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