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From: rvdb@hou2c.UUCP (R.VANDERBEI)
Newsgroups: net.puzzle,net.math
Subject: Re: Polar Bear Problem Sequel
Message-ID: <594@hou2c.UUCP>
Date: Thu, 31-Oct-85 20:55:05 EST
Article-I.D.: hou2c.594
Posted: Thu Oct 31 20:55:05 1985
Date-Received: Sat, 2-Nov-85 05:37:07 EST
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Organization: AT&T Bell Labs, Holmdel NJ
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Xref: watmath net.puzzle:1121 net.math:2451

>> 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.

... but real close!

>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)

You changed my answer as well as the definition of great-circle! (The
only great-circle running E-W is the equator.)