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From: lew@ihuxr.UUCP
Newsgroups: net.math
Subject: followup to "Everything you know is wrong!"
Message-ID: <563@ihuxr.UUCP>
Date: Wed, 17-Aug-83 17:34:02 EDT
Article-I.D.: ihuxr.563
Posted: Wed Aug 17 17:34:02 1983
Date-Received: Thu, 18-Aug-83 02:20:45 EDT
Organization: BTL Naperville, Il.
Lines: 19

Perhaps not everyone will believe me when I say that my "proof" was
given tongue-in-cheek. Anyway, many people easily saw the flaw in it.

Takashi Iwasawa pointed out that every polyhedron circumscribed on
a sphere (faces tangent to the sphere) has a surface/volume ratio
of 3/r. You can see this by dividing the enclosed volume into
pyramids with the faces as bases, and radii of the sphere as heights.
the 3/r comes from the volume of a pyramid being B*h/3.

Steve Sommars wondered about the generalization of the minimal
surface property of a sphere to N dimensions. Actually, I don't
know how you'd prove it in 3 dimensions, for that matter. There
must be a clever way.

The 3/r S/V ratio of the circumscribed polyhedra seems to provide a way,
but this only shows that the sphere has the minimum surface area among a
restricted class of shapes (of a given volume!)

		Lew Mammel, Jr. ihuxr!lew