# Talk:Boy's Surface

• Htasoff 20:27, 2 July 2011 (UTC) I ralise this page is very much still in the works. Nevertheless, considering the topic's relation to many of the pages I am working on, I wanted to check it just to make sure all our pages were being decently consistent. All my comments were written keeping in mind that the page is still in progress.
• Htasoff 20:27, 2 July 2011 (UTC)My main comment is that much of what is currently on the page is definitions and introductions to topological terms and concepts. I think that this would be better done on the Topology Glossary helper page that I just started based on Leah's suggestion. Many of the terms in topology have nuances in their definitions (ie. manifold, embedding, immersion) that can only be sufficiently explained in a section devoted to the term itself (I've found immersion to be a particularly tricky one, and am still constantly trying to straighten out what, exactly, characterizes it.)
• Phoebe 23:18, 13 July 2011 (UTC) This is a cool image and fascinating page. You got a lot of interesting stuff in it. I'm really interested in this topic. I think there are several hard terms and conclusions needed more precise explanation (see my comments under each section). I understand they are really hard to explain and hard to understand. So try to add more contexts. :) Looking forward to the accomplished page!
• I made several minor edits on your page. They are really minor... Plural form, an extra comma, something like that...

## Intro

• Phoebe 22:56, 13 July 2011 (UTC) Okay, before I went on looking your definitions of the terms, I'm overwhelmed by those fancy math terms in the intro and in the basic description. Maybe you can inform the readers that you are gonna explain every one of them shortly after.
• Gene Good plan. It would be great if you could give some sort of an intuitive intro (this one is a bit too much like Wikipedia's, too). Wording: should be "The[this "The" ain't needed] Boy’s Surface is an immersion on of the projective plane in three-dimensional space."

• Rebecca 01:01, 22 July 2011 (UTC) Why don't you link to the "real projective plane" page when you first mention it?
• I think the first paragraph of this page is too complicated. I would hold off on mentioning the real projective plane until late in the page because it's a confusing topic. I think the image description should be cut down to "The object in this image is called Boy's Surface, which is a single sided surface with no edges."
• "The model was constructed as well as donated by Mercedes-Benz." What about... "The model was constructed as well as donated by Mercedes-Benz, and it can be seen in the image below."

## Basic Description

• Htasoff 20:27, 2 July 2011 (UTC) "Topology focuses on objects that remain constant regardless how distorted the object is."
• This is not correct; you may very well have meant "Topology is the study of properties that remain constant regardless how distorted the object is", which is correct.
• It's kinda repetitive here. You mentioned Werner Boy and others things in the intro before. It's just a minor thing.

• Rebecca 01:03, 22 July 2011 (UTC) I think you need to rearrange the basic description. My suggestions are below:
• I would start the section with ...
Boy's Surface is:
• A non-orientable surface. Nonorientable means (definition).
• An immersion of the real projective plane in 3 dimensional space. This means..... (explanation).
• One possible parametrization of the surface obtained by sewing a Mobius strip to the edge of a disk.
• I think this a better way to do it than to explain things before you give the definitions- people wont be able to follow what you're saying without the definitions anyway.
• Then I think you should move this to after the bullets. "Boy's surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. This probably sounds like a whole new language, but below the Boy's surface will be described in much detail. We will provide definitions as well as examples of vital terms!

Boy's Surface was discovered in 1901 by German mathematician Werner Boy when he was asked by his advisor, David Hilbert, to prove that an immersion of the projective plane in 3-space was impossible. Today, a large model of Boy's Surface is displayed outside of the Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany. The model was constructed as well as donated by Mercedes-Benz."

### Manifolds/Surfaces

• Htasoff 20:27, 2 July 2011 (UTC) I laud your attempt to intuitively introduce the audience to the concept of a manifold, however the definition contains a quite a few nuances that make me think it would best be done on the Topology Glossary page, where it can be explained in better detail.
• I like your analog of the square and tossed blanket, but I think you can explain what a manifold is better here. I still don't understand what exactly manifold is. Try to add a specific definition of manifold. Is it a certain shape? A general surface? Or a topological space?You can put pictures and tell the readers which one is a manifold and which one is not and why. Pictures and specific examples always help a lot.
• Gene The Boy's surface is one of the shapes that is well known in Topology,. Topology is a branch of mathematics. You can think it as an abstract and more advanced version of geometry. Topology focuses on objects that remain constant regardless how distorted the object is. [How 'bout a simple example?]

