Sorted! WFL On 1/3/11, Eugene Salamin <gene_salamin@yahoo.com> wrote:
From: Fred lunnon <fred.lunnon@gmail.com>
To: math-fun <math-fun@mailman.xmission.com> Sent: Mon, January 3, 2011 10:06:44 AM Subject: Re: [math-fun] Cylinder puzzle
Very neat argument --- but I still don't believe it.
Why should it not work for a single cylinder?
Just to placate those who haven't heard of principal values, or get distracted by minor matters like compactness (?), I'll give this large finite length and assert that the ratio S/V approaches 2 rather than 3, cones notwithstanding. ________________________________ For a single cylinder of finite length, my proof applies to the volume of the cylinder contained within the solid angle subtended at the origin by the lateral surface. This is 2/3 of the total volume of the cylinder. The remaining 1/3 of the volume lies within the solid angle subtended by the end caps. Requiring the intersection of more than one cylinder not only renders the object compact, but also eliminates the end caps.
-- Gene
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