Dear Fellow Biomechanicians,

Can anyone help with this problem? I need to calculate
the surface area of an ellipsoid whose defining equation is:

2 2 2
X Y Z
---- + ---- + ---- = 1
2 2 2
a b c

I need the solution for the case where a, b, and c are all
different, and for the special case where b = c. I also need to
be able to calculate the surface area for a sector of an
ellipsoid (i.e., a hemi-ellipsoid or less, but symmetric about
one of the axes).

I have seen a paper where both of these solutions are given
(and they are complex), yet when I try to derive them myself, I
get different answers, even when using a symbolic algebra
program. I would appreciate seeing a total derivation.

In my first try, I got the area equal to:

4 2 2 2
--- * pi * (a + b + c )
3

This seems intuitively obvious (i.e., if a = b = c you get
the correct equation for the surface area of a sphere) but
apparently is NOT correct. I found my error that led to this
solution, but still have had little luck getting the correct