• Rebecca 01:04, 22 July 2011 (UTC) Manifold should be bolded.
• The tossed blanket example is helpful and well explained. Nice work!

### Non Orientable

• Htasoff 20:27, 2 July 2011 (UTC) I don't understand the explanation of non-orientability. I like the earth analogy, but I can't follow the rest, especially how the image illustrates the concept.
• I can understand this part well. Like the earth analogy and Mobius Strip. But I don't really understand how boy's surface is non-orientable. I guess it's because I can't see what's the back of the boy's surface from the main image.

• If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.
• I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right.

### Immersion, The Real Projective Plane, and Embedding

• Htasoff 20:27, 2 July 2011 (UTC) Though I fall victim to shortening "Real Projective Plane" to "Projective Plane" many-a-time, they are distinct things, and should not be introduced as synonymous.
• Htasoff 20:27, 2 July 2011 (UTC) Important: The Boy's surface is an immersion Not and embedding. The self intersections let you know that it is not.
• Htasoff 20:27, 2 July 2011 (UTC) Overall, I think this is a topic for the Topology Glossary helper page. Moving the discussions and definitions of these terms to the helper page will free up this page and let it focus more on Boy's surface. It will also allow a more in depth discussion of these terms, which can be extremely nuanced. On that note, I was very confused by the introductions to immersion, embedding, ect. that was provided.
Those definitions are necessary for this page. I think you can keep them on your page and then put them on the Topology Glossary as well.

I noticed that you have this listed under geometry, but not topology (but in your page is says that this is a topology subject). I didn't want to add it to topology myself in case the form messed anything up (it's happened to me).

[[User:Nordhr|Nordhr] 18::44 27 Jun 2011

Hey Anna, what would you like to do with this: "The projective space is a modified Euclidean space where every line in the projective space forms into a circle by meeting another point in the space. This is true for all line, even parallel lines. The projective space becomes the construction of the many circle with an additional circle at infinity. It is a fact that the real projective plane cannot be shown in three space without it passes through itself somewhere."

Hey Leah, I think we are going to have to simplify that down a little and maybe provide a picture as an aid in understanding? Ljeanlo1 17:32, 1 July 2011 (UTC)

• About that algebraic equation, tell us what v and e represent. I know v stands for vertices and e for edges, but it's best if you make it clear.
• I got lost in understanding "immersion." I have no idea what that definition from WolframMathWorld means. Need more explanation.

• Rebecca 01:08, 22 July 2011 (UTC) If you could somehow make a sphere that looks 3D and show arrows going around it, that might be helpful.
• I would suggest moving the mobius strip picture up next to the paragraph "The mobius strip is shown below...." * You could refer to it as the picture on the left or right.
• "Straight forward" should be "straightforward"
• You say that non-continuous means that every input has only one output. Your picture of non-continuous doesn't show this though. It shows two inputs mapping to one output, not one input mapping two outputs. I'm not sure which is actually true, but they should be consistent.

## Constructing Boy's Surface

• For the last sentence in the second para: Like the graph, that seems as though it has distinct endpoints, it is similar to the example with the earth, if you go far enough, most likely to infinity, you are going to return to your place of origin.
1. Like the graph. Which graph?
2. Found five commas in this sentence. You break this sentences into too many parts.
3. Despite those two points, you made it clear why you go back to the starting point.
• Last sentence before the video: By applying this reasoning to the 3D graph, the positive x-axis can be connected to the negative y-axis, the positive y-axis to the negative z-axis and the positive z-axis to the negative x-axis. I don't get it. How they could be connected together? Need more illustrations here (pictures if possible). And does it have to be like these three combination pairs (aka. + x and - y, +y and -z and + z and -x )?
• Need more explanation of the video. What I got from this video is that you can return to the origin. Then what happened after 0:50? Please forgive me if I'm getting picky....!!!! These are just my feelings and you don't have to agree to me.

## Parametrization

• Explain to us what complex number means via the mouse over in case other people are not familiar with it.
• As for the parametrization equations, make sure you explain how you get $X = \frac{g_1}{g}$, $Y = \frac{g_2}{g},$ and $Z = \frac{g_3}{g}$ and tell us what $Im, Re$ mean. I just realize that you guys are not done with the page. Just make sure you make those equations clear.