# Talk:Euclidean Algorithm

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# Response to Checklist

Great work. I've put comments in red for some things that need to be fixed AnnaP 17:38, 15 July 2011 (UTC)

## Messages to the Future

• Made three suggestions to future editors.

## References and footnotes

• I created all of the three images.
• Direct quotes are cited.
• References are listed with links at the bottom of the page.
• Right when you start Euclid's proof (which seems to be the exact text), note which translation you're using. If you're using your own phrasing, make that more clear.
Made it clear that they are my words not Euclid's: Editor's Note

## Good writing

### Quality of prose and page structuring

• The beginning paragraph defines EA but just roughly tells readers how EA works. I explain how it works in MME section.
• Each section is related to the main topic, and you can see them in other websites that talks about EA too.
• Subsections in the mathematical explanations are listed from easy to hard, from fundamental to expanding. The heaviest math is at the very last bottom of the page, the Steiner's algorithm.
• Make sure that all of your sections have the same internal structure. So, when you first start talking about the algorithm, you first describe the algorithm (in terms of inputs), then give a numerical example, and then do the proofs. I think that this is a great structure, but then you have a different structure in Extended Euclidean Algorithm where you give a proof, then description, then example. Try to rework the Extended Algorithm section so that you move the proof to the end.
I can do that but I'm a little bit concerned with whether people will understand the description or not if I put it first. The Lead In is not actually the proof, but more like a lead in... What do you think?
Having the "lead in" be so heavy with equations is pretty off putting. It makes much more sense to put the description in words. Leaving math at the start of that section means there will be some readers who will simply stop reading at that point. If they come to the equations after being provided with more verbal explanation, they're more likely to push through and try to understand the equations. Does that make sense? I still think that this change should happen. AnnaP 13:37, 19 July 2011 (UTC)
I see. It makes more sense to me now. I moved the proof to the end. Thanks, Anna.

### Integration of images and text

• No large chunks of words or calculations.
• You may notice that this page has only three images. I don't know if I should include more images or not. Since EA is basically about numbers and algorithms, I don't know what kind of image should I add.

### Connections to other mathematical topics

• There are several links to other mathematical topics in or outside of Math Images.

### Examples, Calculations, Applications, Proofs

• The equations, calculations, and examples are introduced and made clear to readers.
• Every statement or property has its proof. Some even are proved in different ways in order to show readers a different point of view. (Modern proof vs Euclid's proof)
• Some descriptions and proofs may seem long and tedious? I'm just trying to make every step as clear to everyone as possible. I'll change them if many think some sections are too long.
• I disagree that your descriptions are too long. In fact, some could be lengthened. When you go through your first example of the algorithm with 168 and 64, add some guiding text between each of the lines, saying things like "Since 40 is the remainder, we...." Guide the reader through the first two steps completely, and then you don't necessarily need text for the rest of the steps.
Got it. Added more guiding texts to the first example.
• In your first proof of the algorithm, why don't you make a bulleted list of the two things to prove (eg, that it is a divisor and that it is the greatest one), and then have bolded headings above the sections where you proof each of the two claims.
Fixed it. What do you think about it now?
• Break this statement: Therefore r_1 = a - k_0b = dm - k_0 dn = (m - k_0 n) d (substitute dm for a and dn for b) into several steps to make it more clear and put the steps on different lines. Something like: Therefore r_1 = a - k_0b = dm - k_0 dn
and
dm - k_0 dn = (m - k_0 n) d
Fixed it and fixed other places with the same situation too.
• When you say "Consider the second equation. " it's unclear what equation you are referring to. You can use equation numbering to help with that.
Fixed it. Add the numbering. Also add the numbering for sections in the same situation.

### Mathematical Accuracy and precision of language

• I try to make everything error free. Corrections and suggestions are always appreciated.
• Any definition that readers may not know is defined. The definition of every mathematical term, theorem or rule is either explained in the body text or via a mouse-over, or linked to another page.
• When you say "If e is even and v is odd, then gcd(e, f) " do you mean "f" instead of "v"?
Yes, ma'am. My mistake.

### Layout

• Texts are short, not very long, and broken up by images or broken in paragraphs.
• Mathematical terms are boldfaced.
• No awkward white chunks.
• No weird computer codes.
• Readers won't find the page crowded.
• Put each step of your proof of the precondition on its own line to help the reader see it more clearly.
Totally agree. Put them in lines.
• In your "Shortcomings" section, make sure to make parentheses big where you need to. For example, you have gcd$(\frac{|e-f|}{2}$, the smaller one of e and f). , but you can turn that into $gcd \left (\frac{|e-f|}{2}, \mbox{the smaller one of e and f} \right).$ Click edit to see how I did that. Doing this for the equations in that section will make them much more readable.
Fixed them. It is, indeed, more readable this way.