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From: dlnash@ut-ngp.UTEXAS (Donald L. Nash)
Newsgroups: net.bizarre
Subject: Bizarre mathematics
Message-ID: <2452@ut-ngp.UTEXAS>
Date: Thu, 3-Oct-85 10:59:27 EDT
Article-I.D.: ut-ngp.2452
Posted: Thu Oct  3 10:59:27 1985
Date-Received: Sun, 6-Oct-85 05:04:45 EDT
Distribution: net
Organization: UTexas Computation Center, Austin, Texas
Lines: 20

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Here's a bit of bizarre math stuff which may warp your mind.  Imagine
if you will, the graph of the function y = 1/x from x=1 to x=infinity.
I'm sure that everyone out there is smart enough to draw this picture
mentally.  Now rotate this graph about the x-axis.  You get a long,
skinny funnel of infinite length.  If you work out the integral which
determines the surface area of the funnel, you will find that it also
is infinite.  Now comes the bizarre part.  If you work out the integral
which determines the volume enclosed by that funnel, you find that it
is not infinite, but that it is pi cubic units!  Think of the significance
of that:  You can fill the funnel with paint, but you can't paint its
surface, because you will never have enough paint!

Bizarre....

					Don Nash

UUCP:  ...!{ihnp4,allegra,seismo!ut-sally}!ut-ngp!dlnash
APRA:  dlnash@ngp.UTEXAS.EDU


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