7 quick responses to Brayton Gray's query about visualizing the immersion of the projective plane.............DMD _____________________________________________________ From: Johannes.Huebschmann@agat.univ-lille1.fr (Johannes Huebschmann) Date: Thu, 10 Feb 2000 22:58:22 +0100 (MET) Subject: Re: projective plane There is model of Boy's surface made of steel bands at Oberwolfach . J. Huebschmann ____________________________________________ Date: Thu, 10 Feb 2000 22:00:52 -0300 (ART) From: Mariano Suarez Alvarez Subject: Re: projective plane The 3d-viewing package Geomview (which you can download from http://www.geom.umn.edu) has an example file you can use for viewing RP^2 as immersed in R^4, or rather projections onto coordinate hyperplanes. The program allows one to rotate the figure in 4d, and the projections are modified accordingly, in real time. It takes a little time to get used to moving things in 4d and to understand the pictures; another sample file which is simply the four basis vectors of R^4 is great for practice. (It can be a bit addictive, too; the program can do lots of nice things, like let you walk inside threefolds and orbifolds, etc. Also, with a little work and a glance at the manuals, it can display models created within Mathematica or Maple, or custom programs.) -- m ----------------------------------------------------------------------- Mariano Suarez Alvarez Departamento de Matematica - Universidad Nacional de Rosario Pellegrini 250 - Rosario 2000 - Argentina ____________________________________________________________________________ From: Haynes Miller Subject: Re: projective plane Date: Thu, 10 Feb 2000 20:02:08 -0500 (EST) Check out the Geometry Center's http://www.geom.umn.edu/zoo/toptype/pplane/boy/ Haynes Miller ___________________________________________________ From: "donald kahn" Subject: Re: projective plane Date: Fri, 11 Feb 2000 03:08:17 -0500 > hi, i think that there is a picture of boy's surface (which is an immersion of the projective plane in 3-space) in hilbert and cohn-vossen "geometry and the imagination" chelsea publishers.i don't have my copy here, but if my feeble mind is still working, i remember it was made from wire or sticks.if all the above is true, it should still be in the library in gottingen. best regards, don > . don kahn, school of mathematics, u of mn, mpls, mn. 55455 phone or fax 612 625-0031, home phone 612 378-2591. e-mail at dkahn@isystems.net __________________________________________________________ Date: Fri, 11 Feb 2000 09:30:27 +0100 From: Jaume =?iso-8859-1?Q?Aguad=E9?= Subject: projective plane Dear Brayton Gray: This may answer your querie posted in the Topology Discusion List. Recently, I gave a general talk to undergraduate on the projective plane and found in the web very nice animated pictures of Boy's surface. They are there: http://www.geom.umn.edu/zoo/toptype/pplane/boy/movies.html There are some other places in the web which contain useful ideas about Boy's surface. In my talk, I used a large cardboard model of Boy's surface made by myself. The PostScripy version of my talk is available at my home page: http://mat.uab.es/aguade/Z2.ps Best regards, Jaume Aguade -- ********************************* Jaume Aguadé Departament de Matemàtiques Universitat Autònoma de Barcelona 08193-Bellaterra, Spain tel. (34)-93 581 1867 fax. (34)-93 581 2790 aguade@mat.uab.es http://mat.uab.es/aguade http://mat.uab.es/topalg ********************************* _______________________________________________________________ From: "Andrew Baker" Date: Fri, 11 Feb 2000 09:49:02 +0000 Subject: Re: projective plane You might have a look at Ronnie Brown's site http://www.bangor.ac.uk/SculMath/ which has a set of pages about Bernard Morin and the Brehm model. By the way, a few years ago I was at Oberwolfach and saw someone standing on his toes feeling the top of the sculpture. It turned out to be Morin who was checking that it was accurate! On the subject of surfaces if you haven't already found, it have a look at the ACME Klein Bottle site- real glass ones available! Andy Dr A.J. Baker, Department of Mathematics, University of Glasgow, G12 8QW, Scotland. email a.baker@maths.gla.ac.uk WWW http://www.maths.gla.ac.uk/~ajb tel. (0141) 339 8855 ext. 6140 fax (0141) 330 4111 ______________________________________________________________ Date: Fri, 11 Feb 2000 12:55:41 GMT From: Brian Sanderson Subject: Re: projective plane That model was at Oberwolfach. I went a little mad with this topic some time ago. The resulting views and animations and a short paper can be found on my web page. Enjoy -- Brian.Sanderson@warwick.ac.uk * Tel: +44-1203-523738 http://www.maths.warwick.ac.uk/~bjs/ * Home: +44-1788-890092 Mathematics Institute * Fax: +44-1788-891554 University of Warwick, Coventry CV4 7AL, UK Date: Thu, 10 Feb 2000 14:37:47 -0600 (CST) From: Brayton Gray Subject: question for discussion list I remember seeing a fairly nice model for the projective plane immersed in R^3 made of steel bands - possibly at Oberwolfach or Bonn - I can't remember where. My question: does anyone who might remember this model, or any good model, know of a good source for this on the web - or better yet, a maple program, or something that can be rotated? Something for students to look at. Brayton Gray -- Brian.Sanderson@warwick.ac.uk * Tel: +44-1203-523738 http://www.maths.warwick.ac.uk/~bjs/ * Home: +44-1788-890092 Mathematics Institute * Fax: +44-1788-891554 University of Warwick, Coventry CV4 7AL, UK