At 03:27 PM 4/23/01 -0400, KH wrote:
>If you had the proper projection on a flat map, you could do it with radii.
>You would need the azimuthal equidistant projection. This projection
>horribly distorts the shapes & sizes of the land masses, but the straight
>line distances are true.
Nope. Only selected distances will be true (from the center of the
projection). All other distances will be miserably distorted. This is
guaranteed by the nonzero Gaussian curvature of the earth.
>Anyone figure it out yet? I'm inching to know.
Nice play on words!
>Based on the author's geographic bias (as well as mine), and looking at some
>distances on my globe (with my wooden ruler and without actually drawing on
>it) I would guess it is somewhere in the central US, somewhere in the
>triangle between Dallas, Denver, and Chicago.
Close. I think Salt Lake City is closer. (I used a globe and
compasses--the dividing kind.) The answer depends on your model of the
earth's surface and on how the distances are measured. The best approach
to getting a good answer is probably generalized least squares, calculating
all distances based on a good ellipsoidal model of the earth (no projection
involved). That's standard surveying stuff. You still have to incorporate
assumptions about the method of measuring those distances.
Think I'm being picky? My son's summer camp has a signpost just like Vos
Savant's puzzle, because it attracts campers and counselors from all over
the world. The camp is in the middle of the woods surrounded by zillions
of other camps, summer homes, etc. You might search for years to find that
signpost even if I told you where it was to within 20 kilometers (that's
one eighth of a million hectares to search in)--which represents one part
in 1,000 accuracy in modeling the shape and size of the earth's
surface. As the problem is phrased, there is no fast, simple procedure to
get a practicably accurate answer.
Bill Huber
Quantitative Decisions
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