Now I have solved the original problem that inspired all of this madness in 
the first place.

The object was to find a non-iterative solution for the angle subtending a 
known arc and chord on a circle.

I just couldn't let go of this problem until I got it.

Even with what I've come up with now, I still haven't "got it."

This concludes my arclength solution for the weekend.  Maybe one or two of 
you might profit from my fixation on this problem, which has gone on for at 
least 6 years.

.... but I can think of some more unhealthy fixations than math... and 
others more healthy, like mowing the yard... you may be amazed to discover 
that I actually did mow it yesterday.

http://mypeoplepc.com/members/jon8338/polynomial/