Talk:Squaring the circle: Difference between revisions

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|dykdate=7 June 2022|dykentry=... that although the problem of '''[[squaring the circle]]''' with [[Straightedge and compass construction|compass and straightedge]] goes back to [[Greek mathematics]], it was not proven impossible until 1882?|dyknom=Template:Did you know nominations/Squaring the circle}}

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== TheEspen illustrationGaarder Haug ==

Re [https://en.wikipedia.org/w/index.php?title=Squaring_the_circle&curid=201359&diff=957948636&oldid=957945798 this edit]: I'm beginning to wonder if there is a [[WP:COI|conflict of interest]] here. Is {{u|MetricoGeo}} in some way linked to the author of the paper?--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 09:16, 21 May 2020 (UTC)

You cannot say that they are the same area; the very point of the article is that that would require ascribing a finite value to pi (more precisely, the square root of pi). It is misleading and presumptive to put in the caption that they have the same area value. The graphic could also stand with no caption at all.

:Who wrote the new section on squaring the circle? It was not me (MetricoGeo)! This I am sure someone can investigate.

ps If you still think that the image shows a circle and square of the same area then copy it to your computer and zoom in on it. There is actually no circle in the image at all.

:So why did David Eppstein delete it? The Squaring the circle page has a series of references to even books and popular science and non-peer reviewed web-cites. As asked before, how many peer reviewed papers on Squaring the Circle has been published in the last 20 years (in decent journals)? Whoever put in the new section (unknown to me) also seems to have put it under the right section. It is not a section that endorse it. It is simply a section made on the Squaring the Circle page long time ago that simply state "Other modern claims". And under this section two non-peer review books are mentioned. But a peer reviewed paper, that claim to give new light on the problem and also do not hide that it "We could argue that this is bending the rules and moving the problem of transcendental ⇡ into a transcendental velocity between the reference frames, rather than directly into the construction of the Circle and the Square. Still, one could just as well argue that the previous attempts to Square the Circle have not taken into account that observations of space and time are a↵ected by motion, and that space and time are closely connected." https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1514&context=tme is deleted by Eppstein. [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 10:32, 21 May 2020 (UTC)

:Ahaha, I wondered about this deletion, then investigated a bit further. Eppstein that quickly deleted what someone referring this this paper had put on the Squaring the Circle wiki page, is the same guy (active on wikipedia for years) that deleted Haug's wikipedia page some years ago. A wikipedia page that had been there for more than 10 years. Eppstein is clearly allergic to Haug's work, and he want to delete as much of references to Haug's work as possible? The conflict seems to be about Eppstein do not like Haug's view on physics? Who should declare conflict of interest here, do we need to dig up the old wikipedia archives of deletion and debate? Could Eppstein be slightly biased here??? I am just asking! I am not going to edit or write a single world on the Squaring of Circle page, this I leave up to the very Objective types such as Eppstein. Very objective to have series of references to very popular stuff and delete references to work in good journals (if he do not like that person). I suspect it will be deleted, more and more pages of wiki are dominated by science-activists. These are often highly educated scientist, but with very biased view the do not even want to see problems from other angels than their own biased view. (UTC) [[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 11:46, 21 May 2020 (UTC)

--[[User:Justanother|Justanother]] 14:04, 22 August 2006 (UTC)

*Sorry - why is this claim important? The "Other modern claims" section isn't meant to be a list of everybody who's claimed to have squared the circle, just a few of the most important ones. The [[Indiana Pi Bill]], for example, is notorious. Why is this paper from a mathematics education journal considered important enough? Furthermore presenting phrases like "presented an practical way of squaring the circle" is likely to mislead the reader. '''''[[User:Hut 8.5|<span style="color:#FF0000;">Hut 8.5</span>]]''''' 12:42, 21 May 2020 (UTC)

:You are confused. In the first place, it is not claimed that illustrations are exact. They never are. But they convey ideas well. In the second place, the value of &pi; is indeed finite, and so is its square root; if you think otherwise, you're very very confused. Perhaps you mean that its decimal expansion is only finitely long (in popular confusions, that seems to matter). [[User:Michael Hardy|Michael Hardy]] 18:07, 22 August 2006 (UTC)

** Yes, "accelerate the train to a speed relative to the embankment of <math>c\sqrt{1-\frac{1}{\pi^2}}</math>" (roughly 2.84 &times; 10⁸ meters per second) is not exactly "practical". [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:12, 21 May 2020 (UTC)

"The "Other modern claims" section isn't meant to be a list of everybody who's claimed to have squared the circle,". It should naturally be limited to peer reviewed work published in scientific journals and for non-peer reviewed claims only too well known historical disputes that are well documented, such as yes for example The Indiana Pi Bill. How many well known, well documented historical disputes on Squaring the Circle (in modern times, last few hundred years) of any magnitude exist? A handfull at most! This should be minimum requirement for anything on the whole page? Or is the wiki-page an opinion page now where wiki editors can bring in links to work (even non peer reviewed) they just like, and then delete what they dont like, or references to work form people they dont like for whatever reason? But from what I see here now, it clearly looks like what was deleted will be deleted, we now understand why Eppstein deleted it so quickly! His argument for deletion was clearly just something he came up with that made it sound reasonable, but that the writer of the new section was looking straight through (see recent history on the page and arguments). People spending lots of time editing on wiki have likely high status among other active wiki editors, backing each other, so yes I think we know how this ends. Can someone list all the references given on the page and rank them roughly, based on scientific validity and quality, documentation etc., grope into peer-reviewed and non peer reviewed etc.? [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 13:03, 21 May 2020 (UTC)

:Squaring the circle is based on achieving it with a finite number of steps with compass and straightedge. This is known to be impossible. The [https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1514&context=tme paper] introduces all sorts of concepts from the Theory of Relativity and non-Euclidean geometry which are at best speculative.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 13:57, 21 May 2020 (UTC)

I have to confess, I've sometimes wondered if the people (is it two of them now?) who have expressed objections of this kind to this illustration, are under the impression that the impossibility of squaring the circle means that a square and a circle can never have the same area? That's not actually what it says; it just says you can't do the ruler-and-compass construction. [[User:Michael Hardy|Michael Hardy]] 21:41, 23 August 2006 (UTC)

:Wikipedia is not the place to promote work that has not attracted attention and interest from the scholarly community, whether or not that work is technically correct. Including Espen Gaarder Haug's paper is not appropriate, and this has nothing to do with any supposed personal animosity against Espen Gaarder Haug. (I doubt there is any such animosity; [[Wikipedia:WikiProject Deletion sorting/Academics and educators/archive 2|deleting articles on non-notable academic types is commonplace]].) [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:07, 21 May 2020 (UTC)

"** Yes, "accelerate the train to a speed relative to the embankment of <math>c\sqrt{1-\frac{1}{\pi^2}}</math>" (roughly 2.84 &times; 10⁸ meters per second) is not exactly "practical". [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:12, 21 May 2020 (UTC)" XOR'easter is here searching for arguments to delete the reference to the paper. Had XOR'easter read the whole paper would he have seen that this is only one of the special solutions and that even a printer head moving at v>0 as stated in the paper will do. So his indication that one need to move so fast as it is not practical even close to possible is totally false.

::I said finite when I should have said constructible. My bad. From [[pi]] "An important consequence of the transcendence of π is the fact that it is not constructible." My point is that that caption is a lie. Do you argue that point with me?? You say "In the first place, it is not claimed that illustrations are exact.". But doesn't "A square and circle with the same area." make, for all intents, that exact claim? Why bother with that caption. Do you think that you can create a squared circle with pixels? I doubt it. This is not about mathematics, it is about whether a caption in a lie or not.--[[User:Justanother|Justanother]] 15:54, 24 August 2006 (UTC)

Further XOR'easter writes "is not the place to promote work that has not attracted attention and interest from the scholarly community, whether or not that work is technically correct.". I cannot see how any author of any paper has written anything about own paper on Squaring the Circle page and thereby doing self promotion. The paper is one of the very few peer review papers published on Squaring the Circle the last 20 years. And this despute I think will get interesting in the coming months and years, far outside wiki !! XOR'easter are you in any way part of Eppsteins circle? Where you part of working and voting for deleting the wiki page about Haug years back? [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 14:23, 21 May 2020 (UTC)

:::An image is not the same as the object it depicts. The image presently discussed is not a square and a circle with the same area; it ''depicts'' a square and a circle with the same area, subject to the limitations of its format. But every image is limited in precision by its format; this is an inherent property of images. By your reasoning, every image caption in Wikipedia should begin with "Illustration of..." or "Photograph of...". Or perhaps, "A rectangular array of pixels making up an approximate representation of...". [[User:Fredrik|Fredrik Johansson]] 16:22, 24 August 2006 (UTC)

:The "printer head" proposal is still a [[thought experiment]] involving lasers and synchronized clocks, not a practical method. Promotion is not limited to ''self''-promotion. And with [https://en.wikipedia.org/w/index.php?title=Squaring_the_circle&type=revision&diff=957974186&oldid=957962457 this edit], you crossed the [[WP:3RR|3RR]] line, meaning that you could already have been blocked (and willy-nilly casting aspersions upon the character of those who disagree with you is [[WP:NPA|not likely to earn you friends]]). [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:31, 21 May 2020 (UTC)

::::Hi. The problem with your analogies is that this particular article is about the possibility, or impossibility, of physically constructing (presenting) a circle and square of the same area. To then present a circle and and square and caption "whoop, there it is" is misleading. I see this as a special case in that the medium is very much the message. Here is a decent analogy: Suppose there is an article about the impossibility of capturing the image of a spirit (ghost) on film and someone add a photoshopped pic of just that and labels it "Spirit captured on film". I wouldn't be too happy about that one either. That is the real extension of my reasoning. --[[User:Justanother|Justanother]] 14:16, 25 August 2006 (UTC)

Interesting. So XOR'easter want to change that one sentence to theoretical solution rather than practical, do anyone have problems with this, I doubt that the dispute has anything to do with this? Is any other discussed solution to the Squaring of the Circle more practical as they exclude 100 years + last discovery on Minkowski Space-Time?

