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*From*: John Denker <jsd@AV8N.COM>*Date*: Thu, 19 Aug 2004 01:30:30 -0400

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).

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