# Talk:Perko pair knots

Richard Scott likes this.

# Response to Checklist

Original response to checklist, in black, completed by Kate 19:42, 20 July 2011 (UTC)

## References and footnotes

• All images cited on click-through
• Footnotes and references used

## Good writing

### Context

• Basic description and Why It's Interesting give historical context and connection to science

### Quality of prose and page structuring

• Section headings and first sentences explain purpose of each section
• Relevance of each section is clear
• More complicated math is hidden and/or placed near end of MME

### Integration of Images and Text

• Images are referred to explicitly
• Captions and text explain the purpose of each image
• The main proof is a series of images
• Rebecca 03:07, 21 July 2011 (UTC)Is there some picture you could add to the Why It's Interesting section? It's probably OK the way it is, I just think a picture might draw people eyes to the section more.

### Connections to other mathematical topics

• I didn't see anywhere to make relevant connections - there is nothing else on the site about knot theory

### Examples, Calculations, Applications, Proofs

• The main content of the page is the proof that the two knots are the same
• Examples are given and explained in the Dowker notation section
• Applications of knot theory in general are explained very generally in Why It's Interesting, I don't know of any applications for these specific knots

### Mathematical Accuracy and precision of language

• All statements are accurate to the best of my knowledge
• Unfamiliar terms are defined (Two of the 3 sections in the MME are devoted to explaining terminology/notation that readers unfamiliar with knot theory can't be expected to know)

• Rebecca 03:04, 21 July 2011 (UTC) "Belief in ether soon faded, but interest in identifying and cataloging different types of knots stayed. " maybe "remained" instead of "stayed"?

### Layout

• Paragraphs are short, many images are used
• Page has been viewed in a variety of window sizes, spacing and layout seems as good as it can get given the information that needs to be displayed
• Hide/shows used in several places to prevent intimidation

• This page is really good and really clear. It's very easy to follow. There's not a ton of info, but that's okay. The one problem is that you say some things a couple of times. Right now, the page is short enough that these redundancies are fresh in the reader's mind, but after the proof is complete, this may not be so noticeable. Richard 7/14
• Are the Reidemeister moves a method of solving "knot problems" or are they tools you use to solve them? To me, it sounds like you're using the word as both, which may be right for all I know. Richard 7/14
• Kate 20:53, 14 July 2011 (UTC): I don't really understand what you're asking. Can we talk about it tomorrow?

## Basic Description

xd 18:33, 12 June 2011 (UTC) I think you need a better transition between "To say that two knots are the same is to say that one can be deformed into the other without breaking the knot or passing it through itself." and the next one about the projection. I don't quite see the link between them. Since you have an explanation about projection in the Reidemeister moves section, I think you can get rid of this part.

Kate 18:09, 14 June 2011 (UTC): I really wanted to have projections explained in the basic description section, because they're important and not that hard to understand, so I changed it around. Does it read better now?

## Reidemeister moves

xd 18:33, 12 June 2011 (UTC) I don't understand the part of "projection of a knot was printed on very stretchy rubber" and you can stretch and none of the crossings are affected. How is that so?
Kate 13:17, 13 June 2011 (UTC): Thanks for pointing that out, I'll try and think of a better way to explain it. Personally, I think of those pictures printed on fruit roll-ups - you can stretch them all over the place, but you're only warping the image, not "really" changing it.xd 20:37, 13 June 2011 (UTC) ok. if you can find a way, then all the better, if not, i think you can avoid mentioning that.
Kate 18:08, 14 June 2011 (UTC):Yeah, I'm not going to bring up Fruit Roll-ups, but I really do need to explain planar isotopies, because I'm going to be using them in my proof, so hopefully I'll think of a way to elaborate on that explanation.
• First redundncy: you already mentioned the projection in the Basic Description. You basically state the same info again, but this time you do introduce new ideas about the projection in this section. I think it's fine, just something to look out for. Richard 7/14
Kate 20:21, 14 July 2011 (UTC): Good point, changed it.
• Typo: "...or after moving the knot trough any ambient isotopy." Richard 7/14
Kate 20:21, 14 July 2011 (UTC): Made irrelevant by change in response to previous comment.

## Provong that the perko knots are equivalent

• Title of this section: pair is singular. So should it be "is" not "are"? Don't get mad at me it's just that I don't know and it sounds kind of funny and I'm sorry I'm trying to fix your grammar just trying to help but maybe you could add the word "knots" to this title to make it all better dont hate me? Richard 7/14
Kate 20:21, 14 July 2011 (UTC): Hahaha! I didn't notice I did that, but I think it happened because it's weird to say that something "is" equivalent - equivalent to what? I changed it to "knots are".
• Typo: "...Kenneth Perko provided an abridge proof..." Richard 7/14
• I think it'd be cool if you labeled which is perko a and perko b in the picture. Richard 7/14
Kate 20:21, 14 July 2011 (UTC): Actually, the only places where I've seen them labeled that way have been projections that don't match mine, so I'll just remove those two names.
• You say "Reiemeister images" here. I'd stay consistent with "moves". Richard 7/14
Kate 20:21, 14 July 2011 (UTC): Oops! I didn't even know that happened, Reidemeister images aren't a thing…

## Why it's interesting

• Second Redundancy: The guy wrote the book in 1899. This one like I said above might not be so bad with the extended proof. Richard 7/14
Kate 20:21, 14 July 2011 (UTC): I think I'm going to keep this because if you expanded the MME the old date occurred a long time ago.
• TI think you could have waaaaaaaaay more fun with this part. You could do something that shows an ambient isotopy to a shoe tying knot or something. You could link to the Spongebob shoe tying song (This suggestion not so much.) And I'm serious when I say you should maybe link to entanglement--a knot game... Richard 7/14
Kate 20:21, 14 July 2011 (UTC): Those are some good suggestions, I'll think about it and try and figure out something to add.