837:: It is being pointed out that pi is sometimes defined using the trigonometric functions to avoid the particularities of geometry. But it is not being mentioned that in order to avoid these particularities the trigonometric functions must be defined over their infinite series representations. In this regard it should be noted that such definition is more common in analysis. Also, the
708:
1310:
and pleasing aesthetically. I also tried making the formulae smaller (still centered in the text), but that looked bad. Another option is to eliminate the boxes altogether and make all formulae large and centered; but then the article is harder to read for the layman; and may discourage readers from reading the text. I'm open to new ideas. --
166:. I've listed this article for peer review because I"m planning on nominating it for Featured Article status. The reviewer should be someone familiar with the Featured Article criteria, and not afraid to nit-pick the article. The reviewer need not have special mathematical skills (many other editors have taken care of that). Thanks!
1309:
That is a good question. I think the article should be mostly words, a narrative. Formulae should be de-emphasized, and place in boxes, generally. However, in that section, I cannot find a way to move those to the right, without eliminating the photo of
Ramanujan, which I consider very informative
1185:
Okay: I've moved the summary of hex/dec/60 approximation up into the
Fundamentals section ... which is good, since a reader quickly looking at the article to grab some digits will see them near the top. As for the MonteCarlo & ContinuedFractions: I dont think they fit comfortably in the history
585:
The article contains the text "For most calculations involving π, a handful of digits provide sufficient precision. Thirty-nine digits are sufficient to support most cosmological calculations, because that is the accuracy which is necessary to calculate the diameter of the universe with a precision
1136:
Surveying has nothing to do with restricting itself to sources that explicitly are only discussing the use of pi. That is why it is called surveying. A more valid argument of course is missing notability of a particular use compared to other uses. And in this regard I probably agree with you – I
1002:
Of course, the
Fourier transform method has applications in several science fields, including telecommunications, multimedia encoding, signal analysis, in algebra for improving the speed of algorithms, etc. This gets a bit lost in this Usage section, e.g., it isn't mentioned in the Engineering
252:
However, for most readers this is probably just going to be a list of things they have never heard of. Is there some way to put these in a context that is more meaningful for Joe reader? For example, many of these, but not all, have ties to the geometry of space. The odd ones out are perhaps
500:
Ah, I see what happened. Two consecutive paragraphs in the Name section contain the phrase "ratio of circumference to diameter". I fixed one, but not the other. You were looking at the unfixed one; I was looking at the fixed one. I've fixed them both now.
1209:: It should be noted in a sentence that continued fractions provide the best rational approximations of a number given a maximum denominator, and further that the values 22/7 and 355/113 determined in the antique correspond to two of these approximations.
183:– Overall it looks decent, although I continue to have concerns about the multitude of formulae being presented to what is likely a non-mathematical audience. I've attached a list of comments below; please pardon my somewhat terse style.
642:
In some locations, names of persons are given with their nationality and profession; in others it does not. It would be good to be consistent and list the nationality and profession throughout. Some FAC reviewers seem to like that.
1095:
Turns out this is rarely discussed under aspects of functional graphs but commonly under random mappings. A Google search for "random mapping cycle length" reveals tons of sources. Do you think you can identify some good ones?
553:"...their efforts are sometimes ingenious, but doomed to inevitable failure..." This statement seems full of opinion and emotive language. From an impartiality perspective, it may be better if it were in the form of a quote.
639:"but it is not certain how he arrived at the value, which he may have obtained from Archimedes or from Apollonius of Perga": the statement about uncertainty seems redundant here, since it is clearly implied by the "may".
578:"Accounting for additional digits needed to compensate for computational round-off errors, a few hundred digits would suffice for any scientific application." This statement seems absurd for a number of reasons.
909:
True. But I think lots of values that were "frequently used". Later in the article, it says "Archimedes' upper bound of 22/7 may have led to widespread belief that π was equal to 22/7" which is from a source.