:::::You ''can'' represent the square and circle of equal area ''exactly'' in a computer and render them from that representation. Although I doubt this image was rendered from such a representation, there is nothing impossible about it. Whether the construction is ''physically'' possible has nothing to do with it. It is also impossible to physically construct a straight line, but I'm not seeing any complaints about that. [[User:Fredrik|Fredrik Johansson]] 15:08, 25 August 2006 (UTC)

I am looking up old wiki archives now. So Eppstein was as stated earlier one of the persons active on wiki that bashed Haug on wiki talk pages for his lack of qualifications years ago and successfully got the 10+ year wikipge about him deleted, with the help of vote from? XOR'easter surprisingly was one of the others bashing Haug for his physics in 2018 and working hard to delete the wikipedia page about him. A wiki page that had been there long over 10 years was attacked by XOR'easter and Eppstein. Did Eppstein message you XOR'easter for support also here now? I am just asking you XOR'easter, if this is what happened now? Do you think you and Eppstein think the past here could make you the slightest biased? Is this how wikipedia work these days? Has it become corrupted with circles of people spending much time here, becoming buddies defending each others editing, rather than trying to get the best out of wikipedia? Just asking, please explain to us non frequent visitors how this now will work? Will Eppstein and XOR'easter and a few others in the Eppstein-circle now vote for deletion of what a user wrote, and show how democratic and fair wiki editing is, with voting process and all? Yes we know the result of this dispute (for the year being), take care!! [[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 15:01, 21 May 2020 (UTC)

::::::Help me out here. How would you "represent" a square and circle of equal area in a computer and I don't mean simply storing or generating the equations. That is no different then writing them down on a piece of paper and even I can do that.--[[User:Justanother|Justanother]] 16:43, 25 August 2006 (UTC)

:::::::That's what you do. Use a computer algebra system that can work symbolically with series expansions, and you can easily represent pi exactly and do calculations with it. Yes, you can do that too (you can do everything a computer does, except perhaps slower), though the arithmetic involved in rendering the circle based on the exact representation (write down exactly how large a part of pixel (x,y) is covered by the circle and then round that to an even number of 255ths for each x and y) is going to be so tedious that you'll wish you did use a computer, and I'll not stay up waiting for you to finish. :-) [[User:Henning Makholm|Henning Makholm]] 18:09, 25 August 2006 (UTC)

LOL out of the thousands of wiki editors, here we have Eppstein quickly deleting a reference to Haug's work someone put on the Squaring the Circle Page (and it was not put there by me either). Then out of the blue: XOR'easter shows up, coming to defend Eppstein's decision, throwing in all types of weak arguments and threatening by blocking's people. XOR'easter off course totally unbiased, except for Eppstein and XOR'easter both part of the little circle that worked hard to delete a wikipedia page about Haug that had been there for over 10+ years before they got it deleted. XOR'easter back in 2018 bashed Haug's physics work also on wikipedia, so the Eppstein-circle is off course unbiased, but as people spending lots of time on wiki to get some wiki status, we yes know how it ends = deletion of references to science not in favor of scientist activists!! [[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 15:29, 21 May 2020 (UTC)

My points are:

:{{tq|So XOR'easter want to change that one sentence to theoretical solution rather than practical}} &mdash; no, I don't want any of those sentences included at all, for reasons I have already explained clearly.

* It is indeed possible for a square and a circle to have the same area (the impossibility asserted by the theorem is not that that is impossible, but rather that the rule-and-compass construction is impossible.

:[[Wikipedia:Articles for deletion/Espen Gaarder Haug (2nd nomination)|The deletion of the Espen Gaarder Haug article]] was the result of community consensus, arrived at through open discussion and debate, and [[Wikipedia:Deletion review/Log/2018 October 11|confirmed in a second round of discussion]], not the conspiracy you seem to want it to be. Sorry to disappoint! [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 15:42, 21 May 2020 (UTC)

Interesting: XOR'easter wrote "His physics "work" has been rightly ignored by the scientific community. XOR'easter (talk) 15:15, 25 September 2018 (UTC)". Is your claim "has been rightly ignored" based on number publications in certain journals or of the number of references within just months or years it is published? Is it correct for a physicists like yourself to claim work published in peer reviewed journals, some under well known platforms as Springer and Elsevier to be called "rightly ignored"? Even the way you word yourself clearly indicated Prejudice, because how many fresh papers do we know if will be well cited or not, just months and a few years after publication?

* Everybody knows that illustrations in geometry articles are ALWAYS approximations, whether made with pixels or with ink on paper. A theorem of geometry may say (paraphrasing) "This square has the same area as that rectangle", and accompany it with an illustration. The square and the rectangle as abstract mathematical objects do have EXACTLY the same area, and the square and the rectangle in the illustration in the book are approximations. Everyone realizes that they're obviously always approximations, so it is not a ''lie'' to say they have the same area. The assertion that two things have the same area is naturally understood to refer, not to the physical illustration, but to the abstract mathematical objects that they illustrate.

And yes there are thousands of editors on wikipedia, do you think you and Eppstein that worked hard on deleting the wikipage about Haug, and bash his research, not are in any way biased? You pretend it was a large number of unbiased voters, this was not at all the case, mostly what now looks like a little circle off frequent wiki backing each others editing rather than try to maximize best for wiki . Can you also look up if peer reviewed research with few or no references by other peer review research is referred to on other wiki-pages? For me it seems like Eppstein and you are highly biased, and that you out of the thousands of wiki editors should have got others not involved in that episode to make the decision on what someone now tried to contribute with on the Squaring there Circle page now. You have not come with any solid argument that not have been easily refuted. What is the point of a talk page and discussion page when a little closed Eppstein-circle (that clearly are very biased) just can overrun any common sense and arguments ?[[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 16:22, 21 May 2020 (UTC)

[[User:Michael Hardy|Michael Hardy]] 03:01, 25 August 2006 (UTC)

:I'm also getting worried about [[WP:SOCK]] here. At this rate the article will be protected.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 16:44, 21 May 2020 (UTC)

:::Hi. I appreciate your point of view. I am not a mathematician and I actually came to the article by way of the [[Timecube]], which was referenced in another article I was reading. I had never encountered the "squaring the circle" and I found it interesting. The more we discuss, the more interesting I find it. My conclusion is while a square and a circle can, in theory, have the same area, there is NO way to represent that in the physical universe, not with ink or pixels nor with molecules or atoms or subatomic particles or whatever. That is pretty cool to me and I found that the caption detracted from my feeling of wonder. I think the simple caption "Squaring the circle" serves well. --[[User:Justanother|Justanother]] 14:06, 25 August 2006 (UTC)

::Sock- or meat-puppetry seem quite possible. I wonder if the allegations of conspiracy aren't a bit of [[psychological projection|projection]]. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 16:59, 21 May 2020 (UTC)

That two people having worked to delete a wikipedia page about Haug and bashed his research on wikipedia are exactly the same two (Eppstein and XOR'easter) that now have deleted what someone else than anyone on the talk page, have edited on the Squaring the Circle page, is clearly amazingly biased against Haug (Eppstein and XOR'easter). And now attempts to get focus away from this fact. If you think it is me that put in the recent reference or edit on the Squaring the Circle page, then you are very wrong, and now indicates this to take attention away from the biased non-wikipedia policy editing. Just that you are frequent on wikipedia and have contributed to editing many articles do not automatically mean you can "monopolize" your bias, as I see the one editing the page (that got deleted) now are pointing out. But yes we know how this ends, the little biased circle empty for good arguments, now work to block and expel people that have edited a page against their biased view [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 17:10, 21 May 2020 (UTC)

