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From: david@cvl.UUCP (David Harwood)
Newsgroups: net.math
Subject: etc Euler formula
Message-ID: <555@cvl.UUCP>
Date: Mon, 17-Jun-85 14:20:38 EDT
Article-I.D.: cvl.555
Posted: Mon Jun 17 14:20:38 1985
Date-Received: Fri, 21-Jun-85 07:27:36 EDT
Distribution: net
Organization: Computer Vision Lab, U. of Maryland, College Park
Lines: 19

Re Euler formula:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	There is an intuitive constructive 'proof': Verify that the
formula is true for a trivial 'object'; supposing that any object may
be constructed from this with the addition of vertices, we observe that
if the added vertex splits an edge, then F + (V+1) = (E+1) + 2, else
if it splits a face, then (F+2) + (V+1) = (E+3).
	(Of course, I am ignoring the holomogy of these 'objects'.)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	Sorry about the typo for the last formula (F+2) + (V+1) =
(E+3) + 2.