Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84 + RN 4.3; site inset.UUCP Path: utzoo!linus!philabs!cmcl2!seismo!mcvax!ukc!icdoc!ist!inset!jmc From: jmc@inset.UUCP (John Collins) Newsgroups: net.sources Subject: Re: Solving Pi Message-ID: <652@inset.UUCP> Date: Thu, 8-Aug-85 22:46:47 EDT Article-I.D.: inset.652 Posted: Thu Aug 8 22:46:47 1985 Date-Received: Mon, 12-Aug-85 08:06:45 EDT References: <187@ski.UUCP> <11307@watnot.UUCP> Reply-To: jmc@inset.UUCP (John Collins) Organization: The Instruction Set Ltd., London, UK. Lines: 29 Xpath: icdoc ivax In article <11307@watnot.UUCP> cagordon@watnot.UUCP (Chris A. Gordon) writes: >Here is a more simple sum-evaluation of pi (thought I don't know if it will >work with the original program): > > oo > ---- k-1 > | | \ (-1) > pi = +--+ > ---------- > | / 2k-1 > ---- > k=1 The convergence of this series is *TERRIBLE* You'd have to evaluate many thousands of terms to get anywhere (you are still messing around with the third decimal place after 500 terms!). Moreover the alternation of the signs makes life even more difficult - each term cancels most of the work of the previous term. Use of Aitken acceleration has a dramatic improvement though - but the resulting series can be shown to be equivalent to the series for 6 * arcsin(.5) which was given in a previous message. -- John M Collins ....mcvax!ist!inset!jmc Phone: +44 727 57267 Snail Mail: 47 Cedarwood Drive, St Albans, Herts, AL4 0DN, England.