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

Revision as of 17:05, 5 May 2009

Revision as of 18:04, 5 May 2009

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**<s>"Finally, in infinite descent, a given solution is used to construct a smaller solution." I read this sentence and thought I understood the concept being explained. Then I read [[infinite descent]]. Then I reread this sentence, which I now realize does a fairly poor job of explaining infinite descent. My familiarity with the concept is limited to that which I have just read, so I have no suggestion as to how to concisely summarize it, but I strongly urge you to rework the current explanation.</s>

**: I hadn't wanted to talk about the (more common) use of infinite descent in impossibility proofs such as [[Fermat's Last Theorem]]. Rather, my goal was to prepare the reader to follow the logic of why the EA must stop eventually. Nevertheless, I've re-written those sentences to to give a broader understanding of the argument. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 09:36, 5 May 2009 (UTC)

**<s>"The validity of the Euclidean algorithm can be shown by two-step argument." Since the title of the section is ''proof of validity'', perhaps this sentence should include the word 'proof': "The validity of the Euclidean algorithm can be proven with a two-step argument."</s>

**:I had avoided that wording for fear that mathematicians would cavil that the "proof" was not rigorous. I prefer your wording, however, so I replaced it. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**::If you're worried about what mathematicians will think of the section, perhaps providing a rigorous proof would be better than simply avoiding the word 'proof'. In any case, I'm happy with it as is. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 18:04, 5 May 2009 (UTC)

**<s>"This agrees with the GCD(1071, 462) found by prime factorization above." Erm, there is no mentions of 1071 or 462 in the ''Background'' section. Why not just give the prime factorization here?</s>

**:Perhaps I'm not following you but the the paragraph about prime factorization and GCD in the Background section uses 1071 and 462 as an example. For example, it says, "since 462 can be factored into 2×3×7×11 and 1071 can be factored into 3×3×7×17, the greatest common divisor of 462 and 1071 equals 21 = 3×7, the product of their shared prime factors." We could repeat that here, but it seems redundant. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**::>.< I swear you put that in after I made the comment! :P --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 18:04, 5 May 2009 (UTC)

**<s>"The sequence ends when there is no residual rectangle, i.e., when the square tiles cover the previous residual rectangle exactly." This paragraph desperately needs to end with: "The length of the sides of the smallest square tile is the GCD of the dimensions of the original rectangle." or something like that.</s>

**:Excellent suggestion, thanks! [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 17:04, 5 May 2009 (UTC)

**"where the magnitude of rk is strictly less than that of rk−1" The use of 'magnitude' here strikes me as being a bit odd. Why not just write a simple inequality? r_k < r_k-1

**:The "magnitude" wording also covers versions of the algorithm when the remainder can be negative. For example, -37628 < 4, but 4 has a smaller magnitude. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**::True. I wonder if using absolute value notation |r_k| would be better. Up to you. In any case, magnitude or absolute value should be linked to avoid confusion for math noobs. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 18:04, 5 May 2009 (UTC)

**<s>"Euclid finds the quotient and remainder by repeated subtraction" Last time I checked, Euclid is dead. Past tense, perhaps?</s>

**:Perhaps passive voice, instead. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)

**::Perhaps I've struck the issue. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]'''

**<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)

* More to come. Good work thus far. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)