Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions

Revision as of 16:26, 14 May 2009

Revision as of 13:13, 16 May 2009

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**:Reworded caption, thanks. The animation might be helpful, but that would require someone to create and position precisely 1440 1-by-1 squares. It's possible — are you volunteering, by any chance? [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:59, 4 May 2009 (UTC)

**::I'm not familiar with how to convert a series of images into an animation, but I'd be willing to make the images (or at least try). If I make them, can you make the animation? --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 18:52, 4 May 2009 (UTC)

**<s>"The greatest common divisor is often written as GCD(a, b) or, more simply, as (a, b)." Yes, the second version is simpler, but that notation is also used for ''lots'' of other things in mathematics. What (a, b) represents depends on the context of the problem, and I think it would be wise to mention this so as not to mislead our less mathematically-inclined readers.</s>

**:Mentioned ambiguity of "(''a'', ''b'')" notation, and swapped order of last two sentences in paragraph for better flow. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:10, 5 May 2009 (UTC)

**::Eh, better, but instead of "although the simpler notation is also used for unrelated mathematical objects, such as two-dimensional vectors." how about "although the latter notation is also used for various other mathematical concepts, such as two-dimensional [[vector]]s."

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**<s>"''r''_''k'' &equiv; ''r''_''k''−2 mod ''r''_''k''−1" Is there some article to which we can link '&equiv;'? I'm not sure I know what it means.</s>

**:It means "equivalent to" in [[modular arithmetic]]. I'll make a link. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**<s>I don't think the ''implementations'' section belongs in this article. [[WP:NOT|Wikipedia is not]] a how-to guide, and this section does not contain any new relevant information.</s>

**::Your initial reaction is similar to mine. Bu let me argue that the implementations contribute at least epsilon to the article for most readers, and for some readers may convey the algorithm's idea better than anything else. I note that [http://en.wikipedia.org/w/index.php?title=Euclidean_algorithm&oldid=276556143 when I arrived] at this article — then rated at nearly GA level by the Math WikiProject — the implementations were the article's main content, having been debated and perfected for over [http://en.wikipedia.org/w/index.php?title=Euclidean_algorithm&oldid=250714 seven years]. Some editors champion the pseudocode as the only valid way of defining the algorithm precisely. In deference to these editors and in deference to the many readers like them, I feel we should retain the Implementations section. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:18, 9 May 2009 (UTC)

**:::Deference to these editors? Pfft. Perhaps you have forgotten the disclaimer: "If you don't want your writing to be '''edited mercilessly''' or redistributed for profit by others, do not submit it." As for the readers, they come here for a lot of things that they really shouldn't (medical advice comes to mind). The very most we can do in regards to instruction content like this is to provide an informative link &mdash; perhaps to a WikiHow article or a programming site. I realize that you have the best intentions by wanting to keep the material, but the fact of the matter is that it really doesn't belong here. The other points you've brought up are largely irrelevant. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 9 May 2009 (UTC)

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**::Great catch, although I predict that most non-mathematicians would assume that "multiple = integer multiple". [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:18, 9 May 2009 (UTC)

**:::Aye, it's the finnicky mathematicians I'm worried about here. :) --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 11 May 2009 (UTC)

**<s>"The algorithm was likely known by Eudoxus of Cnidus (about 375 BC). The use of the technical term ἀνθυφαίρεσις (anthyphairesis, reciprocal subtraction) in Euclid and Aristotle (Topics IV) suggests that the algorithm predates Eudoxus." I see what you're getting at, but to some readers, these sentences may seem to contradict each other. Suggested rewrite: "The use of the technical term ἀνθυφαίρεσις (anthyphairesis, reciprocal subtraction) in Euclid and Aristotle (Topics IV) suggests that what we now know as the Euclidean Algorithm may have predated [[Eudoxus of Cnidus]], a Greek mathematician who died in approximately 350 BC." or some such. Meh. That's not exactly perfect either. Give it some thought.</s>

**::That's a good suggestion, and very helpful. I toyed with the wording beforehand, but I didn't come up with anything as good as yours. I've uploaded a third wording that may combine the best of our efforts. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 04:13, 10 May 2009 (UTC)

**:::Ah, much better! More direct than mine, too. I'm confused about the last bit, though: "use of the technical term ἀνθυφαίρεσις (''anthyphairesis'', reciprocal subtraction) in Euclid and Aristotle (''Topics'' IV)" Did Euclid and Aristotle collaborate on a book called "Topics IV"? What's going on here? --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 11 May 2009 (UTC)

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**:::Looks very good up until this sentence: "Dedekind also defined the concept of a Euclidean ___domain, a number system in which (roughly speaking) a version of the Euclidean algorithm can be defined." Unfortunately, the speaking is so rough that I have no idea what it means. "(roughly speaking)" is unencyclopedic, and the statement that follows doesn't provide any real information.

