Re: spherical geometry

[John Denker <jsd@AV8N.COM>]

David Bowman wrote:
> ... find a formula for the heading angle of the
> geodesic connecting 2 arbitrary fixed points (of known latitude
> and longitude) on the earth's surface as measured by an observer at
> one of those points.

Tee, hee.  That's another excellent problem.  In case
anybody hadn't noticed, both of David's spherical-geometry
problems are deeply physics-related, in the sense that
they depend on the intrinsic properties of the sphere.
This is in contrast to my "navigation puzzle" which mainly
depended on the vagaries of the coordinate system that we
arbitrarily imposed on the sphere (plus some weird
psychological impediments).

I hope I won't spoil the fun by hinting that this is
another poster-child for quaternions (aka unit bivectors
in Clifford Algebra).
  http://www.av8n.com/physics/rotations.htm

I've done variants of this problem
 a) using Euler angles, and
 b) using quaternions ...
and the Euler-angle approach was really ugly.  I've
never seen a non-ugly non-quaternion approach (but
I'd be interested in seeing one if it exists).