I really like this page, and the way that you've structured it works really well.
I think it would be useful to move up your first few sentences about the sphere into the basic description, since it doesn't require difficult math (leave stuff with trig in the mathematical description, though). Also, could you give an example of a function that isn't implicit, so that the reader can see the contrast?
Also, can you actually plot the shapes you're talking about and have the images right there to look at?
I'd also rather see the applet that plots implicit surfaces embedded in the page, and the meatballs applet is getting cut off on my browser (there's clearly more of it off to the right than I can see).
One last thing: Are you planning on developing Implicit Equations and linking this page to it? Even if you aren't, you might want to include that link in the page anyways.
Overall, you've done some great work here, keep it up!