🚀 go-pugleaf

In article <5cmpbo$nds@agate.berkeley.edu>,
Louis Hom <lhom@nature.berkeley.edu> wrote:
>So, I'm trying to collect posters' favorite Things in Math & Science.
>	For example, one of my favorite things is the solid that you get
>when you rotate y=1/(log x) about the x-axis -- it has finite volume but an
>infinite surface.  So if you had a container that shape, you could fill it
>up with some finite quantity of paint, but it would never be enough to
>actually paint the surface of the thing.

	Or, a cylindrical can whose base is the Koch snowflake would
do the trick, and would actually fit on a shelf.

	I think it would be more mind-boggling to point out that
the can holds a finite amount of paint, but it takes an infinite amount
of paint to paint THE INSIDE.  Aren't you technically painting the
inside when you fill it up with that finite amount of paint???

	Of course, this problem stems from the abstraction that the 
layer of paint you lay down on a surface is infinitely thin, which 
isn't true in reality, and serves as an amusing reminder that areas
and volumes are not comparable mathematically the way they are in 
the real world.

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