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New Ellipse circumference formula, using agm
Posted:
Dec 22, 2012 2:17 AM


And this bypasses the elliptic integral of the first kind:
C = C = 2*pi*(1e)[(agm(1,(1e)/(1+e))e*(1+e)*(d/dx)[agm(1,(1x)/(1+x))]x=e)]/((1+e)*agm(1,(1e)/(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,(1x)/(1+x)))/d
I use d at 1E24.



