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From: bs@faron.UUCP (Robert D. Silverman)
Newsgroups: net.puzzle,net.math
Subject: Re: Polar Bear Problem Sequel
Message-ID: <373@faron.UUCP>
Date: Tue, 29-Oct-85 11:52:58 EST
Article-I.D.: faron.373
Posted: Tue Oct 29 11:52:58 1985
Date-Received: Thu, 31-Oct-85 23:32:19 EST
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Organization: The MITRE Coporation, Bedford, MA
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Xref: linus net.puzzle:1018 net.math:2078

> it's almost true everywhere - almost.

Do you really mean 'it's almost true everywhere' or do you mean 
'it's true almost everywhere'  ?

I hate to clue everyone in but:

IF your answer means that the Borel measure of the set of starting points
is 1 you're wrong. It is zero. The set of starting points is that set
such that the radius of a great-circle running E-W is the same as that
of another great-circle running E-W which is 1 mile south. The only place
this happens is the great-circle 1/2 mile north of the equator. Moving
1 mile south places you on the great-circle 1/2 mile south of the equator
and this obviously has the same radius as the original circle.
Thus, of the entire set of great circles (cardinality C) only 1 satisfies
the conditions (i.e. measure is zero)

Postings which claim the circles 1 mile north of the equator are solutions
are wrong. This is easy to see because lines of longitude are closer
together 1 mile north of the equator than they are at the equator. Thus,
if you travel 1 mile south to the equator, 1 mile west, and then 1 mile
north you will be closer than 1 mile to your starting point.
 
At latitude 90-theta, an East-West great circle has radius 2 PI r sin(theta)
where r is the Earth's radius. Why can't people do simple high school geometry?
 
Thus, it's FALSE almost everywhere.

Bob Silverman   (they call me Mr. 9)