:::: Your conclusion is wrong. The impossibility of squaring the circle is '''not a statement about the physical universe'''. It is a statement of a particular '''model''' of certain aspects of the physical universe, namely the model of "ruler-and-compass Euclidean geometry with no implicit continuity assumptions". In that '''model''' there are no circle-square pairs with equal areas, which mathematicians and physicists consider a ''deficiency'' of the model, i.e. the model is '''wrong'''. Indeed, what most phycisists and quite a lot of mathematicians will think of when you say "Euclidean geometry" is not that wrong model, but another one, namely "'''R'''² with the Euclidean metric". And ''there'' all circles ''have'' equal-area squares, easily. The model in which circles can be squared (which is the one the image seeks to illustrate) is universally considered a better fit with the physical universe than the one where they cannot. (However, it is not an exact match: General Relativity says it is incorrect, and if you want to be completely anal about it circles cannot be squared in the GR universe, simply because ''a perfect square is an impossible figure in GR'', except - perhaps - in extremely extraordinary times and places). [[User:Henning Makholm|Henning Makholm]] 15:06, 25 August 2006 (UTC)

:Do you have any actual arguments for the inclusion of this content, or are you just going to accuse people of being biased? Because the latter [[Ad hominem|isn't an argument]]. '''''[[User:Hut 8.5|<span style="color:#FF0000;">Hut 8.5</span>]]''''' 17:19, 21 May 2020 (UTC)

:::::Wrong again, huh? My conclusion was "my conclusion" and I still like even if I cannot intelligently discuss theoretical physics with you. Though perhaps I should say NO way to physically represent it since that is what I meant, and that is what I took the original attempt with ruler-and-compass to be a subset of. But perhaps I am completely missing what mathemeticians love most about the problem and trivializing it for you. Sorry, then. But I certainly think that attributing to the image that it seeks to illustrate an alternate model where you can '''draw''' a squared circle is a bit of a stretch. Actually, quite a large stretch.--[[User:Justanother|Justanother]] 16:43, 25 August 2006 (UTC)

At the risk of stepping into what is clearly at least a one-sided personal dispute (with poor grammar and spelling to spice it up), I support the reverts and oppose the inclusion that was attempted. It was strangely phrased (with implicit praises to the author), it gave undue weight, and is out of step with the rest of the article. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 17:23, 21 May 2020 (UTC)

::::::Not a stretch at all. Illustrating a circle with the same area as a square is piece of cake, even though the illustration is necessarily approximate in pixels. That concept exists in the Euclidean geometry model, but not in compass-and-straightedge geometry model, which is really the point of the whole concept of "squaring the circle" and this article. [[User:Dicklyon|Dicklyon]] 17:41, 25 August 2006 (UTC)

"The paper introduces all sorts of concepts from the Theory of Relativity and non-Euclidean geometry which are at best speculative." Please be more specific. Are you of the opinion that special relativity is speculative or what? Have you not studied the Squaring of the Circle page in its current form? "Although the circle cannot be squared in Euclidean space, it sometimes can be in hyperbolic geometry under suitable interpretations of the terms.[12][13] As there are no squares in the hyperbolic plane, ". Why are then this new edit discriminated?

::::::To Justanother: I see now that I may have misunderstood what you were trying to say. Apologies. I still think you are wrong, but in a different way: when you say that one cannot physically represent the circle you are forgetting that the word "represent" implicitly says that there is an idealization taking place: the representation will always be cruder than what it represents. So a roughish circle and square drawn in freehand with charcoal on a bumpy wall can quite well ''represent'' the mathematical perfection of a circle being squared. If you want to have the circle as a mathematically perfect ''and'' tangible object, with no representation going on, of course you can't: There will always be bumps and fuzziness at the atomic level no matter how well you trim and polish it. But that is independent of whether you intend to square that circle or not. [[User:Henning Makholm|Henning Makholm]] 17:58, 25 August 2006 (UTC)

So why was the edit deleted? Well non of the arguments so far have held water. So it now seems to boil down to XOR'easter latest claim argument for deleting, namely "curprev 16:28, 21 May 2020‎ XOR'easter talk contribs‎ 37,202 bytes -614‎ Undid revision 958015295 by 141.0.150.76 (talk): no, this paper has not received attention, and this edit violates 3RR after a warning thank Tag: Undo" Has not revived attention? Compared with what? Can someone go though when the links to the various pages the Squaring the circle pages link too, when they where added and what attention they had got at that time? I doubt the Eppstein-circle will do any serious quantitative work on that, as it will almost for sure fall in their disfavor! Best luck forward with the biased editing, and also I see XOR'easter now is so irritated he tries to get me banned from even writing discussions on the talk page. Will he also try to delete what has been discussed here? [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 17:43, 21 May 2020 (UTC)

:::::::I think perhaps we see here the difference in mindset between the mathematician and the engineer (smile). First, let's get representation out of the way. Yes, anything can represent anything else. That, after all, is the basis of language; that we can represent things and we can share a set of representations. So let me strike any use of the word representation on my part when I simply meant construction. So "My conclusion is while a square and a circle can, in theory, have the same area, there is NO way to construct that in the physical universe, not with ink or pixels nor with molecules or atoms or subatomic particles or whatever." So the point I make about the illustration is the one I brought up previously regarding this being a special case where the caption on a representation may imply that it is a construction.--[[User:Justanother|Justanother]] 20:52, 25 August 2006 (UTC)

:As I said above, the "Other modern claims" section is not meant to be a comprehensive list of everybody who has claimed to have squared the circle. If it did then it would be enormous. It just includes a selection of the more prominent ones. The [[Indiana Pi Bill]] is very well known. [[Carl Theodore Heisel]] is a sufficiently well known crank to get his own Wikipedia article. The other example has at least been mentioned in a book written by someone else. So what attention has this particular claim got - has it been discussed in books, articles, papers etc? Because if it hasn't then it's hard to argue it has had any impact at all. This claim is hardly cutting edge research, it was written by a nonspecialist (according to his now-deleted Wikipedia page he's a specialist in mathematical finance) and was published in a journal focusing on undergraduate mathematics and mathematics education. '''''[[User:Hut 8.5|<span style="color:#FF0000;">Hut 8.5</span>]]''''' 17:58, 21 May 2020 (UTC)

::::::::It seems that you are setting your criteria for "constructing in the physical universe" so narrowly that the physical universe can contain no circles at all. That is fine, but has nothing to do with squaring those nonexisting circles. However, for any reasonable sense of "exist" that allows any (Euclidean) circle to exist physically, it holds that a square with the same area can also exist. [[User:Henning Makholm|Henning Makholm]] 21:35, 25 August 2006 (UTC)

::Sorry for sleeping through so much of this discussion, but I think it's worth mentioning that the journal the article was published in, ''[[The Mathematics Enthusiast]]'', is not included in [[MathSciNet]] nor [[zbMATH]], unlike almost all serious mathematics journals. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 18:07, 21 May 2020 (UTC)

Come on stop pretending not biased. Look at the many references on the Squaring the Circle page:

:::::::::Hmmm, good point. Perhaps the physical universe then contains no circles at all and your formulas are but representations of an idealized universe. Useful represenations though, no? Yes, I see that if we posit that circles exist then so can this. I stand corrected, or perhaps enlightened is a better term.--[[User:Justanother|Justanother]] 21:42, 25 August 2006 (UTC)

Youtube: I assume they get linked to based on number off views. "James Joyce Quarterly" included in [[MathSciNet]] nor [[zbMATH]]? long series of references not included in these. You have made a biased decision. Your first reason you stated for doing so clearly did not held water. Then the XOR'easter was "called in" with all arguments refuted. So please list now why the last edit was deleted? Can we get a summary from XOR'easter that deleted it last time may be?[[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 18:18, 21 May 2020 (UTC)

::::::::Now I'm really confused. I thought I was going to be able to tell if you were an engineer, or a mathematician. But your words imply you must be neither. The article, by the way, is about mathematics. [[User:Dicklyon|Dicklyon]] 21:03, 25 August 2006 (UTC)

:The ''James Joyce Quarterly'' does not pretend to be a mathematics journal, so its exclusion from mathematics indices is unsurprising. Unlike ''The Mathematics Enthusiast''. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 18:24, 21 May 2020 (UTC)

Yes makes exceptions and come up with criteria to fit own biased view. Youtube is not a math journal so that you have accepted I see. Some workbook in mathematica is not in the list so that can be linked to, non peer reviewed books not in the list that can be linked to, lectures of various sorts can be linked to. You stated "is not included in [[MathSciNet]] nor [[zbMATH]], unlike almost all serious mathematics journals. " so almost? how many serious journals not in this list, is it 1 to 5 if so you must remember them, is it more than 10, more than 50? So the argument now for your vote for deletion is that the journal is not in these two lists?[[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 18:32, 21 May 2020 (UTC)

:::::::::What does my profession have to do with the price of tea in China (yes, now I am an international economist). My point vis-a-vis the article is one of communication and logic, semantics if you prefer, not of mathematics. And I don't think I was picking a nit for the reasons given previously.--[[User:Justanother|Justanother]] 21:45, 25 August 2006 (UTC)

:The only YouTube video used as a reference is a [[Numberphile]] video, which is no worse than semi-respectable, and it is about the [[Indiana Pi Bill]], which is a topic of well-established notability regardless. And even if some of the existing references are poor, that's not an excuse to add more. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 18:38, 21 May 2020 (UTC)

