Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site mmintl.UUCP Path: utzoo!linus!philabs!pwa-b!mmintl!franka From: franka@mmintl.UUCP (Frank Adams) Newsgroups: net.math Subject: Re: Pascal's Inverse Triangle Message-ID: <481@mmintl.UUCP> Date: Fri, 12-Jul-85 14:06:07 EDT Article-I.D.: mmintl.481 Posted: Fri Jul 12 14:06:07 1985 Date-Received: Mon, 15-Jul-85 00:40:24 EDT References: <2216@utcsstat.UUCP> <1677@saber.UUCP> <788@wanginst.UUCP> Reply-To: franka@mmintl.UUCP (Frank Adams) Organization: Multimate International, E. Hartford, CT Lines: 13 Summary: Center terms approach limit The center terms of the inverse triangle approach 1/sqrt(2). This can be seen by noting that, assuming that a limit x is approached, x = 1/(x + x). Algebra gives us the result stated. This isn't a formal proof, but it can be extended to one. Generally, each column converges to a distinct limit. If a column converges to a, the next column will converge to b = 1/(a + b), which when solved gives b = (-a + sqrt(a^2 + 4)) / 2. The first case is a = 1 and b = (-1 + sqrt(5))/2; generally we get a nested sequence of square roots. These results are quite straightforward. Off hand, I see no approach to getting any deeper results. This seems to be any interesting problem.