Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83 based; site hou2c.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxt!houxm!hou2c!rvdb 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 References: <855@whuxlm.UUCP> <593@hou2c.UUCP>, <373@faron.UUCP> Organization: AT&T Bell Labs, Holmdel NJ Lines: 35 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.)