From: utzoo!decvax!harpo!npoiv!hou5f!hou5b!hou5c!hou5e!mat
Newsgroups: net.math
Title: Re: Squares - (nf)
Article-I.D.: hou5e.218
Posted: Thu Jan 27 12:19:40 1983
Received: Sun Jan 30 06:05:20 1983
References: uiucdcs.1389

Question is about measuring the length of a diagonal by zigzagging along
lines parallel to the co-ordinate system ( sides of a square ).  For some
really good stuff along these lines, read B. Mandelbrot's book ``Fractals,
Form, Chance, and Dimension''.  But a quick description of what is happening:
You are right in saying that the path length is always 2; it IS always 2.
You are never actually measuring the diagonal.  You are measuring a path
which approximates the diagonal.  The approximations are continually
improving in their mean-square error, but their path lengths remain the
same.
					-More than one way to measure the
					-goodness of fit of a cat skin.
						Mark Terribile