581:
I think here it may just need a statement about practicality. For example: "In reality, the number of digits needed for any practical computation involving π is less than 20." Not sure how you'd cite it though.
1291:
section more important than the other ones? I would suggest that you pick some particularly important formulas for centered display presentation, and box the other ones (without overwhelming the right border).
852:
I believe that you are correct ... but the sources I read did not explicitly say that, and for
Featured Article status, everything has to be given a footnote which names a source. Ditto for the Landau fact.
559:"meaning that all possible sequences of digits (of any length) are equally likely": I think the likelihood is at a given length, rather than any length. Thus '111' does not have the same likelihood as '11'.
1164:: I'm a bit confused about this section. Approximations are discussed at length in the History section. Now it gets its section on its own but it is rather short. Can this be improved organizationally?
457:
774:
Thanks so much for the scrupulous review. I'll start implementing your recommendations tomorrow. My plan is to get it to FA status, then nominate it to appear on the WP main page on
936:
so it doesn't get lost within the flow of images at the right border of the page. This would also move some of the other images and boxes further up near the text they belong to.
875:
includes the series and has a reference to a book this is supposed to be in, which I unfortunately don't have access to. You referenced
Beckman, does it include a reference?
465:
It looks unchanged. My question is whether π is specifically used for the circle, or for any closed/convex shape. The passage doesn't communicate which perception is correct.
751:
Can this be addressed? Bellard, Fabrice. "A new formula to compute the nth binary digit of pi". Archived from the original on
September 12, 2007. Retrieved October 27, 2007.
1081:
I don't recall seeing any sources that specifically mention graph theory related to pi. Can you give some sources on that? I can take it from there if you start me off. --
1350:
That is a tough call. I think the "Usage" section could get very dry and ugly if it turns into a large list of things that employ pi. The pi article has a subarticle
691:"The approximation 355/113 was known in the fifth century in China" belongs in the history section. Does the citation for that statement apply to the sentence before?
804:
banned the submission of papers regarding the squaring of the circle in order to "keep the lunatic fringe in check" (per the author). If not, it might be useful on the
1040:
Ah, I did not see the other mention ... I remove the other one. Again, I'm not sure I see that kind of detailed information about the FT in the sources that are
568:"very evenly distributed" is an opinion, but I'm not quite clear what it is expressing. Is it just a judgment call on the part of the author, or did he perform a
556:"The digits of π appear to be very irregular or random": 'very irregular' is vague. How does it differ from just 'irregular', or from 'random' for that matter?
652:
In "Geometry and trigonometry" could discuss the formula for an n-dimensional sphere and show how it collapses to the expected formula in three dimensions .
586:
of one atom...." There are several sources that mention the 39 digits; but I dont recall any saying a specific smaller number like 20. I can look again. --
288:
PS: I might collapse this discussion, so other potential reviewers don't see this and think you've volunteered to do a full Peer Review. Is that okay? --
89:
971:
I don't recall any of the reliable sources mentioning that. I Googled it, but found nothing except a few unreliable web sites that discuss it. --
1441:
section be phrased in a better way? It reads a bit awkward currently, and "curves" for serifs is probably not the best choice of word, either.
379:
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section. It is probably best to leave them outside that, as stand-alone auxiliary sections, not tied to any particular historical era. --
319:
1068:
Related to
Stirling's formula, pi is a re-appearing constant in formulas expressing cycle length values in functional graphs. Indeed,
378:
There are redundant terms: 'also', 'now', 'some', 'a variety of', 'several', 'many', &c. These need to be culled judiciously. See
830:
I understand that I am probably not as competent as your fellow WikiProject
Mathematics colleagues. Nonetheless, I'll give it a try:
575:
In paragraph the "Motivations for computing π" section, the point about breaking records is made twice. Once should be sufficient.
