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Re: spherical geometry

David Bowman wrote:

I don't recognize your formulation. The integral expression I got
was substantially different. I don't know if you version boils down
to mine or not. I'm not about to try transforming your version in
various ways to see if it becomes my solution. When you get the
result in a closed form report back and then we'll compare results.

Okay, one last attempt. If I interchange the order of integration I now find:

area = s - 2 * integral from 0 to s/2 of {dY/sqrt(1+tan^2(A)*sin^2(Y)}

That integral almost looks like an elliptic integral, except for the
sign in front of the trig fn. It has the correct (trivial) limiting
values for A = 0 and 90 degrees. Carl
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5040