Re: Re[2]: Info and a Question

Bret Taylor (bret@IAG.NET)
Tue, 20 Aug 1996 19:10:00 EDT

At 11:09 PM 8/19/96 EDT, you wrote:
>>
>>Thanks for all your work. Your question is one I give to my students
>>annually with the standard question, "This 'can' has a finite volume but an
>>infinite surface area so that means you could fill it up with paint but
>>never be able to paint the outside. How can you explain this paradox?"
>>
>>In ten years, I have had one student give a clear expanation. How about the
>>rest of y'all?
>
>
>So, what was your student's explanation???
>
>Brian
>
>P.S. thanks to all who responded - I already have some interesting new
>ideas to ponder - I especially like the fractal connection. BS
>
Sorry, I answered late at night. The answer my student gave has been
mentioned elsewhere in the replies. But, here it is again.

One student said, almost immediately after hearing this question, "In order
for you to fill the can with paint, the paint must be infinitely runny ot
else it would eventually get clogged in the bottom of the can (at the
molecular or atomic level). If you assume the pain isa infinitely runny,
then it can be spread infinitely thin so any finite amount of paint could
cover an infinite amount of area. Therefore it would take only a drop to
paint the can."

Clearly, I shortened his response, but he did same the same thing in about
twice as many words. I was impressed.
Bret Taylor Lake-Sumter Community College Leesburg FL

"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden

John 3: 3 3