Sorry to point it out XOR'easter but your claim here is evidently false. You state ":The only YouTube video used as a reference is a [[Numberphile]] video," this is false The link too "2000 years unsolved: Why is doubling cubes and squaring circles impossible?" is also another youtube. And I see you are working hard to get me blocked for posting out politely error and weaknesses in your argumentation. And even if on a academic platform also "the Squaring the Circle and Other Impossibilities, lecture by Robin Wilson, at Gresham College, 16 January 2008 " is just a film, what is the criteria for ranking filmed lectures higher than peer reviewed journal research? I have nothing against these linkes, the YouTube and lecture film is informative and useful, what I am against is your biased view and from now working to block me even to point out the weakness and error in your argumentation! [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 18:46, 21 May 2020 (UTC)

::::::::::Your comment re "difference in mindset between the mathematician and the engineer" led me to believe I was going to learn which mindset your were. Nothing at all about your profession. If you have a point about improving the article, please do re-state it, as it has long since been lost in the banter. [[User:Dicklyon|Dicklyon]] 22:05, 25 August 2006 (UTC)

:Sorry, but no. I said ''used as a reference'', because I meant ''used as a reference.'' [[Wikipedia:External links|External links]] are not the same as references. And that video is by [[Burkard Polster]], a mathematician and published author who is, if anything, more conscientious than Numberphile. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 18:54, 21 May 2020 (UTC)

okay point taken on your last argument, so only 1 youtube that has passed and used as reference in addtion to non peer reviewed books, dictionary etc.. And more YouTube etc used in external links. Glad we got it right! Thanks!

==Two objections to this article==

It seems to me that much of the arguements on this talk page revolve around the following, "The circle can be squared, but not with a compass and straitedge (or even with a ruler)".<br>

It seems to me that this article essentially boils down to, "If we deny ourselves the tools that solve this problem (squaring the circle), then this problem is unsolvable. But, if we allow the use of the tools that solve this problem, then it is indeed solvable." It seems to me that such a statement could be made about most any complex mathematical problem. Although it was a tremendous mathematical breakthrough to demonstrate that the circle indeed cannot be squared through the use of a compass and straightedge and although it may be an interesting historical note to point out how many countless untold man-hours of work have been wasted on attempting to prove this one way or another, now that we can actually square the circle (albeit using tools other than compass and straightedge), this problem loses much of its meaning.<br>

Furthermore, we have two statements which, when analyzed, would seem to create a logical fallacy.

* Since we can never exactly determine the precise value of the square root of pi, let alone the square root of pi, we can never truly draw a square with the same area as a circle.

* We can never truly draw a square with the area of a circle exactly, since pen/paper or computer pixels, whatever, can never be absolutely precise enough.

Since pen/paper, whatever, is inherently "not good enough", then can't we say that this problem is solvable, as pen/paper or computer pixels or whatever are able to come as close as we can calculate? In other words, even though the calculations are "off", so is the medium that we are using to represent the problem and the medium that we are using to represent the problem is off by a greater amount than our calculations are off by. Thus, we can draw a square with the same area as a circle, or at least it's the same area as far as we can accurately measure.<br>

Note, there were two objections to this page in the preceding statements.

*If we deny ourselves the tools that solve this problem (squaring the circle), then it is unsolvable. But, if we allow the use of the tools that solve this problem, then it is indeed solvable.

* Although we can mathematically prove that we can never accurately draw a square with the same area as a circle, our drawing methods are "off" by a greater amount than our calculations are and thus, as far as we can determine based on our drawing methods, it can be drawn. [[User:Banaticus|Banaticus]] 06:19, 19 September 2006 (UTC)

[[User:Banaticus|Banaticus]] 06:19, 19 September 2006 (UTC)

Still what is the summary for deleting the new edit with the reference (an edit never done by me)? What arguments are you holding on to for this decision?

:But the arguments on the talk page are just that; arguments. Is there anything about the article that you see needs improving? [[User:Dicklyon|Dicklyon]] 13:29, 19 September 2006 (UTC)

And why I am getting warnings I will be blocked because of this discussion ? (I mean XOR'easter clearly reported me, despite I point out exactly why I mean he and Eppstein is biased. And I have politely answered any argument!). If loosing arguments, get your opponents blocked!! [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 19:01, 21 May 2020 (UTC)

Banaticus' objections are silly. His first bullet point is right, but it's silly. The point is that the fact that those particular tools are inadequate is very very far from trivial. Yet Lindemann proved it, by building on the work of many predecessors. As far as "drawing methods" go, Banaticus' statement is obviously correct, even without any of the work of Lindemann or his predecessors. But who cares? It's really not relevant to this article. [[User:Michael Hardy|Michael Hardy]] 16:13, 19 September 2006 (UTC)

:{{u|EdJohnston}} [https://en.wikipedia.org/w/index.php?title=User_talk%3AMetricoGeo&type=revision&diff=958038271&oldid=958024753 warned you] that you are risking a block because you are not, in fact, being civil. Instead of showing that you understand the points made by myself and four others, and responding to them in ways that indicate you are [[WP:NOTHERE|here to build an encyclopedia]], you throw around accusations of bias and conspiracy. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 20:00, 21 May 2020 (UTC)

I am asking why the edit will has been deleted. I have pointed out that among thousands of wikipedia editors the one first deleting with a weak argument not holding water was one of the persons before working to delete Haug's wikipedia page. And this was not a new page, this was a page that had been on wikipedia for 10 years. Next I pointed out that the one coming with other arguments to delete was XOR'easter. It is a false claim to claim I [[WP:NOTHERE|here to build an encyclopedia]]. This because I have not written a single word on the Squaring the Circle page, not under any other names. I have however witnessed what I still claim is biased. History will tell, anyone can read this also in the future (as already backed up) and see the arguments posted here. You claim I am holding on to conspiracy theories! This is also false. Among thousands of wikipedia editors we now have 2 that have attacked Haug and bashed his research in the past evidently that have deleted the edit referring to his work. If I am considered to be a conspiracy theories for pointing out this, and questioned if this not lead to bias then please feel free to call me for so. And I am again now asking why the edit is deleted. The point of a talk page must be see what arguments hold some scientific standards. Lets list the arguments given:

::now that we can actually square the circle (albeit using tools other than compass and straightedge), this problem loses much of its meaning.

1. XOR'easter claims I am a conspiracy theorist for pointing out that Eppstein and XOR'easter can be biased because they have been writing very negative about Haug's research before and being part of a very small grope deleting the wikipage about him, all evident from the wikipedia archives. Is this a good argument for deleting a edit on the Squaring the Circle page not done by me?

:Again: silly! "Now that"?? As if we couldn't do that before? People have '''''always''''' been able to "square the circle" that way, but that doesn't deprive the problem of any of its meaning. The problem is not about drawing pictures. Everyone's always been able to draw sufficiently accurate pictures. [[User:Michael Hardy|Michael Hardy]] 17:28, 19 September 2006 (UTC)

2. XOR'easter pointed out the solution presented in the paper at all not was practical by using a special case presented in the paper that gives a solution at velocity (roughly 2.84 &times; 10⁸ meters per second) is not exactly "practical". I pointed out this was not the case if he had read the whole paper, as one have solutions for any v>0. So this was just nonsense. Also I pointed out that Squaring of the Circle in general a theoretical exercise and asked why this was less practical than other solution. Then he seems to conclude that he basically had no point with his point that he wanted deletion for other reasons.

::Agreed! Really any considerations about actual drawings are totally irrelevant to this topic. A good way to think of this particular topic is to consider some of the highly complex problems that CAN be solved using ruler and compass (e.g. regular 17-gon, and many others), and compare these with the fact that squaring the circle does not belong to the class of "problems solvable by ruler and compass". [[User:Madmath789|Madmath789]] 17:37, 19 September 2006 (UTC)

3. Eppstein pointed out that The Mathematics Enthusiast, is not included in MathSciNet nor zbMATH, unlike almost all serious mathematics journals. I pointed out this was not the case with series of references on the wikipage. It refers to 1 youtubes, to non peer received books, it has also external links to more youtubes, to mathematica work books etc. Eppstein also do not answer what he mean with “almost all”. Is 10, 20, 50 journals still of quality that he think should have been on that list?

:::"If we deny ourselves the tools that solve this problem (squaring the circle), then this problem is unsolvable. But, if we allow the use of the tools that solve this problem, then it is indeed solvable." I think a lot more emphasis should be placed in this article on the fact that this problem is, indeed, solvable. It's just that it's not solvable with finite methods. For instance, the opening image and paragraphs could be rewritten as follows:

:::Image -- Squaring the circle: the areas of this square and this circle are equal. In 1882, it was proved that this figure cannot be constructed using only finite methods, although it is constructible using other methods.<br>

:::'''Squaring the circle''' is the problem proposed by [[ancient]] [[geometers]] of using finite methods (construction using an idealized [[compass and straightedge]]) to make a [[square (geometry)|square]] with the same area as a given [[circle]]. In 1882, the problem was proven to be impossible using finite methods, although the problem can be solved using other methods. The term ''[[numerical integration|quadrature]] of the circle'' is synonymous.