**::::I changed the wording slightly to "Dedekind also defined the concept of a [[Euclidean ___domain]], a number system in which a version of the Euclidean algorithm can be defined (as described [[Euclidean algorithm#Euclidean domains|below]])." I'm hoping that the wikilink to the fuller explanation within the article itself will satisfy the readers' curiosity. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:04, 14 May 2009 (UTC)

**:::::That's better, but the wording is still a bit odd. "...in which a version of the Euclidean algorithm..." isn't worded in the best possible way, as it leaves the reader thinking "Uhh... what version?" Any adjective before "version" would make this read more smoothly.

**<s>"In 1829, Sturm showed..." Not sure why this chunk comes after the Dirichlet/Dedekind bit. I'm assuming that Dirichlet/Dedekind did their work after 1832, which may not be correct. If that is correct, then this section is somewhat out of order. If is not correct, then this is still out of order and specific years should be added for clarity (if possible).</s>

**::I was trying to discern between two developments of the EA in the 19th century: the ''general'' development of new number systems and ''specific'' applications of the EA such as Sturm's theorem. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 06:42, 11 May 2009 (UTC)

**:::Ah. This distinction is clearer now. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 23:06, 11 May 2009 (UTC)

**<s>"In 1829, Sturm showed that the algorithm provided an efficient method for counting the number of real roots of polynomials in any given interval." Again, be sure to include given names when introducing people. Also, "efficient method" is currently linked to [[Sturm chain]]. [[WP:MOSLINK]] advises that the article being linked to should be made clear by the words being linked. In this case, I fully expected the phrase to link to an article about the efficiency of algorithms. I suggest rewording the sentence to include "Sturm chain" and then linking that directly.</s>

**:Both good calls. I added "Charles" to Sturm, and I re-arranged the sentence to clarify the Sturm-chain method. I also removed a double link within the paragraph. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:26, 14 May 2009 (UTC)

**<s>"A generalization of this result is known as [[Sturm's theorem]]." The use of the indefinite article "a" implies that there are multiple generalizations of the result, in which case I would recommend swapping out "a" with "one" or explaining the other generalizations. Or both. If this is the only significant generalization, I recommend swapping out "a" for "the". I wouldn't worry about it too much though; if the number of pertinent generalizations was not made clear in your research, "a" will do just fine. </s>

**:Since it wasn't really germane to the EA itself, I dropped the "generalization" sentence. I might add another EA application later, though, to flesh out that paragraph somewhat. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:26, 14 May 2009 (UTC)

**<s>"No new general algorithms were developed until 1979" Erm, I seriously doubt this. I think you may need something more specific than "general algorithms".</s>

**:Reworded to be briefer and to keep within the bounds of the references. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:26, 14 May 2009 (UTC)

**<s>"The PSLQ algorithm, a "jazzed up" version of Euclid's algorithm, has been recognized as one of the top ten algorithms of the 20th century." This is totally irrelevant trivia and really doesn't fit in with the section.</s>

**:Yes, I should've listened to my conscience on this one. Gone. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:26, 14 May 2009 (UTC)

**I'm not sure that the Game of Euclid section belongs in the ''Historical development'' section. It does seem to be worth mentioning in the article, but it really doesn't fit in with the content introduced here. It might be better off being listed in the See Also section.

**:Another difficult call. I sympathize with the critique, but I'm not sure where else to put the discussion. Hitherto I've included the discussion and early in the article, because it's mentioned prominently in some textbooks, it's been the subject of a few research papers, and because I suspect that it might help make some readers more comfortable with the topic, less daunted by the otherwise unbroken wall of math and more likely to push on. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:26, 14 May 2009 (UTC)

**It seems odd that the ''Bezout's identity'' section is a subsection of ''Applications''. Applications sections, in my (probably biased) experience, generally deal with how the subject applies to real world problems, not theoretical mumbo jumbo. Some readers will probably jump down to ''Applications'' thinking that they are going to be reading about how the EA can be used in sailing or accounting or whatever. To avoid crushing their tiny little hearts, consider changing ''Applications'' to ''Mathematical applications'', though I may be alone in thinking that this is a good idea.

--'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)

:::Thank you very much for your careful reviewing! The article is definitely improving. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)