Original - The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle (parameters are R = 5.0, r = 3, d = 5).
Reason
An excellently made animation that instantly communicates the concept of a hypotrochoid.
Support In my opinion, graduating the axes make the example a little more concrete: It would be far easier to reproduce the figure with the grid than without. Shoemaker's Holiday (talk) 23:43, 19 May 2009 (UTC)[reply]
Support This is what online learning is about, wikipedia can lucidly describe a concept using animation technology, while a traditional book/blackboard can't! Lilaac (talk) 17:44, 20 May 2009 (UTC)[reply]
Comment I only just realized that there's actually a lot of similarly excellent animations made by Sam Derbyshire on his user page, many of which are probably as good as this one. I guess we can't nominate all of them, which is a shame, since lots of them seem to be FP quality (although for some reason they seem to be of a very large file size and therefore load slowly; this one appears to have been optimized by Anevrisme). -- BlastOButter42SeeHearSpeak21:31, 20 May 2009 (UTC)[reply]
That's a good point actually, I realised my images had quite annoyingly large filesizes but I optimised it with Photoshop and couldn't get much better results. I'd be curious to know how Anevrisme managed to do it! Thanks for the kind words, if anyone can think of other nice maths things that deserve to have images like this I'd be really happy to hear about it, as I find it very entertaining and instructing to make them! (Though I'm not a particular fan of just having to parametrise stuff like deforming a torus into a mug, there's not much going on mathematically in that case...). -XediTalk00:04, 21 May 2009 (UTC)[reply]