From: israel@math.ubc.ca (Robert Israel) Newsgroups: sci.math.research Subject: Re: Image of Boy's Surface Date: 4 Jul 1997 00:44:13 GMT In article <33BC21EC.249D@worldnet.att.net>, Marjorie Piette & Steve Ellis writes: |> Can someone direct me to a nice image of Boy's surface? (As I |> understand it, Boy's surface is an immersion of the projective plane in |> 3-space.) An electronic version I could paste into a document would be |> nice. A Mathematica program for constructing such an image would be |> fine. Thanks. Joe Fields has a picture of it at http://zariski.math.uic.edu/~fields/gifs/BoysSurface.gif with a description of how to make a paper model at http://zariski.math.uic.edu/~fields/topology/Boys_surface.html Pictures of a skeleton of the surface are at http://http.cs.berkeley.edu/~sequin/SCULPTS/BoysSky.gif and http://http.cs.berkeley.edu/~sequin/SCULPTS/BoysCar.gif (from a sculpture by Carlo H. Séquin, see http://http.cs.berkeley.edu/~sequin/SCULPTS/sequin.html) A parametric representation suitable for Maple or Mathematica is: x = cos(s)(sqrt(2) cos(s) cos(2 t) + 2 sin(s) cos(t))/D(s,t) y = cos(s)(sqrt(2) cos(s) sin(2 t) - 2 sin(s) sin(t))/D(s,t) z = 3 cos(s)^2/D(s,t) where D(s,t) = 1 - sqrt(2) sin(s) cos(s) sin(3 t) 0 <= t <= Pi, -Pi/2 <= s <= Pi/2 See Apéry, Adv. Math. 61 (1986) 185-266. Robert Israel israel@math.ubc.ca Department of Mathematics (604) 822-3629 University of British Columbia fax 822-6074 Vancouver, BC, Canada V6T 1Y4