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

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.

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