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Ellipse circumference in workable closed form
Posted:
Dec 16, 2012 1:17 AM


http://arithmeticgeometricmean.blogspot.com
8e^2(1e^2)*d/dk(K(k=e^2))+2(1e^2)*pi/(AGM(1,sqrt(1e^2)))
The derivative of K is estimated with a small delta applied to the form involving the AGM:
[pi/(2*AGM(1,sqrt(1(e^2+1E26))))pi/(2*AGM(1,sqrt(1e^2)))]/[1E26]
At least 14 digits accuracy for all eccentricities from zero up to the point of where the aspect ratio is 1 million to 1.
Thomas Blankenhorn



