source file: mills2.txt Date: Tue, 14 Jan 1997 09:35:30 -0800 Subject: RE: CPS From: PAULE Kami Rousseau wrote, >This means that the CPS are a generalisation of the Euler Fokker >generas. That's one way of looking at it. Judging, however, from the preponderance of hexanies, eikosanies, and hebdekotamies (whatever), I would venture that having repeated factors goes againt the purest spirit of CPS. However, there is another connection between Euler-Fokker genera and CPS. The union of all CPS i/(k+1) (1,a(1),a(2), . . . ,a(k)), where the a's are mutually prime and i ranges from 1 to k, is Eu (a(1),a(2), . . . ,a(k)). In k-dimensional space, the "interior" of the Euler-Fokker genus is broken into non-overlapping regions, the "interiors" of the CPSs. That is because the only intersections in the above CPSs are between CPS iand CPS i1, namely, CPS (j+1)/k (a(1),a(2), . . . ,a(k)), whic are mere "borders" of dimension k-1. Now it is customary to view these Euler-Fokker genera as cubes, hypercubes, etc., but if we view the CPSs as regular polygons, polyhedra, etc. (by making the axes at 60-degree angles from each other), we obtain fascinating results about regular tilings of k-dimensional space, since obliquely stretched cubes tile just as well as cubes! Try it! Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 14 Jan 1997 19:21 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14041; Tue, 14 Jan 1997 19:24:54 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA14035 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA28645; Tue, 14 Jan 1997 10:23:35 -0800 Date: Tue, 14 Jan 1997 10:23:35 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu