# Talk:Dihedral Groups

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# Response to Checklist

Comments are up! AnnaP 13:44, 20 July 2011 (UTC)

Flora 07.20 11:42 Thanks very much for your suggetions.

## Messages to the Future

• Suggestions of material for future generations to add, when appropriate.

## References and footnotes

• All images are properly attributed in the page you see when you click on the image. All images are labled except what I created.
• Direct quotes from textual sources are cited.
• References for text are at the end of the page, with option links to the footnotes within the text.

## Good writing

### Context (aka Generating interest aka Who cares?)

• This page is made for students from high school to college. It contains both easy and complicated math.

### Quality of prose and page structuring

• The beginning paragraph(s) of the page clearly define the topic or purpose of the page as a whole, and may outline the page or preview conclusions that will be reached later in the page.
• The purpose of each section is clearly relevant to the purpose of the page as a whole.
• No thesis, but clear what talked in each section.
• No helper page yet.
• Within the "More Mathematical Expalanation" section, the heaviest math is placed as late as possible within this section.
• After you say "Order refers to the number of elements in the group, and degree refers to the number of the sides or the number of rotations" it might be nice to note that for the dihedral groups, the order is twice the degree
Fixed
• After you say "On this page, we will use the notation D_n to describe a dihedral group. For D_n, we will call it the dihedral group of order 2n or the group of symmetries of a regular n-gon." I suggest offering up an example or two. You can include the picture of a triangle and mention D3, which is order 6. You could also mention D5, which is order 10.
• I'd encourage moving your group representation to later in the page. It requires the most math knowledge. Right now that section is very dense, making it harder to read, so you may want to go back in and add more definitions to make things more clear and readable. I think you could move it to just above the Uniqueness of the Identity section without doing any harm. I know it's a bit weird to move it to after Cayley Tables, but the Cayley tables are much easier to understand than you abstract group representation section.
Because this section is in Definition Section, so I move it down under matrix section. Is it better?
Yes, I think so
• I'm having a hard time understanding the point of the 3D rotational symmetry section. Either remove it or add more explanation
This section is very simple actually. I deleted several confusing sentences. I hope it helps.
That does!

### Integration of Images and Text

• Wherever an image or animation is used to help with an explanation, the reader is explicitly instructed to refer to the image.
• The text explicitly points out what the reader should observe in a picture.
• I have lots of images to help reader to understand what I am talking.
• In your images in your matrix representation, it'd be really helpful if you added in some way of showing the original position of the arrows (say, making them lighter or dashed lines).
I changed the images. Are they much better?

### Connections to other mathematical topics

• Have link to Complex Numbers. But there isn't any other pages about Group Thoery yet.

### Examples, Calculations, Applications, Proofs

• Whenever a new idea is introduced, numerical examples or calculations illustrating a concept, definition, or argument are provided if they might be helpful.
• My last proof of subgroup is very complicated, I cannot use only words to illustrate. I use lots of math notations, but I introduce them before the proof. All the other proofs are easy and only several sentences.
• I add application in Music.

### Mathematical Accuracy and precision of language

• No error in equations.
• It may feel overwhelming in subgroup section.
• I list all the notations, and add balloons to help define terms.
• When you say "The group consists of n reflections, n-1 rotations, and the identity transformation. " I suggest that you either create a blank helper page for identity transformation or write a mouse over
• At the beginning of your section on complex plane representation, make sure to state again that you're drawing the pictures in the complex plain before we see the images. People can skip over the section headings when they read.
Fixed
• I'd suggest removing the link and anchor that you have on the Cayley table section, because when I saw the link, I was thinking I could click it and go to another page. Instead, it just leads back to where I was! So removing it all together avoids that confusion.
I remove one confusing link. In this section, the image I created is called Cayley Table.
I see that, but I think the issue is that I expect the Cayley table link to take me somewhere else. As is, it does nothing to the way I'm viewing the page (ditto the multiplication table links). I think it would be better just to drop the links
• In your matrix representation, I'd encourage mentioning the non commutativity of the Dihedral groups. Since most people know that matrices don't commute, its easy to use matrices to explain why the elements of the Dihedral groups don't commute.
I don't have enough time to fix this, but I mention this point in Future Direction.
• Be careful when you say "you will find that the intersection of R_4 and S_3 is S_1. " Since the group is non commutative, there are two intersections of R4 and S3 that are distinct (eg R4*S3 is different from S3*R4). While you mention this later on, it's important to clarify what you mean by "intersection" when you first mention it.
Fixed
I just realized that your text and caption to the image are inconsistent. Change the image caption to reflect the text.
I hope I understand you correctly. I change the images' title into Image 2 & Image 3, and also change the link in text. I think this helps the confusing links clearly.
Sorry I wasn't totally clear. In your text, you say that R4*S3=S1. In the caption for the image that explains that example, you say R4*S3=S2. Also, the way that you have written this "In the table, the same or different rotations and reflections work together and result in a new rotation or reflection. For example, look first at the vertical axis to find a element, R_4. Then look at the horizontal axis to get the second element for our composition. We choose S_3. " implies that the answer of R4*S3=S5. There needs to be more clarification about which answer is correct, and a better explanation in the text.
Thanks very much for your suggestion. I didn't realize I have this bug. Which I said R_4*S_3=S_2 in Example 1 should be R_4*S_3=S_1. And I also add one sentence about S_3*R_4=R_5. The first element is on left column, and the second element is on top row.

## Layout

• Text is in short paragraphs, and broken up by relevant images throughout.
• To whatever extent possible, pages do not have large, awkward chunks of white space.
• When text wraps around images, images don't force dramatically different "margins" for consecutive lines of text.
• No image in one section of a page vertically aligns with the text or a heading of a different section.
• In hidden text, none of the preview text appears as weird computer code (see Wiki Tricks for help on this).
• The page has been viewed at a few different window sizes to make sure funky things don't happen.

# Subgroup

## Explore Subgroups

Phoebe 03:17, 9 July 2011 (UTC) The hidden part is kind of intimidating for me. Try to rearrange the contents and make it clearer. Flora 19:28, 13 July 2011 (UTC)