322:. I'd appreciate it if you could do a pretty detailed review and identify any shortcomings relative to those criteria. Thanks! --
38:
688:
The "Probability and statistics" says "there are many distributions whose formulas contain π". This is both vague and unsourced.
1480:
902:, ...a value which was frequently used as a convenient approximation before the advent of the computer and electronic calculator.
633:"Some authors explain": 'some' is an indeterminate number. The reference only lists two. Does the reference say "some authors"?
1351:
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336:
I'll wait until you finish the review before I begin implementing your suggestions, so we don't get confused. Thanks again! --
82:
682:"the number of iterations needed for the point (-.75,ε) before escaping, multiplied by ε, was equal to π": escaping what?
486:. It looks like another editor may have undone it (or I somehow accidentally reverted??). I'll just restore my wording. --
462:"Mathematicians use the Greek letter π to represent the ratio of circumference to diameter." Of any closed/convex shape?
569:
1026:
Now it appears twice. :( I meant that its application should be better highlighted resp. the article better organized.
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694:
The caption for the image in the "Continued fractions" section repeats a statement made earlier in the article.
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1385:) 19:30, 15 April 2012 (UTC) ← Possibly it could be mentioned in relation to the question whether pi is normal.
135:
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459:": this assumes the reader understands the parameters relate to the circle. It'd be better to make it clear.
685:
In the "Physics" section, the parameters in the formula for the period of a pendulum need to be explained.
202:
626:, but it does mention some in the reference. Still, it might be good to note that the idea originated with
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1422:
Thanks for the feedback. Your suggestions are good. I'll start implementing them in a day or two. --
546:"An important consequence of the transcendence" is making a value judgment. Why is it important? See
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Plouffe, Simon. "Indentities inspired by
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There are a number of uses of 'which' that seem to be missing a comma, but that's just an opinion.
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I'm probably making too much of a fuss about it. It's not a significant problem. Thanks. Regards,
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could also mention pi's appearance in formulas for contour integration in complex analysis.
900:"Archimedes' upper bound of 22/7 may have led to widespread belief that π was equal to 22/7"
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Several sources need expansion, such as a listing of the publisher, the work, &c.
679:"results in the remarkable Euler": for the non-mathematician, why is this remarkable?
562:"They hypothesis that π is normal has not been proven or disproven." Who are 'They'?
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thought it was being discussed within graph theory but it is not, so no need to cover.
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1118:. I think the article should be limited to that kind of material. Other topics that
664:"A complex number z can be expressed in polar coordinates as follows": you might put (
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accepted by the House of
Representatives before it was rejected by the parliament.
723:
V Kh Salikhov 2008 Russ. Math. Surv. 63 570 doi:10.1070/RM2008v063n03ABEH004543
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pi are in the thousands, and this article cannot hold them all, of course. --
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1354:... I'm wondering if additional examples would be better off in there? --
943:
Done: I centered that picture; fairly near the bottom of the section. --
230:
1437:
I know you haven't added this text, but can the first paragraph of the
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has defined pi as twice the smallest positive root of of the cosine(x).
697:"Poems for memorizing π is have been composed": 'is' or 'have been'?
128:
735:
Raz A, Packard MG, Alexander GM, Buhle JT, Zhu H, Yu S, Peterson BS
775:
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646:"Two new algorithms were discovered in 1995...": new is redundant.
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729:
Ogilvy, C. S., and Anderson, J. T., – 'and' instead of semi-colon
565:"digits of π all consistent with normality": 'are consistent'?
543:"Salikhov has given the approximation 7.6063" Who is Salikhov?
743:"5 Trillion Digits of Pi – New World Record", Oct 17, 2011.
726:
C. Boyer, A History of Mathematics – more than one instance
1072:
wrt. cycle detection should probably have its own subsection.
755:
Hopefully this is helpful. Good luck with your FAC. Regards,
380:
User:Tony1/How to satisfy Criterion 1a#Eliminating redundancy
1012:
I added the Fourier transform to the engineering section. --
350:
Thanks. Yep I'm fairly familiar with the criteria. Regards,
105:
253:
Stirling's approximation and the Riemann zeta function.
