Hmm, ok, you got me
But still, the geoid approximates a surface of equal gravitational potential, and therefore differs from the earth's topographic structure... Or shall I say earth is potato shaped ;-) This is a physical model. Mathematically you will still end up with the ellipsoid...
ch.....:
Good point, going back to the spherical model with the same situation (both points on exact opposite sides) you will end up with an infinite number of "shortest" distance between the two...
So for some layouts you will get multiple solutions, nevertheless if you go to smaller scale I think there will only be one, since the circular circumference of the ellipsoid largens with decreasing latitude. Probably somebody should just do the Math and show us
Back to topic: Agonic line: Variation = 0