From: utzoo!decvax!ucbvax!CAD:tektronix!zehntel!zinfandel!berry
Newsgroups: net.physics
Title: Re: A Mathematical Question - (nf)
Article-I.D.: zehntel.854
Posted: Wed Mar 16 01:23:51 1983
Received: Wed Mar 23 01:37:02 1983

#R:tekecs:-61200:zinfandel:9600004:000:619
zinfandel!berry    Mar 14 13:05:00 1983

If you take a circular lake with circumference 1, and 'deform' the shore by
filling in, How long can you make the shore?  The answer is, there is no limit.
fill in so that the shoreline follows a mapping of any space-filling curve 
(Peano curves spring to mind) and there you are:  Infinite shoreline and finite 
area.

I am reminded ofwhat you get if you rotate a canonical hyperbola about the
x-axis: a sort of cone thing with finite volume but infinite surface area.
Sou you can fill it with paint but never wet the entire surface!

Berry Kercheval		Zehntel Inc.	(decvax!sytek!zehntel!zinfandel!berry)
(415)932-6900