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From: ins_akaa@jhunix.UUCP
Newsgroups: net.math
Subject: Re: Counter-Intuitive Sequences
Message-ID: <1779@jhunix.UUCP>
Date: Wed, 5-Feb-86 17:15:54 EST
Article-I.D.: jhunix.1779
Posted: Wed Feb  5 17:15:54 1986
Date-Received: Sun, 9-Feb-86 04:30:34 EST
References: <748@garfield.UUCP> <595@hou2c.UUCP>
Reply-To: ins_akaa@jhunix.ARPA (Ken Arromdee)
Organization: TARDIS Repairs, Inc.
Lines: 29

>> Consider the following sequence:
>> 		1, 2, 4, 8, 16,....
>> what is the next term ?	
>> Invariably the response is "32".
>> This however does not have to be the case and an alternate sequence arises
>> very naturally. Consider the sequence of n where n is the number of regions
>> the interior of a circle can be divided into using k lines where k starts
>> at 0. If you do that for the first five k you get the above sequence.
>> Suggestive isn't it ? However it turns out that for k=6 n=31 and the 
>> intuitive result falls flat on its face.
>> The "correct" answer (in this sense) is "31".
>>					Robert Janes
>It seems to me that the sequence breaks down when k=3 and n=7.
>Perhaps you meant to state the same problem for a sphere in 4-space
>using hyperplanes for lines.

No, the question should be where n is the same as above, k is 1,2,3, etc...,
and instead of k being the number of lines, k is the number of points on
the circle's edge; these points are all connected to each other and the
resulting lines divide the circle into the n regions.
-- 
"We are going to give a little something, a few little years more, to
socialism, because socialism is defunct.  It dies all by iself.  The bad thing
is that socialism, being a victim of its... Did I say socialism?" -Fidel Castro

Kenneth Arromdee
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