Date: Dec 22, 2012 2:17 AM
Author: thomasinventions@yahoo.com
Subject: New Ellipse circumference formula, using agm
And this bypasses the elliptic integral of the first kind:

C = C = 2*pi*(1-e)[(agm(1,(1-e)/(1+e))-e*(1+e)*(d/dx)[agm(1,(1-x)/(1+x))]|x=e)]/((1+e)*agm(1,(1-e)/(1+e))^2)</font><br>

http://ellipsecircumference.blogspot.com

I like to leave out the a, but this defaults to a=1, of course.

The derivative of the agm(1,x) is found simply using the definition formula:

(d/dx(agm(1,x)=lim d->0 of:

(agm(1,(1-(x+d))/(1+(x+d)))-agm(1,(1-x)/(1+x)))/d

I use d at 1E-24.