From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6155 Path: news.gmane.org!not-for-mail From: Timothy Porter Newsgroups: gmane.science.mathematics.categories Subject: Re: Illusion and Forthrightness in Wikipedia Date: Mon, 13 Sep 2010 20:02:41 +0100 Message-ID: References: <730oimakP9232S03.1284336675@web03.cms.usa.net> Reply-To: Timothy Porter NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1284466631 2691 80.91.229.12 (14 Sep 2010 12:17:11 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 14 Sep 2010 12:17:11 +0000 (UTC) Cc: categories To: "Fred E.J. Linton" Original-X-From: majordomo@mlist.mta.ca Tue Sep 14 14:17:09 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OvURh-0008Qb-4L for gsmc-categories@m.gmane.org; Tue, 14 Sep 2010 14:17:09 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58530) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OvUQR-0003em-K2; Tue, 14 Sep 2010 09:15:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OvUQP-0003AY-61 for categories-list@mlist.mta.ca; Tue, 14 Sep 2010 09:15:49 -0300 In-Reply-To: <730oimakP9232S03.1284336675@web03.cms.usa.net> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6155 Archived-At: The parametrisation given corresponds to the symmetric placing of the trefoil on a torus, the fact that you get the `lumps' is an artifact of that. The knot parametrisation can neatly `turned around' changing the role of p and q. That is also a trefoil! Have fun, Take care. Don't tie yourself in knots :-) Tim On 13/09/2010 01:11, Fred E.J. Linton wrote: > These somewhat off-topic remarks are at least almost as connected > with category theory as the study of knots is, as they have their > origin in my reliance on, and subsequent disillusionment with, the > Wikipedia site for basic information about a certain knot. > > The knot? -- the familiar trefoil knot, aka (2,3)-torus knot. > The offending Wikipedia page? -- http://en.wikipedia.org/wiki/Torus_knot . > The problem? > > A reader might be forgiven for expecting that when a page of mathematical > text offers a parametrization, in the form > > x = (2 + cos((q phi)/p))(cos(phi)) , > y = (2 + cos((q phi)/p))(sin(phi)) , > z = sin((q phi)/p) , > > of each (p,q)-torus knot, and then offers an illustration dubbed > (2,3)-torus knot, that said illustration might have been produced > by means of the p=2, q=3 instance of the parametrization given. > ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]