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

Revision as of 09:59, 4 May 2009

Revision as of 10:32, 4 May 2009

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**"Imagine a rectangular area a by b, and consider any common divisor c that divides both a and b exactly." Wikipedia is an encyclopedia, not an episode of Spongebob Squarepants. No sentence in an encyclopedia should start with "imagine."

:::I presume that you are not objecting to the [[imperative mood]] (a staple of mathematics: "Let x be..."), just the verb "imagine". I re-worded this to use "consider" for both: "Consider a rectangular area a by b, and any common divisor c that divides both a and b exactly." Since this ''is'' an encyclopedia, we should both strive to keep our comments less colorful. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**"the GCD(462, 1071) = 3×7" In all other instances thus far, you have chosen not to use an article before GCD. Did you mean to say "the'''n''' GCD(462, 1071) = 3×7"?

:::Thank you for catching that inconsistency, which I've fixed. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**"Integer factorization is thought to be a difficult problem for large numbers." A bit weaselly, and it's not particularly difficult if you have a calculator handy. Perhaps "can be" instead of "is thought to be" ?

:::I clarified the sentence, although perhaps I should have been more clear about "large numbers". A pocket calculator might help in factoring numbers up to 20,000 (5 digits), but it won't be useful in factoring numbers with 500 digits, the rough size of number used in modern cryptography. Nevertheless, the Euclidean algorithm can quickly find the greatest common divisor of two 500-digit numbers. That was the point I was trying to convey. Should I spell that out in the article, do you think? [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**"A more subtle definition of the GCD is helpful in advanced mathematics, particularly ring theory." This statement should probably be accompanied by a ref.

:::OK. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**"GCD(a, b, c) = GCD(a, GCD(b, c)) = GCD(GCD(a, b), c)" Shouldn't this also include " = GCD(GCD(a, c), b)"?

:::If only for symmetry. Good catch! [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 May 2009 (UTC)

**"Thus, Euclid's algorithm, which computes the GCD of two numbers, suffices to calculate the GCD of arbitrarily many numbers." Odd wording at the end. Suggest switching to "integers" to allow the following rewrite: "Thus, Euclid's algorithm, which computes the GCD of two integers, suffices to calculate the GCD of any number of integers."

:::That's a good point and a good rewording. By using the word "number", I was trying to be general, since this result applies not only to integers, but to any number system for which the EA works, such as real numbers or Gaussian integers. [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 10:32, 4 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)