Tim Daneliuk <[EMAIL PROTECTED]> writes:
> Huh? When traversing along the surface of the earth, it's curvature
> is relevant in computing total distance. An airplane flies more-or-less
> in a straight line above that curvature. For sufficiently long airplane
> routes (where the ascent/descent distance is trivial compared to the
> overall horizontal distance traversed), a straight line path shorter
> than the over-earth path is possible. That's why I specified the
> desire to compute both path lengths. Where's the humor?
It's just not clear what you meant:
A) The shortest path between two points on a curved surface is
called a geodesic and is the most meaningful definition of
"straight line" on a curved surface. The geodesic on a sphere is
sometimes called a "great circle".
B) By a straight line you could also mean the straight line through
the 3-dimensional Earth connecting the two points on the surface.
So the straight line from the US to China would go through the
center of the earth.
C) Some people seem to think "straight line" means the path you'd
follow if you took a paper map, drew a straight line on it with a
ruler, and followed that path. But that path itself would depend
on the map projection and is generally not a geodesic, and neither
is it straight when you follow it in 3-space.
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