Paul Rubin wrote:
> 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.
Yeah, after rereading my original question, I realize that it could
be read that way. My Bad. What I had in mind was this:
A ------------------------------
E ---------------------------
/ \
/ \
Where A was an airplane's line of flight between endponts and E was the
great circle (geodesic) distance over ground. It seemed to me that if
the ascent/descent distance for A is very small compared to the length of A,
the flight distance would be shorter than the over-ground distance. But,
as Rocco points out in another response, this is not so.
I stand (well, sit, actually) corrected!
Many thanks to all of you who took the time to unscramble my English and
lack of geometric understanding...
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Tim Daneliuk [EMAIL PROTECTED]
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