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From: ken@turtlevax.UUCP (Ken Turkowski)
Newsgroups: net.puzzle,net.math
Subject: Re: Polar Bear Problem Sequel
Message-ID: <934@turtlevax.UUCP>
Date: Thu, 24-Oct-85 03:56:25 EDT
Article-I.D.: turtleva.934
Posted: Thu Oct 24 03:56:25 1985
Date-Received: Sat, 26-Oct-85 04:03:34 EDT
References: <361@proper.UUCP> <855@whuxlm.UUCP>
Reply-To: ken@turtlevax.UUCP (Ken Turkowski)
Distribution: net
Organization: CADLINC-->CIMLINC, Inc. @ Menlo Park, CA
Lines: 26
Xref: watmath net.puzzle:1078 net.math:2426

In article <855@whuxlm.UUCP> dim@whuxlm.UUCP (McCooey David I) writes:
>	Where on the earth can one walk 1 mile south, 1 mile west, 1 mile
>	north, AND 1 mile east, and end up at the starting point?
>
>If you think you have a solution, there should be more...  It would be nice
>if some mathematically inclined readers could contribute exact and complete
>solutions (to both sequels).

Once you have an idea that the problem takes place on a sperical geometry,
the answer is easy:

	1/2 mile north of the south pole

In a half mile you reach the pole; continue in the same direction and
follow the rest of the steps, and you trace out a bow-tie path.

However, several philosophical questions the occurs:

After you reach the south pole in the first step, are you still going south?

At the south pole, is there any east, west or south?
All directions from there seem to be north.
-- 
Ken Turkowski @ (CADLINC --> CIMLINC), Menlo Park, CA
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