:::Statements in the body of the article such as, "If one solves the problem of the quadrature of the circle, this means one has also found an algebraic value of π, which is impossible." And, "The mathematical proof that the [[numerical integration|quadrature]] of the circle is impossible has not proved to be a hindrance to the many people who have invested years in this problem anyway." These statements, taken at face value, imply that ''no'' method has been yet found for squaring the circle, that we cannot, using any method, square the circle. These statements (and others like them) should be rewritten so that the focus of the article is in the right place -- that squaring the circle is only impossible using finite methods.

:::Furthermore, perhaps there should be a greater emphasis placed on "finite methods" and defining exactly what that is. The article does already say, "It is possible to construct a square with an area arbitrarily close to that of a given circle. If a rational number is used as an approximation of π..." Yet, as I pointed out, this does mean that the circle can be squared using only the physical tools of compass and straightedge (as they differ from the nonexistant idealized forms of a compass and straightedge). Perhaps, in addition to placing greater emphasis in this article on the fact that this "problem" is solely a "well, let's limit ourselves to using only these tools then try to solve it" type of problem (which should greatly cut down on the number of people who say, "But wait, this problem ''has'' been solved!"), there should be greater emphasis placed on what finite methods are and how "finite methods" in abstract and an idealized compass and straightedge differ from the physical real life tools of an actual compass and straightedge. [[User:Banaticus|Banaticus]] 18:29, 19 September 2006 (UTC)

4. XOR'easter wrote “Instead of showing that you understand the points made by myself and four others,” Please point out exactly what point I do not understand since you comes with such non specific claims and accusation that even can lead to my blockage.

::::I'm going to look at the article within a few days and maybe alter the emphasis in spots, and add some further explication. [[User:Michael Hardy|Michael Hardy]] 23:08, 19 September 2006 (UTC)

Feel free to list more arguments already given and we can discuss if they hold etc. Deletion on wikipedia can not be monopolized by small editor circles. This is why we have such talk pages!

:::::More emphasis has now been placed in the article on the impossibility of squaring the circle only relating to a restriction that only finite methods can be used. The article still needs more work, though. [[User:Banaticus|Banaticus]] 19:08, 25 September 2006 (UTC)

::::::Nice revision, Michael Hardy. :) [[User:Banaticus|Banaticus]] 20:59, 25 September 2006 (UTC)

[[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 20:24, 21 May 2020 (UTC)

Completely agree with Michael Hardy here: Banaticus's point is ridiculous. Not understanding what the phrase "Squaring the Circle" means he conflates it with another problem of drawing a near-enough accurate picture, or on the other side with the abstract existence of said square. Neither of these are at issue: at issue is solvability using particular methods connected to polynomial equations. [[User:Eluard|Eluard]] ([[User talk:Eluard|talk]]) 10:36, 15 March 2011 (UTC)

:My very first statement on this matter was that it is inappropriate to use Wikipedia {{tq|to promote work that has not received attention from the scholarly community}}. You have ignored this and never provided ''verifiable, documentable evidence'' of such attention, even to the extent that one might reasonably expect for a niche-interest topic. The addition you have been trying to defend is a bad addition and would have been so ''even if the paper weren't by Haug.'' In fact, when I made [https://en.wikipedia.org/w/index.php?title=Squaring_the_circle&diff=prev&oldid=957995638 that edit], I barely remembered Haug's name and had only a vague sense that it was familiar. So, your entire conspiracy theory is an irrelevant tangent. And yes, by this point, you are well into the regime of conspiracy theories. You write, {{tq|I have pointed out that among thousands of wikipedia editors the one first deleting with a weak argument not holding water was one of the persons before working to delete Haug's wikipedia page. And this was not a new page, this was a page that had been on wikipedia for 10 years.}} First, no, {{u|David Eppstein}}'s argument wasn't "weak", but really quite reasonable: "there are lots of non-compass-and-straightedge ways of describing squares of area π, so what makes this overcomplicated one special?" [https://en.wikipedia.org/w/index.php?title=Squaring_the_circle&type=revision&diff=957887375&oldid=957883838] Second, yes, there are thousands of Wikipedia editors, but ''not all of them regularly edit articles about mathematics.'' That's kind of an important point. Both David Eppstein and I are regulars in [[Wikipedia:WikiProject Deletion sorting/Academics and educators|deletion debates about scholars and scientists]], and like all regulars there, we've seen far too many to bear strong feelings about any of them. Sometimes we regulars advocate keeping a page, and sometimes we advocate deleting it, and we don't always agree. In [[Wikipedia:Articles for deletion/Espen Gaarder Haug (2nd nomination)|the case of Haug]], we were two out of six people all arguing that he fell short of notability standards. Third, the article on Haug only existed because [[Wikipedia:Articles for deletion/Espen Gaarder Haug|the "delete" result of an earlier AfD in 2008]] was ignored, presumably due to a clerical error somewhere. Fourth, the fact that an article has existed for 10 years doesn't automatically mean it should keep existing; mediocre pages and [[Wikipedia:List of hoaxes on Wikipedia|even outright hoaxes]] have lasted longer than that, just because it's a big place and nobody noticed. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 20:58, 21 May 2020 (UTC)

Squaring the circle is one of the [https://www.cut-the-knot.org/arithmetic/antiquity.shtml Four Problems Of Antiquity]. Although not explicitly stated, it is assumed that these constructions should take place in [[Euclidean space]]. What the Haug paper appears to be saying is that by moving the goalposts into non-Euclidean space, the problem becomes solvable. As a general rule, if you can't get an exact answer on a calculator, you can't do it in Euclidean space in a finite number of steps either.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 21:19, 21 May 2020 (UTC)

==Michael Feldman's Whad'Ya Know on-line quiz==

:I think that rule is oversimplified. Most calculators won't give you an exact answer to <math>1/7</math> or <math>\sqrt{2}</math> either, but both are easily constructed by compass and straightedge. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 21:24, 21 May 2020 (UTC)

This week's question for the Whad'ya Know on-line quiz is "Can you square the circle?" The official answer is no, citing this article as the source. However, this article answers the question, "can you make a square of the same area as a given circle with only a ruler and a compass?" As numerous participants have noted above, without the straightedge-and-compass limitation, the circle can be squared. Just make a square with a side the length of the circle's radius times the square root of pi. I am disappointed to see descriptions of this problem that do not explain the straightedge-and-compass limitation. The quiz question is available this week at:

::Yes. I think the main thing, though, is the goalpost-shifting. As is well known, if you change the rules, the game becomes winnable. The article seems to suffer from a bit of [[Wikipedia:Recentism|recentism]] in this regard, talking more about hyperbolic space than about the quadrature methods known since Hellenistic times. I added a little about Greek solutions, but I think that could be expanded. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 21:30, 21 May 2020 (UTC)

http://notmuch.com/Quiz/

In later weeks, it will be available at:

http://notmuch.com/Quiz/past-weeks.html

[[User:Rrenner|r3]] 13:55, 30 October 2006 (UTC)

{{collapse top|reason=Further comments by [[Wikipedia:Sockpuppet investigations/QuantitativeGeometry|blocked sockpuppets]]}}

: Now accessible at [http://notmuch.com/Tools/quiz-past-question.pl?start_date=20061028&category=3 this link] as of July 2009 [[User:Joe Hepperle|Joe Hepperle]] ([[User talk:Joe Hepperle|talk]]) 22:16, 6 July 2009 (UTC)

::I edited the Wikipedia entry to add Haug's article, not MetricoGeo, whoever they are. I stand by my opinion (shared by many people in my community where I first saw the paper) that it is a valid and interesting contribution. Judging from the above naive attempts at a physics discussion about it, not anyone here who's against it has credentials to judge it. In particular, Haug's work (like the majority of works on relativistic physics - including academic ones) is clearly a thought experiment, so the argument that it's impossible to realise it in practice is ludicrous! - HOWEVER, it could be realised in a particle accelerator or in nanoscale (and it would be interesting - I've seen such works published in Science or Nature). I don't have any personal interest in promoting Haug's work, as I was accused above. I merely briefed his bio to distinguish him from other Espen Haug's on Wikipedia, because his entry didn't exist in English (your impression that my objective note was of excessive praise only realises how unfairly he's been treated here). Now I can see that the asking absence of Haug's scientific contributions from Wikipedia (he's a celebrated expert and author in mathematical finance) is a result of a David Eppstein's personal wars with his imaginary (and real?) enemies. I contacted Haug and he is aware of Eppstein's actions, but he doesn't know Eppstein and his hostile motivations. To give him the praise he actually deserves: Haug is an established researcher in mathematical finance, gained a worldwide recognition as a lecturer and the author of bestsellers on derivative instruments (in English and even translated to Chinese). He collaborated with many distinguished names in his field, and also published physics works together with academic physicists. His works on physics (or natural philosophy) as a sole author are of a typical cross-sectional kind and it takes a bit more than a narrow mind to understand and appreciate them. I refuted all arguments against my edit. In particular, I responded that Haug's paper, typically of works of this kind (quoted in that section or in other similar contexts on Wikipedia) wasn't cited and won't be cited much, but XOR'ester twisted my statement to contrapose Haug's paper with a mathematical article on a more general problem of hyperbolic spaces. Summarising, it looks to me like XOR'easter and Eppstein used all tricks in the book to prevent me from contributing to this entry, and the achieved "consensus" (on this or the scandalous removal of EG Haug's Wikipedia page) is clearly the action of a clique you have formed here. Not the first such a story on Wikipedia from what I've been told. --[[User:UK-WK-ed|UK-WK-ed]] ([[User talk:UK-WK-ed|talk]]) 10:05, 29 May 2020 (UTC)

