Recently, a question was closed. While I am uncertain of each person's motivation for closing the question, it seems that there were a combination of factors. The question is at a very low level. Looking at either the wikipedia page on pi or the wikipedia page on irrational numbers contains the answer (and both were referenced in the answers to the question before it was closed).

This lead to the following exchange of comments:

mixedmath: Is the idea here that a question that is already answered should be closed? This has not been the case so far. Is the idea that people are supposed to look everywhere else before asking a question? Accepting that it's not about the question being too simple, does this mean that we are implicitly imposing the condition that people check wikipedia before posting here? To be honest, this doesn't seem unreasonable. But at the same time, I have given and read answers whose entire purpose is to direct the OP to wikipedia. At the same time, I have given comments to the effect of "Have you checked wikipedia yet?" So I'm trying to find my line, too. Perhaps even a little consistency. Ultimately, I feel that the OP didn't have a concept of irrational numbers before he posted here, so it wouldn't surprise me if he had never thought it possible for a number to not end or repeat. But the Greeks were stunned by this too. While we find them easy now, these are non-trivial concepts, don't you think?

Theo: I don't think I have a consistent line either. The up- and downvote arrows indicate "This question doesn't show research any research effort". While I don't think it should be mandatory that one check all possible sources--and it can be difficult if you don't know what you're looking for--I expect a quick google search at least. Googling "Pi" one gets to Wikipedia and if one gets to the second sentence in the second paragraph there one sees "Consequently, its decimal representation never ends or repeats."

So what I'm trying to get at is that I am uncertain of what reasons we close questions. The content of this question seems nontrivial to me (as it would appear to a layman). I am not defending the question in the sense that I want to know the answer - but instead in the sense that it is not easy to acquire mathematical experience, and approaching mathematicians or any other scholar can be scary and intimidating. I wand this to be an open environment. But I also expect people to put effort into asking their questions - I still don't plan on answering homework questions where the OP doesn't show any effort towards solving the problem himself.

Now I've begun to ramble. To cut this short: should questions such as the linked one be closed, and why should they be closed?

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It needs only 1 more reopen vote. –  Bill Dubuque Jul 22 '11 at 2:14
    
@Bill: In view of Aryabhata's answer below I cast the last vote to reopen. –  t.b. Jul 22 '11 at 2:17
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Things are so much better than the early days - where reopening was difficult if not impossible. –  Bill Dubuque Jul 22 '11 at 2:20
    
This is a great suggestion, and I wish the same for my comments. –  mixedmath Jul 22 '11 at 2:27
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2 Answers

I consider this question to be similar to "What is 1+1" (which should to be closed as NARQ) but not quite.

The fact that $\pi$ is irrational was open for a long time and required some very creative ideas to prove. It is a well known fact now, but for say some laymen, it might very well be an unknown fact (or the fact that irrationals don't terminate) and I see some inquisitive students could possibly have the same question.

I think we should keep it open and protect it (as Qiaochu has already done).

One other option is to rephrase the question as "Is $\pi$ irrational? If not, is it a terminating rational?" and close it as dupe of some earlier question (which I assume exists).

FWIW, if there aren't enough votes to reopen, it won't bother me in the least.

As an aside: Closing is very subjective and one can never be certain of the reasons a question might get closed.

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As requested: here's the copy of the original comments debating closure on the main page.

Someone care to explain the close votes? This seems like a completely reasonable question to me from a layman. – Qiaochu Yuan♦ 13 hours ago

@Qiaochu: As I voted to close, I can say that this question can be answered by a ten minutes read on Wikipedia, regarding the fact that π is irrationals, and that irrationals expand infinitely long in a decimal expansion. While it is a perfectly good question for the layman, I do not believe that it fits this site, more to the fact that questions about π=4 and such has been asked before, and while I have not been through all the questions of the tag [pi] I am fairly certain that this question had been answered before in one of them. – Asaf Karagila 13 hours ago

@Qiaochu: I voted to close because you don't need a 10 minutes read as Asaf says, but you only need the first few sentences on Wikipedia. – Theo Buehler 12 hours ago

@Theo: It may take up to three minutes to go to the kitchen and get a beer, open it, return and get comfy. This will also make the reading process slower, so all in all I allow full ten minutes... :-) – Asaf Karagila 12 hours ago

@Asaf: I also see no problem with this question. It is from a layman, as Qiaochu noted. But it is in good taste. Many worse questions get asked and answered all the time - I don't think we should snub our noses at this one just because it's simple. – mixedmath 11 hours ago

@mixedmath: I don't think that the point is that it is simple. I fail to see why the first two paragraphs in the Wikipedia page on π are not enough. And if indeed they aren't then I'd like to see some elaboration as to why before I'd consider voting to re-open. – Theo Buehler 11 hours ago

@Theo: Is the idea here that a question that is already answered should be closed? This has not been the case so far. Is the idea that people are supposed to look everywhere else before asking a question? Accepting that it's not about the question being too simple, does this mean that we are implicitly imposing the condition that people check wikipedia before posting here? To be honest, this doesn't seem unreasonable. – mixedmath 11 hours ago

@Asaf (contd) But at the same time, I have given and read answerswhose entire purpose is to direct the OP to wikipedia. At the same time, I have given comments to the effect of "Have you checked wikipedia yet?" So I'm trying to find my line, too. Perhaps even a little consistency. Ultimately, I feel that the OP didn't have a concept of irrational numbers before he posted here, so it wouldn't surprise me if he had never thought it possible for a number to not end or repeat. But the Greeks were stunned by this too. While we find them easy now, these are non-trivial concepts, don't you think? – mixedmath 11 hours ago

@mixedmath: Well, maybe we shouldn't pursue this question here but on meta instead. I don't think I have a consistent line either. The up- and downvote arrows indicate "This question doesn't show research any research effort". While I don't think it should be mandatory that one check all possible sources--and it can be difficult if you don't know what you're looking for--I expect a quick google search at least. Googling "Pi" one gets to Wikipedia and if one gets to the second sentence in the second paragraph there one sees "Consequently, its decimal representation never ends or repeats." – Theo Buehler 11 hours ago edit

@Asaf I disagree that the Wikipedia page on π necessarily makes the required inferences obvious to a layperson. – Bill Dubuque 8 hours ago

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Thanks, Willie! –  t.b. Jul 22 '11 at 11:43
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