Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83 (MC840302); site unido.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!philabs!cmcl2!seismo!mcvax!unido!ab From: ab@unido.UUCP (Andreas Bormann) Newsgroups: net.puzzle,net.math Subject: Re: More interesting than the polar bear problem Message-ID: <433@unido.UUCP> Date: Sat, 9-Nov-85 07:58:37 EST Article-I.D.: unido.433 Posted: Sat Nov 9 07:58:37 1985 Date-Received: Mon, 11-Nov-85 06:59:49 EST Organization: University of Dortmund Lines: 59 Xref: watmath net.puzzle:1161 net.math:2505 >/***** unido:net.puzzle / harvard!greg / 5:41 am Nov 4, 1985*/ >Subject: More interesting than the polar bear problem > >Johnny the adventurous flyer flies at constant altitude over the Pacific. >He periodically turns left by one degree. After a while Johnny discovers >that his plane is at the same position *and orientation* as when he started. >Therefore he lands. He deduces that the path he took encloses 140 million/9*pi >square kilometers. Now for some questions: > >1) How many left turns did Johnny make? >2) What was the approximate air distance between two consecutive turns? > >You may assume that the Earth is a perfect sphere with a circumference of >exactly 40,000 kilometers. After my calculations he made 352 left turns and the approximate air distance between two turning points was 22.237 kilometers. I assumed that Johnny flew an exact polygon like this: TAKEOFF 1. | +--==*====runway / \ 2.+ + 352. | | 3.+ + 351. \ / +--- 4. But when he reached his starting point he had to make one more 1deg-turn to get into the same orientation as the runway. So my solution might not be correct. Maybe there are an infinite set of solutions looking this way: TAKEOFF last turning point 1. | | +--==*=+==runway / \ 2.+ + n-1. | | 3.+ + n-2. \ / +--- 4. Possibly the number of left turns is 353 in any case... Andreas Bormann University of Dortmund [UniDo] West Germany Uucp: ab@unido.uucp Path: {USA}!ihnp4!seismo!mcvax!unido!ab {Europe}!{cernvax,diku,enea,ircam,mcvax,prlb2,tuvie,ukc}!unido!ab Bitnet: ab@ddoinf6.bitnet \ Missiles: -=>-->-*> N 51 29' 05" E 07 24' 42" /