Re: spherical geometry

["Carl E. Mungan" <mungan@USNA.EDU>]

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
mailto:mungan@usna.edu       http://usna.edu/Users/physics/mungan/