🚀 go-pugleaf

William R. Penrose (wpenrose@interaccess.com) wrote:
: In article <01bc0db2$216f18c0$b8ad11cf@lucasea-home> "Eric Lucas" <lucas@superlink.net> writes:
: >From: "Eric Lucas" <lucas@superlink.net>
: >Subject: Re: DAMN, THAT'S COOL! (Help a fellow geek)
: >Date: 29 Jan 1997 07:01:09 GMT

: >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.

: But this result doesn't depend on the dimensions of atoms or anything,  It is 
: one of those weird things that calculus does, when you calculate surfaces and 
: volumes of revolution.  Even your infinitely thin paint wouldn't cover it.

	Sure it would.  'Infinitely thin paint' can cover an infinite 
surface area.  Whenever you run out, just scrape what you've painted so 
it's half as thin, thus doubling your supply.
	The inside of the shape described would _already_ be painted if 
full of paint.. by definition.

--
Nathaniel Tagg		Physics grad student		University of Guelph
	"The chances of a neutrino actually hitting something as it 
travels through all this howling emptiness are roughly comparable to that 
of dropping a ball bearing at random from a cruising 747 and hitting, 
say, an egg sandwich."		-- Douglas Adams, _Mostly_Harmless_