Tuesday, April 21, 2009

Cayley Cubic

To further my polynomial education I've been thinking some lately about the Cayley cubic, which in the affine form I was using is given by x^2 + y^2 + z^2 + z(y^2-x^2) -1 = 0.

I made a little movie of some of the real solution set of the Cayley cubic. Here's one of the stills:

I think the quicktime version works better in browsers, or you can download a slightly higher-quality mp4.

3 comments:

Robert said...

Nice movie!
Please, pardon my ignorance, but how did you do this movie?
I know several ways to do math pictures, but nothing really how to do video ..

Thanks, Robert Samal

M. Hampton said...

I made the frames in Sage (www.sagemath.org) and then animated them with ffmpeg.

I give a fairly detailed example of how to do this in the following thread:
http://groups.google.com/group/sage-support/browse_thread/thread/af6c9cceb022017d

Robert said...

Thanks!
Robert