Talk:Boy's surface

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Mathematics rating: B Class Mid Priority  Field: Geometry
Peer review Boy's surface has had a peer review by Wikipedia editors which is now archived. It may contain ideas you can use to improve this article.

I'd like to propose moving the section on the Structure of Boy's Surface in front of the section on parameterization. Wikipedia is addressed to a general audiance, who are more likely to relate to the pictures than the equations. --agr 15:47, 6 Jun 2005 (UTC)

There being no objection, I went ahead and made the change. --agr 18:01, 21 October 2005 (UTC)

I think the images could use more transparency and smoothness. Drawing them opaque and polygonized like this makes it harder to see what's happening. There's a sketchy idea of what I mean on my page [1] but maybe a raytrace would look better. I'd also like to see a more prominent treatment of the locus of self-intersection points (a single triple point connecting three loops of double points). —David Eppstein 21:56, 13 September 2006 (UTC)

I put together: [2] this afternoon. If you think that looks right feel free to insert it as you see fit (I assume you have done most of the organizing of this article.) Let me know if you would like a smaller verision too, it does seem rather big now. — A13ean (talk)
Pretty! And a lot more understandable than what's there now. I'll work on getting it in and making the other images a little less space-consuming. —David Eppstein 05:03, 4 November 2006 (UTC)
Seems like Boys surface is used as a halfway stage in a Sphere eversion http://torus.math.uiuc.edu/jms/Papers/isama/color/opt2.htm, something to this effect should be included. --Salix alba (talk) 22:45, 13 September 2006 (UTC)
Doing some google digging finds [Imaging maths - Unfolding polyhedra] which talks about a discreet Boy's surface, with a reference
U. Brehm, How to build minimal polyhedral models of the Boy surface. Math. Intelligencer 12(4):51-56 (1990).
other interesting links are
A New Polyhedral Surface
discussed the imposibility of tight imersions of the real projective plane.
http://www.jp-petit.com/science/maths_f/maths_f.htm
seems to have some interesting stuff, but its in french? --Salix alba (talk) 18:30, 14 September 2006 (UTC)
As long as you're finding things in Google, there's also Another discrete Boy's surface. A little more explanation: if you have a collection of cuboids in Euclidean space, meeting face-to-face, you can form a collection of 2-manifolds by drawing three equatorial quadrilaterals in each cuboid and connecting pairs of quadrilaterals from cuboids that share faces. Sometimes (in the meshing literature) this collection of surfaces is called the "spatial twist continuum". This paper finds a collection of cuboids from which this construction forms a Boy's surface. It can also be interpreted as a similar construction on the surface of a four-polytope with cuboid faces. —David Eppstein 20:16, 14 September 2006 (UTC)
That wouldn't be you in the references would it ;-)? I think I get the idea. After a bit of smoothing it does make for a nice model
. The tight immersions stuff seems quite interesting space for a new article? --Salix alba 22:06, 14 September 2006 (UTC)

Contents

[edit] Bryant / Kusner

It should be noted that the article by Hermann Karcher and Ulrich Pinkall which can be found here attributes the parametrization formula to Rob Kusner instead of Robert Bryant. Instead it credits Bryant with a general result about rational immersions of some kind of minimal surfaces, of which this parametrization is a special case apparently. regards, High on a tree 21:05, 6 December 2006 (UTC)

It looks like the parameterization used for the statue is from Kusner, which is (as far as I can tell) different from the parameterization currently given in the article which is attributed to Bryant. That parameterization with the credit to Bryant also appears in Apery's book. If there are no objections, we can change the mention in the "statue" section. Thanks, High on a tree! Sorry this is rather late. A13ean 02:35, 26 June 2007 (UTC)
Upon even more in depth digging it turns out that this class of parameterizations is due to a collaboration between Bryant and Kusner, and they are commonly refered to as "Bryant-Kusner parameterizations". So a compromise it is, and unless no one objects I'll make the change. A13ean 02:38, 20 September 2007 (UTC)

[edit] Javaview model

The Boy Surface

Here's a model of Boy's that one can move around, for those of us who like to play with things. If anyone else thinks that it's worth it feel free to link it, but I'll refrain since I made it. — A13ean (talk)

I like it! It's much more helpful IMHO to have something one can rotate freely instead of seeing it animated. So I'll add it. --C S (Talk) 23:36, 13 May 2007 (UTC)

[edit] Left and right handed boys

Something should be said about left and right-handed Boy's surfaces, which are not regularly homotopic. --C S (Talk) 11:17, 8 April 2007 (UTC)

[edit] False claim

The page says that the Boy surface is homeomorphic to RP^2, but that is just impossible, as there are a compact non orientable surface cannot be embedded in R^3... —Preceding unsigned comment added by 201.252.9.131 (talk • contribs)

It's not embedded, it's immersed. —David Eppstein 00:03, 19 July 2007 (UTC)

[edit] Hilbert

I changed 'Hilbert' in the article to 'David Hilbert', hoping that it would help those who (like myself) weren't aware of who 'Hilbert' referred to. I am not, however, certain that it is indeed in reference to David Hilbert, but his biographical information (lifetime, profession, nationality, etc.) strongly suggests that this is true. Please correct my edit if I am mistaken. Thank you. Spinnick597 00:38, 28 September 2007 (UTC)

That's the right one. A13ean 11:05, 28 September 2007 (UTC)