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From: kwmc@hou5d.UUCP
Newsgroups: net.math
Subject: Re: Everything you know is wrong  !
Message-ID: <604@hou5d.UUCP>
Date: Tue, 16-Aug-83 10:48:23 EDT
Article-I.D.: hou5d.604
Posted: Tue Aug 16 10:48:23 1983
Date-Received: Wed, 17-Aug-83 05:46:31 EDT
Organization: American Bell ED&D, Holmdel, NJ
Lines: 27

The following 'proof' appeared in net.math recently ....
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It is often said that a sphere has the smallest ratio of surface area to
volume among possible shapes. (See net.sf-lovers)
... Well, here's proof to the contrary!

For the sphere: ratio = ( 4*pi*r^2 ) / ( 4/3*pi*r^3 ) = 3/r

For the cylinder circumscribed on the sphere:

ratio = (height * circumference + 2 * base) / ( height * base ) =

        ( 2*r * 2*pi*r +  2 * pi*r^2 ) / (2*r * pi*r^2) = 3/r

The same as for the sphere!!!

                Lew Mammel, Jr. ihuxr!lew

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well it seems very tempting to believe it at first UNTIL you realise
that the ratio is dependant on 'r'. The shape of the cylinder could
be molded into a sphere ( of the same volume ) but in which the value
of 'r' is greater, and thus the ratio 3/r IS smaller as it should be.
Remember, for the same volume the 'r's are different, also 3/r is NOT
a constant it varies with the value of 'r'.

		Ken Cochran         hou5d!kwmc