>-----Original Message-----
>From: [EMAIL PROTECTED]
>[mailto:[EMAIL PROTECTED]]On Behalf Of Mike
>Bandsmer
>Sent: Wednesday, February 09, 2000 7:32 PM
>To: [EMAIL PROTECTED]
>Subject: Re: Mersenne: pi
>
>
>At 02:31 AM 2/9/00 -0500, gav wrote:
>> I think my favorite counterexample to arguments like this is Gabriel's
>>Horn. Take the function 1/x, and revolve it around the x-axis. You now
>>have something that looks very similar to a trumpet's bell. Now, find the
>>volume of this from 0 to infinity. It has a finite volume. However, it
>>has an infinite surface area.
>
>I have a little trouble conceptualizing what would happen if you fill this
>horn with paint. If you completely fill this horn with paint (a finite
>volume), the inner surface of the horn should be completely covered with
>paint, right? But the inner surface of the horn has infinite area, so
>wouldn't it take an infinite amount of paint to paint it? Where is my
>intuition going wrong?
It would take infinite area of an infinitesimally thin layer of paint, which
would have no volume due to its thinness. Since paint can't be infinitely
thin,
this also means you can't actually fill the object with paint, because there
will be volume in areas into which paint molecules can't fit.
Mike
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