From: utzoo!decvax!harpo!ihnp4!ixn5c!inuxc!pur-ee!uiucdcs!ardis
Newsgroups: net.math
Title: Re: Squares - (nf)
Article-I.D.: uiucdcs.1397
Posted: Thu Jan 27 09:30:42 1983
Received: Sun Jan 30 10:23:17 1983

#R:uiucdcs:28200003:uiucdcs:28200004:000:493
uiucdcs!ardis    Jan 27 07:27:00 1983

	The "limit diagram" you describe is not a good approximation
(or even a better approximation than the first one) for the diagonal.
Consider the sides to be vectors.  You always measure vectors that are
either horizontal or vertical.  So, you will always compute the same
sum.  In other words, you are factoring the diagonal vector into horizontal
and vertical components.  The limiting case of this still factors the
vector, it just does so with an infinite number of segments of the vector.