From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6165 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Illusion and Forthrightness in Wikipedia Date: Tue, 14 Sep 2010 09:54:07 -0700 Message-ID: References: <730oimakP9232S03.1284336675@web03.cms.usa.net> Reply-To: Vaughan Pratt 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 1284505944 6876 80.91.229.12 (14 Sep 2010 23:12:24 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 14 Sep 2010 23:12:24 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Wed Sep 15 01:12:23 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 1Ovefg-0000Rj-QM for gsmc-categories@m.gmane.org; Wed, 15 Sep 2010 01:12:17 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52774) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OveeY-0004lZ-M8; Tue, 14 Sep 2010 20:11:06 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OveeW-0002gP-0f for categories-list@mlist.mta.ca; Tue, 14 Sep 2010 20:11:04 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6165 Archived-At: On 9/13/2010 12:02 PM, Timothy Porter wrote: > 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! Granted a (3,2)-torus knot is also a trefoil knot topologically, but how does that help Fred? With the standard parametrization the plan view lacks the lumps bugging Fred but it has four crossings when Fred wants to keep it at three. What's the minimal modification to the standard parametrization x + iy = (cos(qt) + 2)exp(ipt) (sticking with z = sin(qt)) that gives a smooth trefoil with 3 crossings, for (p,q) either of (2,3) or (3,2)? I have this feeling there ought to be something slicker than (cos(qt) - 4)exp(ipt) - 3 exp(-it) with (p,q) = (2,3) (what I gave before, reflected about x+y = 0) but I can't see it. (I also don't know what -4 and -3 should generalize to for other than (2,3), but Fred hasn't asked for that yet.) Monoidal but not symmetric (trying to stay in scope here). Vaughan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]