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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
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Organization: Harvard
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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