Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site harvard.ARPA Path: utzoo!linus!philabs!cmcl2!harvard!greg From: greg@harvard.ARPA (Greg) Newsgroups: net.puzzle,net.math Subject: More interesting than the polar bear problem Message-ID: <475@harvard.ARPA> Date: Sun, 3-Nov-85 21:41:47 EST Article-I.D.: harvard.475 Posted: Sun Nov 3 21:41:47 1985 Date-Received: Tue, 5-Nov-85 21:08:18 EST Distribution: net Organization: Harvard Lines: 15 Xref: linus net.puzzle:1060 net.math:2113 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. If you know too much math, please don't post the spoiler right away. -- gregregreg