So I posted this on facebook:
This is a serious problem all over wikipedia. The math-heads strip out any sort of tutorial or explanitory information, and leave only formal definitions. A fine example is the “sheaf” article. There’s no mention that the word comes from a sheaf of wheat, which would kinda help people get over that initial WTF.
I had a chat to Brett, and the upshot was that I was about to post this to facebook:
So anyway. I just had a bit of a chat to a D&D buddy who occasionally does a little mathematics that is maybe a shade further along than what I am used to dealing with.
Reflecting on his replies and my internal reactions to them, you want to know what I think? Well, I’ll tell you. I think that the core of my complaint is that the mathematics pages on wikipedia don’t have enough pictures, and that’s really all I’m bitching about.
The reply to this comment on the Sheaf talk page kinda covers it:
“Hi; I’m trying desperately to understand many of these advanced principals of mathematics, such as sheaves, but no matter how many times I review the material, it doesn’t sink in.”
(reply:) “… if you are new to math, it’s not enough to review the material; you should also do problems. If you want to learn math, you can’t do it with a summary like Wikipedia.”
If you want to understand mathematics, you have to put the work in. There is no other way. Euclid’s rebuke to King Ptolemy comes to mind.
But you know – looking back at that original SMBC comic I can’t help feeling that the plaintive cry for a pretty picture or two isn’t entirely uncalled for, and that maybe other people feel the same way.
Look – it doesn’t matter, ok? At the moment all I’m after, really, is a pretty picture of the hyperbolic plane tessellated with octagons projected onto a flat plane in a certain specific way that I have in mind (the hyperbolic analogue of the equirectangular projection, if you must know). I’ll settle for a grid of lines all at 45 degrees.
I suspect that the Beltrami-Klein model might be the best starting point. Isometries on it are just matrixes IIRC. I just need to work out how one family of parallel lines needs to be spaced out, and getting from there to the equirectangluar plane should be straightforward – just read off the distance from each point to the two axes.