Lately I’ve been trying to wrap my head around various mathematical concepts that are required for generating 3-dimensional objects. That is hard enough, but some mathematicians have gone further, to 4 or even higher dimensions. If you want a visual explanation of such mysteries, I highly recommmend the series of videos available on the site http://www.dimensions-math.org.
The videos are really 3d animations rendered with POV-Ray and they are stunning - perfectly smooth and crisp forms which are the result of POV-ray’s approach to rendering, which does not use meshes but rather ray-tracing. POV-ray is an open-source, free, cross-platform 3D rendering program. I’ve installed the unix version on my mac using fink, as the mac version of POVray is not compatible with Leopard at the time of writing this. I haven’t tried it out yet, though.
The Dimensions site features background information for each of the chapters which you should read before watching each video, with links to further excellent resources on the web. I’m still working my way through it all, but it’s a real treat for the eyes and the mind, so go check it out! Best of all, it’s totally free!
Here’s a quick preview - click on the image on the left for a sample from the movie.
Note that the downloaded version of the movie has multilingual versions without subtitles, and the quality’s much better. BTW: I’m not affiliated with the producers of Dimensions at all, and I’m not being paid to say this :)