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.