:"Just make a square with a side the length of the circle's radius times the square root of pi." -- Just? There is not, in fact, any way to do this in the physical universe; any such measurement will be only an approximation. -- [[Special:Contributions/184.189.217.210|184.189.217.210]] ([[User talk:184.189.217.210|talk]]) 21:48, 6 February 2017 (UTC)

Highly remarkable, but no big surprise, as I told in the beginning we know how this end! MetricoGeo got even blocked on own talk page from discussing why was blocked from just asking critical questions about the editing of C Eppstein and XOR'ester. MetricoGeo clearly never wrote a single word on the Squaring the circle page, that is clearly UK-WK-ed that have done. MetricoGeo was falsely accused for this despite explaining not written a single comma on the Squaring the Circle page. Eppstein and XOR'ester refused answering questions when it was pointed out weaknesses in their arguments for deleting the edit done by UK-WK-ed. Instead they use well known control and manipulation techniques such as claiming "“Instead of showing that you understand the points made by myself and four others,”" without answering what MetricoGeo or others asking precisely what not have understood in their arguments. Interesting the last message MetricoGeo was allowed to state on own talk page arguing for why should not be blocked was

== Squaring the circle and the longitude problem ==

"Is Squaring the Circle in Minkowski Space-Time also not purely mathematical? You have yourself pointed out it is not practical so then it falls in under pure mathematical and geometrical?. As I have pointed out before on the talk page of the Squaring the Circle Page the one sentence put in by others than me that the paper referred to gave a practical solution could naturally be edited. But CXOR'easter then claimed this at all not was an issue causing the deletion. So again I keep asking why it was deleted? Now you will block me for asking you questions about your arguments? Is it considered a personal attack to point out serious flaws in your argumentation? Or can perhaps blocking someone for question and pointing out flaws in your argumentation be seen as a attack on free speech ???? MetricoGeo (talk) 09:07, 24 May 2020 (UTC)" https://en.wikipedia.org/wiki/User_talk:MetricoGeo

According to De Morgan's ''A Budget of Paradoxes'', there was a good deal of confusion in 18th and 19th century England on the problem of squaring the circle. Many believed that Parliament had established a prize for solving the problem. De Morgan claims that this was because people confused the problem with the Longitude Problem (for which a prize existed). Should this be added to the article? [[User:Magidin|Magidin]] 15:54, 30 October 2006 (UTC)

:I would think that would be worth a mention, if you have a good source. [[User:Dicklyon|Dicklyon]] 16:01, 30 October 2006 (UTC)

::Well, De Morgan makes the point several times; I can look it up and give precise quotes. He was often attacked (especially by a two particular individuals, Sir Richard Phillips and a Mr. Smith) of trying to "cheat them" our of their alleged parliamentary prize for their efforts at squaring the circle. He also connects the confusion with the Longitude problem. I'll look it up (my copies of De Morgan are at home). [[User:Magidin|Magidin]] 16:37, 30 October 2006 (UTC)

And then after this message, clearly blocked from even arguing why not should be blocked from discussing why was blocked. Clearly free speech and constructive critics of why things have been edited is not allowed if one touch upon the editing of the Eppstein circle. Do Eppstein and XOR'easter really think this is fair behavior? Off course they think so...or at least will keep pretending so. [[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 18:37, 31 May 2020 (UTC)

::Sorry for the long delay. I had other demands on my time, and it wasn't as easy to find as I thought. Here is was de Morgan says in ''A budget of paradoxes,'' pp. 96:

:::''Montucla says, speaking of France, that he finds three notions prevalent among cyclometers: 1. That there is a large reward offered for success; 2. That the longitude problem depends on that success; 3. That the solution is the great end and object of geometry. The same three notions are equally prevalent among the same class in England. No reward has ever been offered by the government of either country. The longitude problem in no way depends upon perfect solution; existing approximations are sufficcient to a point of accuracy far beyond what can be wanted. And geometery, content with what exists, has long passed on to other matters. Sometimes a cyclometer persuades a skipper who has made land in the wrong place that the astronomers are at fault, for using the wrong measure of the circle; and the skipper thinks it is a very comfortable solution! And this is the utmost that the problem has to do with longitude.''

::Should I add a new section with some of this? [[User:Magidin|Magidin]] 19:03, 19 November 2006 (UTC)

:::Sounds good to me. [[User:Dicklyon|Dicklyon]] 19:14, 19 November 2006 (UTC)

::: For the particular supposed connection with the longitude problem I think an entire section would be too much. However, it might be feasible to split out the first paragram of the "as a metaphor" section into a brief discussion of circle-squaring as a favorite crank pastime, and your reference would fit perfectly there. The problem here is more that it is hard to write such a section in a way that will not attract POVness criticism. [[User:Henning Makholm|Henning Makholm]] 19:19, 19 November 2006 (UTC)

:::: Sorry; I finished writing a short section on it before you posted your comment. I am not sure how it will attract POV criticism: it is certainly the case that 18th and 19th century circle squarers seem to have believed a prize existed and that it was connected with the longitude problem, and it is also a fact that no such prize was ever offered. I think it does not fit well within "as a metaphor", because this is not really part of using "squaring the circle" as a metaphor. On the other hand, I can add to that section the fact that the expression "Descubriste la cuadratura del círculo" ("you discovered the quadrature of the circle") is a common expression in Mexico, as a derisive response to someone who claims to have found the answer to a particularly difficult problem... [[User:Magidin|Magidin]] 19:45, 19 November 2006 (UTC)

::::: My point was that the first paragraph does of "as a metaphor" is not about metaphors ''eihter'', and this and your quote together might make a viable ''new'' section about crank circle-squarers. (I'd do this if only I could think of a good section title). [[User:Henning Makholm|Henning Makholm]] 19:50, 19 November 2006 (UTC)

::::::Ah. Okay, I moved that paragraph and retitled the second section to "Claims of circle-squaring, and the longitude problem". Maybe another title might be better, but "claims of" seems to me to be neutral POV. [[User:Magidin|Magidin]] 20:08, 19 November 2006 (UTC)

:::::::Looks good. [[User:Henning Makholm|Henning Makholm]] 20:14, 19 November 2006 (UTC)

Based on the comment from UK-WK-ed (and the whole talk page, and the archives of Eppstein/XOR'easter previous editing in relation to this case) I think it is a fair question to ask exactly why was the edit by UK-WK-ed deleted again?[[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 18:43, 31 May 2020 (UTC)

== Constructible numbers ==

{{collapse bottom}}

::Hi Espen-I believe this is what you are looking for:Drypuglia

This recent anonymously edited paragaph was reverted:

-

::;Solution to Squaring the Circle:::

::I tried to wade through the comments-some interesting-others not pertinent to the drafting puzzle, but like many problems I have encountered and solved as an engineer I have concluded that there are No Simple Problems only Simple Solution!, and I believe I have found the graphical solution to this puzzle-using the simple tools. After a brief study of the Pi- circle and square diagram I noted that the circle and square intersecting points were close to/or at a 60 degree angle! So I decided to use a transcendental function(Sine) and eliminate Pi as the solution.

::Using only a straight edge and compass I drew an arbitrary circle, with vertical and horizontal lines. I had made some simple calculations that indicated 60 degrees was not the single line, angular solution I was looking for. However it is necessary as part of the solution, well as 45 degree lines. The angle- calculated by area comparison or from the square root of Pi gives the angle 62.4 degrees. At this point it should be obvious that I have substituted one problem for another and indeed this puzzle would remain unsolved (for how does one draw an angle of 62.4 degrees?) were it not for the fact that I have solved the Trisecting an Angle problem having exact solutions. That drawing solution allows angles to be sected at 3,5,7,11,etc. with a high degree of drawing accuracy. Now if we 5-sect our angle of 60 degrees on the same circle we get 12 deg. segments. On the same circle we then 5-sect the 12degrees to get 2.4 deg. segments. with the compass we measure this span and add it to the 60 deg. point of intersection on the circle, to give us the required angle of 62.4. Thus -the solution! In like manner, the Doubling the cube and constructing a Nonagon problems are solved. Any Questions?

