# Talk:Application of the Euclidean Algorithm

## Contents

# Response to the Checklist

## Messages to the Future

- Made two suggestions for future editors.

## References and footnotes

- Original sources of "borrowed" images are marked if you click them.
- Direct quotes are cited.
- References are listed with links at the bottom of the page.

## Good writing

### Context

- Linked to Euclidean Algorithm.
- This topic “Application of the Euclidean Algorithm” is interesting. The main image is appealing. "More Mathematical Explanation" is comprehensive. I gave a lot of applications for readers to know better about Euclidean algorithm.

### Quality of prose and page structuring

- Since this is a "sister" page for Euclidean Algorithm, there is no definition in the beginning paragraph. It's just a lead in.
- Each section is related to the main topic.
- Real world applications in the mathematical explanations are listed from easy to hard, from fundamental to expanding. The heaviest math is place at the bottom, RSA algorithm.
- Can you work on rephrasing your second sentence "To find out the process of generating music rhythms or how it sounds like, go to section" I don't know if you want to encourage your reader to jump all the way to there, so you might just scrap that sentence.
- You need a bit more of an explanation before you jump into the fractions, even if it is to just to say "below are two examples of reducing fractions" or something like that.
- Flip your first and second sentences in the Linear Diophantine Equations section. When you first start it, it's totally unclear
*why*anyone would care about these equations. - This section: "Because gcd(a, b) divides a and b, gcd(a, b) divides ax + by for any integer x and y. Thus, assume gcd(a, b) = am + bn, where m and n are both integers, and gcd(a, b) also divides c because c = ax + by. "

- comes at the reader very fast. It would be better to break up all of those points into separate sentences and then space things out. Instead of saying just "assume" you can say "we will assume" or something like that.

- Instead of "How to change a fraction into a continued fraction? " You mean "How
*do we*change a fraction into a continued fraction?" - I don't understand what you mean here: "There are certain things whose number is unknown. Repeatedly divided by 3, the remainder is 2; by 5 the remainder is 3; and by 7 the remainder is 2. What will be the number? "

### Integration of images and text

- Every image is referred in the context. In every image, the denotations are noted and readers know what each symbol means.
- Readers are clear about which picture they should look at while viewing this page.

### Connections to other mathematical topics

- There are links to topics in or out of Math Images.

### Examples, Calculations, Applications, Proofs

- The equations, calculations, and examples are clear to readers.
- Every statement or property has explanation or proof.
- About the section RSA Algorithm, there was a worked example for RSA before. I used the numbers and examples from Wikipedia, cause I didn't know how to solve them. And wikipedia didn't give a very thorough calculation for encryption and decryption because they are related to more and more complicated calculation and they just put links to the detailed mathematical terms and methods. I don't know whether I should put the example up on this page or not. Or I could leave a future instruction to other people at the bottom of the page. I'm looking for your opinion. Thanks.
- In your adding fractions, you don't explain this idea well enough: "In this way, you don't need to reduce the fraction anymore because the denominator is the least common multiple of 64 and 168. " It's not clear how you make that jump. You should offer more justification for why the numerator (which is a sum) and the denominator are relatively prime.
- Why in this example: "For example, l_3 = m_1m_2m_4m_5m_6m_7m_8. " is m8 the last m? It's unclear why you stop at 8.
- Your Chinese remainder theorem section needs a lot of editing for clarity. I don't have time to do all of this now, but you need to do quite a bit of editing for clarity and grammar.

### Mathematical Accuracy and precision of language

- This page has a lot of complicated concepts and proofs. I'm trying to make everything as clear as possible.
- I try to make everything error free. Corrections and suggestions are appreciated.
- The definition of every mathematical term, theorem or rule readers might not know is either explained in the body text or via a mouse-over, or linked to another page.
- I think when you say "First, find out if it has a solution or not" you actually mean an
*integer*solution. It will have a solution, being a nice, linear equation, it's just not guaranteed to the an integer

### Layout

- Texts are short, not very long, and broken up by images or broken in paragraphs.
- No awkward white chunks.
- No weird computer codes.
- Make sure to jump down a line after you calculate the least common multiple of 64 and 168 before doing the computation.
- Make sure you move your example under continued fractions down so that the fraction itself is below where you are applying the algorithm. It's confusing to have it off to the side and not below.
- I might hide the content under most of the section headings (not the headings themselves) starting with continued fractions. The page expands to be quite long, so it would be better to break up the content by hiding some of it.