---- START NEW MESSAGE --- Received: from cherry.ease.lsoft.com [209.119.0.109] by dpmail10.doteasy.com with ESMTP (SMTPD32-8.05) id A6EDC74020A; Wed, 28 Jan 2004 08:44:29 -0800 Received: from PEAR.EASE.LSOFT.COM (209.119.0.19) by cherry.ease.lsoft.com (LSMTP for Digital Unix v1.1b) with SMTP id <4.00CC1172@cherry.ease.lsoft.com>; Wed, 28 Jan 2004 11:44:16 -0500 Received: from MITVMA.MIT.EDU by MITVMA.MIT.EDU (LISTSERV-TCP/IP release 1.8e) with spool id 2513 for PICLIST@MITVMA.MIT.EDU; Wed, 28 Jan 2004 11:44:08 -0500 Received: from MITVMA (NJE origin SMTP@MITVMA) by MITVMA.MIT.EDU (LMail V1.2d/1.8d) with BSMTP id 6686; Wed, 28 Jan 2004 11:42:54 -0500 Received: from rs25s9.datacenter.cha.cantv.net [200.44.33.10] by mitvma.mit.edu (IBM VM SMTP Level 430) via TCP with ESMTP ; Wed, 28 Jan 2004 11:42:53 EST X-Comment: mitvma.mit.edu: Mail was sent by rs25s9.datacenter.cha.cantv.net Received: from carlos98 (puertoordaz-ras4-157.ras.poz.cantv.net [161.196.166.158]) by rs25s9.datacenter.cha.cantv.net (8.12.9/8.12.6/3.0) with SMTP id i0SGgpM3026938 for ; Wed, 28 Jan 2004 12:42:54 -0400 X-Matched-Lists: [] References: <001301c3e53f$ad6ce0c0$0100a8c0@carlos98> <029c01c3e550$705244d0$ed00a8c0@blackbox> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Message-ID: <001f01c3e5bd$ad9971c0$0100a8c0@carlos98> Date: Wed, 28 Jan 2004 12:42:03 -0400 Reply-To: pic microcontroller discussion list Sender: pic microcontroller discussion list From: Carlos Marcano Subject: Re: [OT:] Curves intersection To: PICLIST@MITVMA.MIT.EDU Precedence: list X-RCPT-TO: Status: U X-UIDL: 371856132 From: "Eugene Rosenzweig" > I do not know how to solve 1-x^2-sin(x)=0 without approximation. > However, I have looked up on Google the Taylor series expansion for sin(x), > which is sin(x) = x - x^3/3! + x^5/5! - x^7/7! + .... > The equation for y=1-x^2 is upside-down quadratic intersecting at y=1 and > x=1/-1 so, from visual inspection, sin(x) intersects it twice, once on > positive x, between 0 and 1 and once on negative, somewhere not too far from > x=-1. > I took the first two terms of sin(x) series, substituted into the equality > and ended up with cubic: > 1-x^2-x+x^3/6=0 > I cannot even remember how to solve cubics so I found this online solver > http://www.1728.com/cubic.htm and three values for x. > The first one doesn't make sense but the other two are the ones we need: > x=0.63715 > x=-1.3937 > The positive x solution is very close but the negative one is not, due to > approximation of sin(x). Adding terms to sin(x) approximation would improve > that but I cannot find an online calculator to solve a quintic :-) > > I have also used a shareware plotting program graphmatica and that had a > tool for finding intersections and came up with very similar results. Good usefull tips! Regards, *Carlos* --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.572 / Virus Database: 362 - Release Date: 27/01/04 -- http://www.piclist.com hint: The list server can filter out subtopics (like ads or off topics) for you. See http://www.piclist.com/#topics .