🚀 go-pugleaf

Louis Hom 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.  

Yep.

> 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.

Whoa!  If I have a finite quantity of "mathematical paint" which
has zero thickness, you're saying it will only cover a FINITE area??
Please provide a proof of this rather remarkable statement.

If, on the other hand, you're talking about "real" paint, then
show me a PHYSICAL surface with the properties you mention which
cannot be covered with Sears Latex (such an argument gets messy, 
not only from all the spilled paint, but because you have to make
certain assumptions about the molecular dynamics of paint, the 
notion of packing fraction of dissimilar molecules and aggregates,
etc. etc. ).  

I'd love to see a proof of this assertion using either "mathematical
paint" or (hehehe) Sears Latex. I can't wait to see it.

> My interest in starting this collection grew out of a desire to
> write something about the Math/Science Aesthetic and realizing that I
> didn't have a lot of interesting examples readily at hand.

Of course, there's a  infinite number of surfaces with the "property"
you mention.  Rotate y = -exp(-ax*x) (x over all space) about the 
y-axis and fill it with paint (Sears or Mathematical).  Vary the 
"a" from (0,inf) to get your infinite number of surfaces.

> I don't know if  I will ever write such an essay, but I think 
> it would be fun to gather some examples at least.  Maybe I'll archive 
>them on my web page or something. 
>         Anyway, thanks for reading, and thanks for helping out.
> --
> _______________________________________________________________________________
> Lou Hom >K '93
> lhom@nature.berkeley.edu
> http://www.ocf.berkeley.edu/~lhom

Larks