At 09:15 AM 4/24/01 -0600, Bill Thoen wrote:
>Say you come upon a sign that says the following:
> Paris 4658 miles
> <snip four lines>
> Johannesburg 9092 miles
>How would you determine where the sign is located?
...
>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.
Maybe we're all too familiar with the limitations of our GIS software :-)
OK, I broke down and solved the problem with Excel using a spherical model
of the earth. One good solution I can find (there are many good solutions,
but they are all close to each other) is near Elk City, Kansas, USA, at
longitude -95.833, latitude 37.350. This solution is likely within 20
miles of the truth (that's an approximate 95% confidence limit), is within
14 miles of agreeing with all the given distances, and errs in the
distances up to +-0.22%. This is as good as one would expect given that
the locations of the reference cities cannot be pinned down more precisely
than 10-20 miles (e.g., is the sign measuring from their centers or to
their borders?) and given the almost 1/300 flattening of the earth relative
to the spherical model.
Evidently using calipers (my earlier solution suggesting Salt Lake City) or
string (another poster's solution suggesting Wisconsin) on a small globe
are not very accurate methods. Kudos to Flavio who suggested the
"geographic center of the world:" Lebanon, KS, longitude -95.560, latitude
39.779, about 30 miles away.
Given Vos Savant's record (see the "Marilyn is Wrong!" site at
http://www.wiskit.com/marilyn/marilyn.html), it is possible the published
solution will devolve into some inane chestnut like "just ask the nearest
native," its techno equivalent, "pull a reading off your GPS unit" or the
full-time consultant's variant, "check your calendar: that will tell you
where you are today."
--Bill Huber
Consultant and sometime GIS aficionado
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