Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions
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**: 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)
**"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."
:::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)
**"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?
:::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)
**"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.
**"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<sub>k</sub> < r<sub>k-1</sub>
:::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)
**"Euclid finds the quotient and remainder by repeated subtraction" Last time I checked, Euclid is dead. Past tense, perhaps?
:::Perhaps passive voice, instead. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 16:58, 5 May 2009 (UTC)
**"''r''<sub>''k''</sub> ≡ ''r''<sub>''k''−2</sub> mod ''r''<sub>''k''−1</sub>" Is there some article to which we can link '≡'? I'm not sure I know what it means.
:::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)
:::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)
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