Bill Huber wrote:
> ... As the problem is phrased, there is no fast, simple procedure to get a
>practicably accurate answer.
You may have put your finger on a clue here. I bet Jacques' observation
about units was also a hint. Hendry Flavio is on target too. Stanley Ng
also gets a nod for thinking outside the box (but I don't think "right
in front of you" is the answer.) I don't believe it's in space, nor at
the north pole. I think you can get the answer with simple deduction. I
see two clues that eliminate everywhere else but one place.
I think the answer Vos Savant is looking for is how you might deduce the
location if you didn't have MapInfo (or Arc/Info, etc.) My guess is that
"where" may not necessarily be precise. We'll just have to wait until
she reveals the answer next Sunday.
But I'm surprised that with all the GIS mapping power held by this group
that few have tried the obvious: map the cities, and draw circular
buffers around them at the specified distances. The precise place is the
one place where all the circles intersect. Right? But it doesn't work in
MapInfo because the distances are large ...which reveals a subtle
"Gotcha" that is lurking in MapInfo and probably most other mapping
packages.
The "circular" buffers are not what you may think they are when they
would cross a pole. They compress, but this is not simple distortion due
to map projection. Load in the following table and create points on the
Lon/Lat columns with the "projection" set to Lat/Lon WGS 84. Then open
just the cities in a map window. Select Paris and create a 4658 mile
buffer around it. All the radii you can measure to the south are 4658
miles, but to the north they are all short, with due north being the
worst.
City Lon Lat Distance
Paris 2.432778 48.881389 4658
Moscow 37.938056 55.764167 5438
Tel Aviv 34.480000 32.050000 6681
Victoria (Hong Kong) 114.177222 22.274167 7878
Sydney 151.028056 -33.889722 8746
Johannesburg 28.004167 -26.178889 9092
Begs the question, "What's the work-around?" I've also asked MI Tech
Support.
- Bill Thoen
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