>>13720163Before this thread shuts out, here's my idea...
The spherical triangle is made from three great
circles (planes that slice the sphere through the
origin). It is possible to get three different
spherical equations describing the circles as
well as the three intersection points. Then you
can say the domain is a spherical triangle
bounded by those equations. Further, the span
of the triangle in terms of theta (x-y plane angle)
and phi (z-axis zenith angle) can be found as
well from the intersections.
The usual affair of integrating in spherical
coordinates is when you're finding the volume
of something (you'll use the triple integral).
However, if it's like integrating a mountain
range (the surface) over a region on a sphere
(the domain), it'll be the triple integral of the
function f(x)=1 on the spherical volume element
(see pic related).
As for more info, I would recommend the math
bible "Handbook of Mathematics, 5 ed." and
a good multivariable calculus book. I hope I
answered it for you.
