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?
Mike
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