From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.org!not-for-mail From: Emanuel Berg Newsgroups: gmane.emacs.help Subject: Re: distance from Easter Island to Chile Date: Mon, 21 Apr 2014 03:50:23 +0200 Organization: Aioe.org NNTP Server Message-ID: <87zjjfsb6o.fsf@nl106-137-194.student.uu.se> References: <87mwfguasr.fsf@nl106-137-194.student.uu.se> <87mwfg823s.fsf@nl106-137-194.student.uu.se> <8761m3tq89.fsf@nl106-137-194.student.uu.se> NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1398045326 6044 80.91.229.3 (21 Apr 2014 01:55:26 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 21 Apr 2014 01:55:26 +0000 (UTC) To: help-gnu-emacs@gnu.org Original-X-From: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane.org@gnu.org Mon Apr 21 03:55:21 2014 Return-path: Envelope-to: geh-help-gnu-emacs@m.gmane.org Original-Received: from lists.gnu.org ([208.118.235.17]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Wc3S2-0008FF-3Y for geh-help-gnu-emacs@m.gmane.org; Mon, 21 Apr 2014 03:55:18 +0200 Original-Received: from localhost ([::1]:47208 helo=lists.gnu.org) by lists.gnu.org with esmtp (Exim 4.71) (envelope-from ) id 1Wc3S1-0003I9-Jv for geh-help-gnu-emacs@m.gmane.org; Sun, 20 Apr 2014 21:55:17 -0400 Original-Path: usenet.stanford.edu!news.tele.dk!news.tele.dk!small.news.tele.dk!newsfeed.xs4all.nl!newsfeed3a.news.xs4all.nl!xs4all!news.stack.nl!aioe.org!.POSTED!not-for-mail Original-Newsgroups: gnu.emacs.help Original-Lines: 36 Original-NNTP-Posting-Host: VVbyYd/iFZoeWNmD9i++cQ.user.speranza.aioe.org Original-X-Complaints-To: abuse@aioe.org User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/24.3 (gnu/linux) X-Notice: Filtered by postfilter v. 0.8.2 Cancel-Lock: sha1:BCtbAXl5PuILLSQocSd72tWEYlQ= Mail-Copies-To: never Original-Xref: usenet.stanford.edu gnu.emacs.help:205015 X-BeenThere: help-gnu-emacs@gnu.org X-Mailman-Version: 2.1.14 Precedence: list List-Id: Users list for the GNU Emacs text editor List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane.org@gnu.org Original-Sender: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane.org@gnu.org Xref: news.gmane.org gmane.emacs.help:97280 Archived-At: Emanuel Berg writes: > This is so exact it *could* be used in those "school > essays" (in which I told not to use the Haversine > method) On the Wikipedia article on the Haversine, they mention the other formula as well - though it is a bit hard to make sense of... (What is "h"?) "When using these formulae, ensure that h does not exceed 1 due to a floating point error (d is only real for h from 0 to 1). h only approaches 1 for antipodal points (on opposite sides of the sphere) — in this region, relatively large numerical errors tend to arise in the formula when finite precision is used. Because d is then large (approaching πR, half the circumference) a small error is often not a major concern in this unusual case (although there are other great-circle distance formulas that avoid this problem). (The formula above is sometimes written in terms of the arctangent function, but this suffers from similar numerical problems near h = 1.) As described below, a similar formula can be written using cosines (sometimes called the spherical law of cosines, not to be confused with the law of cosines for plane geometry) instead of haversines, but if the two points are close together (e.g. a kilometer apart, on the Earth) you might end up with cos (d/R) = 0.99999999, leading to an inaccurate answer. Since the haversine formula uses sines it avoids that problem." -- underground experts united: http://user.it.uu.se/~embe8573