🚀 go-pugleaf

>>>>> "JY" == Jeffery Young <jsy@media04.cray.com> writes:

 JY> In article <01bc0db2$216f18c0$b8ad11cf@lucasea-home>, "Eric Lucas"
 JY> <lucas@superlink.net> writes:

 >> Louis Hom <lhom@nature.berkeley.edu> wrote in article
 >> <5cmpbo$nds@agate.berkeley.edu>...
 >> > 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.

 JY> But if you could fill it up with a finite amount of paint, wouldn't the
 JY> "interior surface area" be painted.  And isn't the "interior" SA equal
 JY> to the "exterior" SA?

 JY> I know the math, but the physical explanation doesn't sit with me.

It depends how you paint your surface. If you allow the paint to have any
arbitrarily small thickness, you need a finite amount of paint to cover the
surface (miracle paint!)

But I think that the original poster assumed the thickness of the paint had
to be a constant on the external surface.

Eric Daniel