On 2020-09-20 6:24 PM (-4), Bald Eagle wrote:
> I just stumbled across this while trying to regain my sanity,
> and if even Ramanujan couldn't come up with anything but an approximation, than
> I think the rest of us are Fuuuuuuuuuuuuuuuuuuuuuumbling around in the dark.
> 
> :)
> 
> https://www.youtube.com/watch?v=5nW3nJhBHL0

You watch Matt Parker to regain your sanity?  I have some of his videos 
languishing in my "Watch later" list because I'm afraid I'll *lose* my 
sanity if I watch them.

> But don't anyone think that that will stop us from making another attempt, using
> new inspiration and mathematical tools!
> 
> I think the above implies that due to the interesting properties of ellipses,
> that a workable solution will use numerical methods.

I am not convinced that this property is directly relevant to the 
problem I am trying to solve.  I still think the key is in that quartic 
equation I came up with, which should not require numerical methods 
(beyond what's implicit in POV-Ray's built-in functions).  The problem 
is that I am not practiced in solving quartic equations.

P.S.  I have known since 2007 that there is no exact formula for an 
ellipse's circumference.  I discovered that while trying to weld this 
'O' to the rectangular plate using an ellipse made out of blobs.

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