Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site faron.UUCP Path: utzoo!linus!faron!bs 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 References: <855@whuxlm.UUCP> <593@hou2c.UUCP> Organization: The MITRE Coporation, Bedford, MA Lines: 29 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)