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

Revision as of 14:11, 16 May 2009

Revision as of 18:51, 17 May 2009

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**<s>"Euclid's algorithm was re-invented both in India and in China" "re-invent" often implies that an existing concept was significantly improved. I think "independently developed" or "independently discovered" might serve better.</s>

**::Good idea, made additional minor changes in wording. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)

**<s>"the Indian mathematician and astronomer Aryabhata described the algorithm as the "pulverizer"" Erm... why?</s>

**::Good question! The historical record does not say, as far as I can tell. One author speculates that it's because the algorithm "pulverizes" difficult linear Diophantine equations in only a few steps, emphasizing its power to solve problems. Its operation also vaguely resembles a pulverizer that breaks a large stone into medium-sized stones, then into small stones, and thence into dust. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 03:35, 9 May 2009 (UTC)

**:::Both of those certainly make sense. Whichever explanation best adheres to the available sources should probably be added to the article&mdash;I'm sure some readers will have the same question I did. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 03:32, 11 May 2009 (UTC)

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**<s>"would hold true for any other system of numbers in which the Euclidean algorithm could be applied" Should be "to which the", right?</s>

**::Right on! thanks, 06:42, 11 May 2009 (UTC)

**<s>"Dirichlet's insight likely inspired Richard Dedekind to develop theories for new types of numbers, the algebraic integers, and more generally Euclidean domains." As this is written, it implies that Dedekind might or might not have developed those theories. Also, the ending construction implies that "new types of numbers, the algebraic integers, and more generally Euclidean domains" are all separate items in a list, but my hunch is that the second is an example of the first. Suggested rewrite: "Richard Dedekind's theories for new types of numbers, such as algebraic integers and Euclidean domains, may have been inspired by Dirichlet's insight." If you do end up rewriting this sentence, be sure to tweak the following sentence to make sure it flows logically.</s>

**::I made a draft - does it read better now? [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 06:42, 11 May 2009 (UTC)

**:::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.

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**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)

**<s>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. </s>

**::That does seem like a good suggestion; more specific section headings are always better. Changed to "Mathematical applications". [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 14:11, 16 May 2009 (UTC)

**"to the set of multiples of a single number, their GCD g" This would probably be slightly less confusing if "a single number, their GCD g" were replaced with "GCD(a, b)". Much simpler.

**"For example, suppose that a cook has two measuring cups of volume a and b, respectively. By adding and subtracting multiples of these two volumes, the cook can measure out any volume ua + vb. These volumes are all multiples of g = GCD(a, b)." Although I appreciate the real world connection, the inclusion of the cook is somewhat unnecessary and unencyclopedic. This analogy should work with just the measuring cups.

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