I kinda like it this way - it looks like it should be a child's toy, and I'd hope the detachable ring adds to this.
There's one slight problem, that I knit this on slightly too large a pair of needles, and the fabric on the ring part isn't quite as dense as I'd like. I should really have learnt by now that if you're knitting stuffed things you need to move down a needle size or two.

So yeah, it's all done, and I put the pattern up on Ravelry if anyone wants one of their own.

Happy knitting!
Hugh.

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.