1241:: I think it would be fair to note that the legislature
274:
Sure, that is a good idea. I'll take a stab at that. --
483:
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964:: When was it first speculated that pi was irrational?
396:
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1114:. If you look in the References, those are sources
1273:I hope you did find some of these comments useful.
1171:
Yes, that needs to be fixed. I'll work on that. --
318:Sounds good. The Featured Article criteria are at
717:Holton, David; Mackridge, – missing a first name?
452:{\displaystyle \scriptstyle \pi =Area/radius^{2}.}
451:
302:I was going to add more, if that's okay. Regards,
800:of interest per the history section? In 1775 the
732:Halliday, David; Robert Resnick, Jearl Walker
714:The references need some work for consistency.
385:"Another definition of π, which also relies on
187:The lead contains the following long sentence:
622:"Some Egyptologists conclude" is bordering on
233:, the probability of two random numbers being
83:
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649:"may be easily extracted": easy for whom?
163:This peer review discussion has been closed.
676:(which is not explained until later).
90:
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932:could be used centered at the end of the
657:Sphere#Generalization to other dimensions
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867:A quick Google books search brought up
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1287:One more: Why are the formulas in the
720:OED online", "pi" n.1; "pie" , n.2.
229:, the approximate period of a simple
7:
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655:No problem. It's already covered at
193:is found in formulae related to the
320:Knowledge:Featured article criteria
1110:Hmmm. The sources I see are not
28:
1456:Sure, I'll see what I can do. --
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628:John Taylor (English publisher)
1:
999:: hint to Euclidean geometry?
570:statistical significance test
1373:And another one: Should the
1352:List of formulae involving π
1329:Complex numbers and calculus
478:Thanks for finding that. I
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362:21:25, 13 April 2012 (UTC)
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176:12:44, 11 April 2012 (UTC)
1289:Rapidly convergent series
934:Polygon approximation era
896:Polygon approximation era
211:Einstein's field equation
778:, March 14, 2013 :-) --
700:What, no mention of the
207:Stirling's approximation
1481:April 2012 peer reviews
203:trigonometric functions
930:File:Archimedes_pi.svg
453:
1327:Another one: Section
454:
18:Knowledge:Peer review
515:Thank you. Regards,
393:
40:Previous peer review
1207:Continued fractions
806:Squaring the circle
219:Cauchy distribution
1239:In popular culture
449:
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387:Euclidean geometry
227:Kepler's third law
839:German pi article
826:Comments by Nageh
808:article instead.
215:Gaussian integral
181:Comments from RJH
155:Watch peer review
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117:visual edit
835:Definition
1458:Noleander
1424:Noleander
1406:Noleander
1356:Noleander
1312:Noleander
1256:Noleander
1220:Noleander
1188:Noleander
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1124:Noleander
1083:Noleander
1046:Noleander
1014:Noleander
992:section:
973:Noleander
945:Noleander
912:Noleander
873:This site
855:Noleander
780:Noleander
624:WP:WEASEL
588:Noleander
548:WP:YESPOV
503:Noleander
488:Noleander
338:Noleander
324:Noleander
290:Noleander
276:Noleander
257:Regards,
225:problem,
168:Noleander
1475:Category
1404:Done. --
1254:Done. --
1218:Done. --
1116:about pi
1112:about pi
1042:about pi
997:Geometry
231:pendulum
20: |
140:history
121:history
107:Article
49:Toolbox
776:pi day
241:, and
237:, the
217:, the
213:, the
199:sphere
1443:Nageh
1387:Nageh
1379:Nageh
1333:Nageh
1294:Nageh
1275:Nageh
1139:Nageh
1098:Nageh
1028:Nageh
990:Usage
877:Nageh
149:Watch
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32:Pi
22:Pi
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