Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions
Content deleted Content added
Cryptic C62 (talk | contribs) responses/strikings |
Cryptic C62 (talk | contribs) responses/strikings, adding some |
||
Line 126:
**<s>Caption: "The greatest common divisor of ''a'' and ''b'' is the largest square tile that covers an ''a''-by-''b'' rectangle exactly. Here, a 24-by-60 rectangle is covered with 12-by-12 square tiles." In the first sentence, it needs to be made clear that it is not one single square tile that covers the rectangle, but multiple iterations of that square tile. "exactly" is somewhat ambiguous, consider expanding. It would also be helpful to say "ten 12-by-12 square tiles".</s> Addendum: upon reading the relevant paragraph, it might be helpful to make this into an animation which demonstrates the various ways in which a 60-by-24 rectangle can be divided.
**: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]]'''
**"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.
**"neither 6 = 2×3 nor 35 = 5×7 is a prime number, since they both have two prime factors" I think it may be a tad confusing to include the prime factorization at first; perhaps this should be added later: "neither 6 nor 35 is a prime number, since they both have two prime factors: 6 = 2x3 and 35 = 5x7." or something like that. Also, shouldn't it be "neither 6 nor 35 '''are''' prime number'''s'''" ?
Line 148:
**<s>"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."</s>
**: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)
**::Well, if you'd still like to stick with "numbers" rather than "integers", how about this: "Thus, Euclid's algorithm, which directly computes the GCD of two numbers, can be used to calculate the GCD of any group of numbers, regardless of the size of the group." Or something? As long as we avoid phrases like "number of numbers", it should be fine. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]'''
**"This approach begins by showing that, if the theorem holds for n, it also holds for n + 1." I just learned about induction last semester, and this doesn't seem to be quite right, specifically the last two clauses. My understanding of induction is that it is a two-step process. The first step is proving the basis case (usually n=0 or n=1), and the second step is proving that it holds for n+1. The sentence in question is written as though the first step proves the second step, which is not the case.
**"A recursion is an equation relating numbers that form a series a1, a2, a3, etc." This is a very poor definition of a recursion, as it does not adequately explain the concept to a reader with no prior familiarity to it. How about "A recursion is an equation in which ''a<sub>n</sub>'', an arbitrary term in a [[series]], is defined by the values of previous terms in the series, such as ''a<sub>n-1</sub>'' or ''a<sub>0</sub>''". This will also help the reader understand the Fibonacci example a bit more clearly.
**"Several equations associated with the Euclidean algorithm are recursive, such as ''r''<sub>''k''</sub> = ''r''<sub>''k''−2</sub> − ''q''<sub>''k''</sub>''r''<sub>''k''−1</sub>." This example is essentially useless, as neither the meaning of the equation nor the terms used therein have been defined yet.
**"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.
* More to come. Good work thus far. --'''[[User:Cryptic C62|Cryptic C62]] · [[User talk: Cryptic C62|Talk]]''' 19:59, 3 May 2009 (UTC)
| |||