::At the time I posted this solution I did not have a user name. this was shortly after they refused my solution on tri-secting Angles.[[User:Drypuglia|Drypuglia]] ([[User talk:Drypuglia|talk]]) 22:22, 13 November 2022 (UTC)[[User:Drypuglia|Drypuglia]] ([[User talk:Drypuglia|talk]]) 22:13, 25 November 2022 (UTC)

:::The talk page is for discussions to improve the article. It is not a forum for general discussion, nor a place for you to self-promote. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 02:27, 14 November 2022 (UTC)

<blockquote>In 1882, the problem was proven to be impossible, as a consequence of the fact that that pi (π) is transcendental, not algebraic; that is, it is not the root of any polynomial with rational coefficients. That the transcendance of π would have that consequence had already been known for some decades; but the transcendance was finally proved in 1882. Since π is not algebraic, it is also not a member of the subset of algebraic numbers which are constructable (which only include algebraic extensions of the rationals that are compounded from a finite series of solutions to quadratic equations). Once it was proved that constructable numbers were members of such extensions, it was easy to prove that the circle could not be squared (as π is not even algebraic), 60 degrees could not be trisected (it requires solving an irreducible cubic) and the cube could not be doubled (it requires constructing the cube root of 2). Approximate squaring to any given nonzero tolerance, on the other hand, is possible in a finite number of steps, corresponding to the fact that there are members of the specific field extensions of the rationals arbitrarily close to π.</blockquote>

...with comment "Revert addition which I think has it backwards: The major features for constructible numbers (including that they are all algebraic) had been known for at least decades before 1882."

== Quadrature of a sphere ==

Now, I don't disagree with it being reverted, but I do disagree with the reason. It is not incorrect, nor is the fact that constructable numbers were long known at variance with what it says here was proved in 1882. But this background on constructable numbers is not necessary to support the main point, which is that pi being not algebraic proves it can't be constructed. And it's too much side detail for the lead section. Put it into the history section instead, preferably with something about when it was shown. [[User:Dicklyon|Dicklyon]] 02:16, 2 November 2006 (UTC)

[[File:Quadrature of a sphere 97fb6bd5-d62a-4ded-b9c2-a648d9bc752e figure1.png|thumb|Quadrature of a sphere]]

: Let me explain what I think was wrong. We consider the three propositions:

I came across this figure and think it could be used in an article like this one or perhaps some of those listed under [[quadrature]]. We don't seem to have any with a focus or even section on spheres though, so just putting it here for the moment. --<span style="font-family:Monotype Corsiva; font-size:15px;"> [[User:Daniel Mietchen|Daniel Mietchen]] ([[User talk:Daniel Mietchen|talk]]) </span> 20:22, 25 March 2021 (UTC)

:* '''A:''' The constructible numbers form a certain algebraic extension of Q.

:* '''B:''' Pi is trancendental.

:* '''C:''' Squaring the circle is impossible with Euclidean tools.

: As far as I can read the anon's text, it says: "Once A was proved, it was easy to prove C (because B holds)". We all agree, I hope that C indeed follows from A and B, but I disagree with the implication that A was the ''last missing bit'' in the proof of C. My understanding of the historical development is the opposite: A had been known for decades before B was proved, and ''then'', "once B was proved, C followed immediately (because it was well known that A holds)". Am I making my point clear? [[User:Henning Makholm|Henning Makholm]] 19:45, 2 November 2006 (UTC)

== Using other apparatus ==

::Yes and no. I understand what you are saying, but I don't understand why you read it that way. B was clearly the last missing bit. It says B was found out: "In 1882, the problem was proven to be impossible, as a consequence of the fact that that pi (π) is transcendental," and it says that it had been known that if that could be shown, then game over. Your "A" is more narrowly drawn, but knowing that pi is transcendental was well known to be enough to know what it was not constructible. Perhaps the way it is worded confused you. It could perhaps be more clear. But no need to introduce the more narrow definition of what is constructible here, as long as it's clear that transcendentals are not. [[User:Dicklyon|Dicklyon]] 05:46, 3 November 2006 (UTC)

Bell: Men of Mathematics remarks that with straightedge and compass it's impossible to square the circle, but if other apparatus is allowed then it's easy to square the circle. Is he right? If so, could such a construction be included in this article? What sort of apparatus is required?

::: The sentence "In 1882, the problem was proven to be impossible, as a consequence of the fact that that pi (π) is transcendental" is not the one I think it wrong. I am speaking about the sentence "Once it was proved that constructable numbers were members of such extensions, it was easy to prove that the circle could not be squared (as π is not even algebraic)". I have trouble understanding why you don't think this sentence declares A to be the last missing bit - otherwise, what is the point of the word "once"? [[User:Henning Makholm|Henning Makholm]] 19:35, 3 November 2006 (UTC)

By the way, Olds' approximate construction in his book Continued Fractions is the same as Jakob de Gelder's. <!-- Template:Unsigned --><span class="autosigned" style="font-size:85%;">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:209.159.248.94|209.159.248.94]] ([[User talk:209.159.248.94#top|talk]] • [[Special:Contributions/209.159.248.94|contribs]]) </span>

::::Oh, I see. We are having a violent agreement. I thought you were quibbling about the current state of the article, but you're talking about the part some guy put in and you took out. Sorry I got out of sync; too much output, not enough input. On re-reading what you reverted, and your reason, I guess I do pretty much agree with you on that. Sorry for the confusion. It might still be worth representing that idea of constuctible numbers, and the history of it, in the article, but not the way it was in the lead. [[User:Dicklyon|Dicklyon]] 20:17, 3 November 2006 (UTC)

:Yes, it's possible to square the circle using other tools. The last paragraph of the [[Squaring_the_circle#Impossibility|"Impossibility" section]] says a little about this. See also [https://mathshistory.st-andrews.ac.uk/HistTopics/Squaring_the_circle/ MacTutor's page on the topic]. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 23:13, 6 April 2021 (UTC)

== Why not with pythagorean theorem? ==

Good. For future reference (and because I have now bothered to look it up): According to V.J. Katz ''A History of Mathematics'' (HarperCollins 1993, pp. 597f), the algebraic properties of the constructible numbers were investigated by [[Carl Friedrich Gauss|Gauss]] in ''[[Disquisitiones Arithmeticae]]'', and their algebraic characterization was completed by by [[Pierre Wantzel]] in 1837, which closed the [[angle trisection]] and [[doubling the cube|cube doubling]] problems. [[User:Henning Makholm|Henning Makholm]] 23:38, 3 November 2006 (UTC)

(4/sqrt(phi))² + x^2 = pi^2

==You're all wrong...==

or: x^2 + (4/(sqrt((1+sqrt(5))/2)))^2 = pi^2

It appears that not a single one of you remembers the Definition for Numbers:

A NUMBER IS AN IDEEA!

I shall add ...

A circle is made of points which are also ideeas of locations.

A line and a curve are made of points .

This are idealized concepts which only exists in Thought.

The manifestation of this ideeas in the "physical univers" are good enough for the purpose of visualization only.

Pi , sqrt 2 , and the rest of irrational numbers have geometric form ( a triangle 1,1,rt2, or a circle with diameter 1- circumference = pi ) .

Squaring the circle is just ... "matter for thought." Just like Zeno's Paradox ... we can't ever draw anything completely ... therefore PI .

All is just an illussion! ("deceptive appearance" )

<small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/{{{IP|{{{User|75.50.147.71}}}}}}|{{{IP|{{{User|75.50.147.71}}}}}}]] ([[User talk:{{{IP|{{{User|75.50.147.71}}}}}}|talk]]) {{{Time|2007-04-03T14:52:04}}}</small><!-- Template:UnsignedIP -->

: Crank. -- [[Special:Contributions/184.189.217.210|184.189.217.210]] ([[User talk:184.189.217.210|talk]]) 21:56, 6 February 2017 (UTC)

Squaring is a process and there are no straight lines in nature. Everything curves along with time. Thus a process where time proceeds, drawing a circle actually produces helix in time. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/87.92.179.215|87.92.179.215]] ([[User talk:87.92.179.215#top|talk]]) 13:40, 29 December 2021 (UTC)</small> <!--Autosigned by SineBot-->

(The transcendence of _ implies the impossibility of exactly "circling the square", as well as of “squaring the circle”).

:{{tq|there are no straight lines in nature}}: this is bollocks, see picture to the right. [[File:Quartz, Tibet.jpg|right|thumb]]

This is true as long as we look at it in Two Dimensional view. But if we look at it in Three Dimensional view, we will have a Cube and Sphere.

