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From: jimmy@rlvd.UUCP (Jimmy Aitken)
Newsgroups: net.puzzle,net.math
Subject: Wire problem - minimum radius of thin stands in a thick strand
Message-ID: <572@rlvd.UUCP>
Date: Fri, 21-Jun-85 00:48:45 EDT
Article-I.D.: rlvd.572
Posted: Fri Jun 21 00:48:45 1985
Date-Received: Mon, 24-Jun-85 02:34:01 EDT
Reply-To: ian@rlvg.UUCP (Ian Gunn)
Organization: Rutherford Appleton Laboratories, Atlas Buildings, U.K.
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Xref: watmath net.puzzle:937 net.math:2091
Xpath: warwick ubu


   An interesting problem was encountered by a friend recently. It involves
a number (n) of optical fibres of the same size contained within a larger
wire. The problem is as follows: Find the minimum radius of the larger wire
in terms of the radius of the n fibres.
   The problem is essentially that of arranging n circles of radius r inside
a larger circle of radius R, such that R is at a minimum. This problem is not
trivial. Ideally, a general equation should be derived for n circles, or 
alternatively a proof that no such equation is possible. As a test, find the
result for the case where n = 10.
   Any proofs, ideas, comments or suggestions would be appreciated.

             Ian Gunn. (...mcvax!ukc!rlvd!rlvg!ian)

-- 
Jimmy Aitken,	..!mcvax!ukc!rlvd!jimmy
		Rutherford Appleton Labs, Didcot, OXON, U.K.
		+44 235 446555