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Re: New Navigation Problem Solutions & Hint 1

On 23-Aug-04, at 2:00 AM, Bill Powell wrote, inter alia:


"Thinking outside the box" requires conscious examination of your
mental logic to avoid self-imposed presumptions and to take full
advantage of ambiguities in the problem statement. Thus I begin by
discussing the problem’s travel instructions to expose some common
presumptions, or at least to clearly state my interpretation of the
problem’s actual requirements.

Each latitude circle defines a plane. For me, "going south" means
crossing latitude circle planes, while remaining in only one longitude
circle plane, and always going across latitude planes in the direction
from north towards south. Thus, going south does not confine one to
traveling on a great circle path on the surface of an assumed
spherical Earth. (If you think it does, then I have no new solutions
to offer you.) For example, I think an airplane can "go south" even if
it is continuously changing altitude during the flight. Etc. for "go
east" and "go north."


It is my feeling that "thinking outside the box" should not lead one to
violate geographic conventions. At least, surfaces of constant latitude
are cones with apices at Earth's center. At best, surfaces of constant
latitude are cones locally perpendicular to the geoid. Departing from
conventions that are well understood is scarcely the same thing as
overcoming "common presumptions".