Talk:Pi (mathematical constant)/Proofs/An elementary proof that 22 over 7 exceeds π

Title

Can we call this article "Approximations of Pi" and list all modern approximations; this seems awfully specific and targetted.--Robert W King 15:03, 14 August 2007 (CDT)

Although specific, this result is quite famous and has inspired further research. Besides the paper by Lucas mentioned in the article, F. Beukers notably found a generalization that not only produces a sequence of rational approximations of π, but also provides an irrationality measure for π. Fredrik Johansson 17:02, 14 August 2007 (CDT)

I agree. Approximations to π is a far broader topic. I was so bold in the initial draft of article as to call this "startling and elegant" and I think that justifies it as a separate article. An article on approximations to π would be rather different in spirit. Michael Hardy 17:37, 14 August 2007 (CDT)

...I agree that it seems very specific, considering how many articles on broad and basic topics are not here yet. But it seems to be hoped that that last fact will not remain permanent. Michael Hardy 17:38, 14 August 2007 (CDT)

My only objection to the title is that it seems or gives the impression that it is an argument, or original research. I think the title should reflect something which is indicitive of mathematical correctness with respect to pi and not a point/counterpoint subject. --Robert W King 20:41, 14 August 2007 (CDT)

Certainly it is an argument. It is not "original research" in the sense of something published for the first time here, and that's clear and explicit in the fact that papers published in the 1940s are cited. I don't understand what it is in the article as it stands that gives you an impression that it's original research or that there's anything that could be called "point/counterpoint". And what's indicative of mathematical correctness is the fact that although few of us would ever think of writing down this integral and thereby discovering this argument, anyone who's had a freshman calculus course can easily check the correctness of the result. Since you mention the title, are you saying that is somehow not consonant with mathematical correctness? A major part of the undergraduate training of anyone who majors in mathematics is the writing of proofs and judging validity of proofs. The word "proof" is daily fare. Do you have some problem with that word? Michael Hardy 21:38, 14 August 2007 (CDT)

There's nothing in the article that I'm concerned about; the title itself is the only issue for me on the grounds that 1.) It's not very encyclopedic; 22/7 is always referred to as an "approximation" of pi. 2.) the title itself does not imply seriousness despite that it is very factual in mathematics. If we were to start using titles like "Proof that...", it would seriously inhibit our credibility; there is a certain position that proponents of this statement ("There is proof that", "I have proof".. etc) always take and I don't think we should cater.

I do not have issue with the word "Proof", I understand it's mathetical implications, but from a literary and encyclopedic standpoint I think it's a poor choice for an article title.--Robert W King 09:35, 15 August 2007 (CDT)