Update...

"Pat's Blog" took the algebra problem I posed this morning and expanded on it (infinite nested radicals) for further discussion/learning here:

http://pballew.blogspot.com/2010/07/solving-infinite-radical-chain.html

All of which reminded me in turn of an older post by "Division by Zero" blog on "continued fractions" (not exactly the same thing, but similar) here:

http://divisbyzero.com/2008/12/09/a-new-continued-fraction-for-pi/

And as another tie-in, I'll just note in passing that some of the famous equations discovered by Ramanujan (who I'd just referenced on Monday), fall into the above categories.