🚀 go-pugleaf

In article <01bc0db2$216f18c0$b8ad11cf@lucasea-home>, "Eric Lucas" <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.
> 
> Pretty cool.  Simple (obvious) explanation:  as the two branches approach
> the asymtote, the distance between them gets infinitely small, leaving
> infinitely little space for the layer of paint.  Now, if you could come up
> with a paint that covers in an infinitely thin layer, you'd really have
> something.
> 
> 	Eric Lucas


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

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

Thanks,
Jeff