:Your contribution has nothing to do with improving the article. And that is what this page is for. Go to a chatroom for chatting. --[[User:Hob Gadling|Hob Gadling]] ([[User talk:Hob Gadling|talk]]) 15:32, 29 December 2021 (UTC)

The Cube Ratio:

Cube Height : Cube Square Diagonal : Cube Rectangle Diagonal = √1 : √2 : √3

The Sphere Ratio:

Sphere Diameter : Sphere Circumference = √1 : (√2+√3)

In this perspective the Pi Ratio is solved:

π = (√2+√3) = 3.14626436994197

[[User:Hanaga|Hanaga]] 16:32, 9 June 2007 (UTC)

::I have come across something like this before. 4/sqrt(phi) is 3.1446 which looks vaguely Pi-ish but is nowhere near the actual value. Even 22/7 is a better approximation. Not very close, no cigar.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 17:19, 29 December 2021 (UTC)

: Nope. Any combination of √n is [[algebraic number|algebraic]]; π is transcendental, i.e. not algebraic. —[[User:Tamfang|Tamfang]] ([[User talk:Tamfang|talk]]) 14:31, 12 July 2009 (UTC)

== A major point is missing here ==

==Diagram could use fixing==

[[:Image:Hipocrat arcs.svg]] has a freaky aspect ratio such that the "circles" are pretty obviously ellipses, which sort of works to disorient the reader. To some extent, of course, it won't be possible to get perfect circles on all screens, but I expect we can get far closer than the image currently does. Also, I apologize for not just fixing it myself-- I have a phobia of vector graphics. --[[User:Alecmconroy|Alecmconroy]] ([[User talk:Alecmconroy|talk]]) 15:32, 27 January 2008 (UTC)

== Article ==

The Wikipedia article on the [[Hobbes-Wallis controversy]] could be mentioned. <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/87.194.34.71|87.194.34.71]] ([[User talk:87.194.34.71|talk]]) 13:28, 21 April 2009 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

Hobbes himself is mentioned, but not the separate article. <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/87.194.34.71|87.194.34.71]] ([[User talk:87.194.34.71|talk]]) 11:54, 22 April 2009 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

Additionally, this article is slightly misleading. While Hobbes did describe himself as having "squared the circle", it is more accurate to say that, on the assumption of a certain value of pi that Hobbes himself admitted was an estimation, he showed a geometrical construction (line and compass) of a circle with a same area as a given square. <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/50.73.127.69|50.73.127.69]] ([[User talk:50.73.127.69|talk]]) 19:54, 4 August 2011 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

== Squaring of the Circle, Wikkepedia ==

We find it discouraging that Wikkepedia can be very dogmatics and mathematics can be dogmatic about such issues although Wikkepedia is as good as its feeders . We have clearly proven that Wikkepedia is wrong when it says that "circle is not squarable" . We have proved it wrong, and we will below enter our clear method and proof and also reference this new mathematics that has the diagram of a square of a circle at the end of the diagram section using a brand new mathematics. ----www.inverese19 mathematics .com .. please punch and rview . Our complete method will be posted below <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Dodged|Dodged]] ([[User talk:Dodged|talk]] • [[Special:Contributions/Dodged|contribs]]) 17:37, 25 July 2009 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

:Cranky nonsense, and irrelevant even if it were valid. -- [[Special:Contributions/184.189.217.210|184.189.217.210]] ([[User talk:184.189.217.210|talk]]) 21:58, 6 February 2017 (UTC)

== Freemasons ==

Is "squaring the circle" (using a somewhat a posteriori approximation to &pi; based on the golden ratio) part of initiation into freemasonry? [[Special:Contributions/74.98.43.217|74.98.43.217]] ([[User talk:74.98.43.217|talk]]) 22:08, 1 October 2009 (UTC)

== claims of squaring the cicle and new value of PI ==

There are clams that PI is exacly 3.1416 and that you can square the cicle by means of Ruler and Compass.

http://www.alkyone.com/mak-pi-gr/en/en_release.htm

The person who makes this claims is Mr. Moschos Ath. Karagounis,

Mechanical Engineer of the National Technical University of Athens (NTUA).

There is quite a talk about this recently.

Now, at first i thought this to be pseudomathimatics but the fact that this person is part of greek academia and my maths are not to his level, makes it imposible for me to disprove it.

So, I write this post, so a more advanced wiki editor could make sence of it and decide what to do with it.

Also, There is another page, http://www.squaringofthecircle.gr/ where he gives another number for Pi , but with somewhat same claims.

[[User:Nkast|Nkast]] ([[User talk:Nkast|talk]]) 10:13, 10 October 2010 (UTC)

:See [[Ferdinand von Lindemann]]. People can say whatever they like in self-published mathematics papers on the web, but Pi is considered to be a [[transcendental number]]. See also [[WP:REDFLAG]].--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 10:18, 10 October 2010 (UTC)

== Archimedes Solution ==

I have a problem with 'Archimedes Solution' section of the article. The line tangent to point P on the circle can never intersect the axis at point T. By definition, the line tangent to the circle at point P is parallel to the indicated axis. Is a better citation warranted? <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/173.65.133.176|173.65.133.176]] ([[User talk:173.65.133.176|talk]]) 13:29, 1 June 2011 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:You've misread the part of the article. P is not in the circle; as the article says, "''Let P be the point '''on the spiral''' when it has completed one turn.''" The tangent in question is tangent to the spiral at point P, not to the circle. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 17:03, 1 June 2011 (UTC)

:: I apologize that I am years out of school, and a lot of this knowledge has left me. How does Archimedes solution (creating a triangle with the area of a circle) solve the issue? Is there a method of forming a square from any triangle, using a compass and a straight edge? If so, we should add the relevant link/explanation. --[[User:Bertrc|Bertrc]] ([[User talk:Bertrc|talk]]) 00:40, 7 August 2011 (UTC)

:: Additionally, instead of merely referencing his first proposition as though it was some compllicated algorithm, can't we just say that the area of a circle (pi*(r^2)) equals the circumference of the circle (2*pi*r) times the radius of the circle (r) divided by 2, while the area of all right triangles equals the long leg (in this case, the circumference of the circle) times the short leg (in this case, the the radius of the circle) divided by 2. This is clunky when written out, but for a wikipedian who is good with formulas, it could be displayed rather concisely. -- [[User:Bertrc|Bertrc]] ([[User talk:Bertrc|talk]]) 00:26, 7 August 2011 (UTC)

:: Lastly, if a square can be made from any right triangle, is there a proof that Archimedes spiral cannot be constructed with a straight edge and compass, other than the fact that doing so would allow the squaring of a circle? -- [[User:Bertrc|Bertrc]] ([[User talk:Bertrc|talk]]) 01:05, 7 August 2011 (UTC)

== Other Tools ==

So squaring a circle with just a straight edge and compass is impossible. Has anybody ever thought of or written about other tools that can solve this? eg, I could wrap the circumference of a circle with a length of rope (or with a piece of paper turned perpendicular to the plane of the circle, or I could cut out the circle and roll it, etc.) If I straighten the rope (or paper), I now have a line of length 2*pi*r. if r is 1, I can easily split the line in half to get a line of length pi. Given a line of length x, is it possible to construct a line of length sqrt(x) (with which I could easily construct a square) or is that some other unsolvable problem? That was just an idea off the top of my head. Are there other tools that people have considered (like folding the paper, etc.) --[[User:Bertrc|Bertrc]] ([[User talk:Bertrc|talk]]) 01:02, 7 August 2011 (UTC)

: See [[quadratrix]]; [[Archimedean spiral]]. —[[User:Tamfang|Tamfang]] ([[User talk:Tamfang|talk]]) 08:30, 26 February 2013 (UTC)

Good question. I was wondering about that too. All that's mentioned is construction and algebra in Euclidean space. I want to know if other methods have been tried, like trying to express pi in sin/cos/tan functions or maybe in a non-base-10 number system. If anyone tried and failed at such methods it would be nice to mention it in the article. <small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/82.169.42.228|82.169.42.228]] ([[User talk:82.169.42.228|talk]]) 01:50, 14 December 2015 (UTC)</small><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

== Constant: "Square Root of Pi" and "Half of Pi" ==

I apologize -- I am not skilled in Wikipedia.

There will always be conflict when we do not differentiate between "concepts" and "representations of concepts". Any form generated by hand is purely a representation. Pi is misused when we attempt to represent it in some partial form, and then cry foul when it is appreciated in conceptual form. As you can see from the link below, the areas of a circle and square can be exactly the same (even in conceptual form).

What seems important is to acknowledge that there is a constant that exists: "Simply put, the pure geometric difference between a circle and a square lies in the difference between 'the square root of pi' and 'half of pi'" - Thomas Bishop

Please refer to this link:

http://c.ymcdn.com/sites/www.optimalmindsgroup.com/resource/resmgr/Divosophy/BishopSquareCircle.png

[[User:Bishopclinics|Bishopclinics]] ([[User talk:Bishopclinics|talk]]) 05:49, 6 January 2013 (UTC)

:Of course there exists a square with the same area as any given circle. That doesn't have anything to do with the problem of squaring the circle, which is to ''construct'' a square with the same area as any given circle using only compasses and straightedge. The compasses and straightedge aren't actual compasses and straightedge, rather they are idealised compasses and straightedge with properties not found in real objects (e.g. the straightedge is infinitely long). '''''<font color="#FF0000">[[User:Hut 8.5|Hut 8.5]]</font>''''' 11:33, 6 January 2013 (UT

==Related Areas==

When you superimpose a circle over an equivalent area square, as in the illustration, you note that there are 4 related areas that are outside the circle but inside the squire and also also 4 other related areas that are outside the square but inside the circle. Then a little logic will tell you that the individual areas of all of these related areas is the same constant value. So what I would like to know is what the precise value of this constant is, and does it have any mathematical relationship with the area values of any of the other sub areas of either the circle or the square. I think its value is approximately 7.5% of the area of the square (and also the circle) But I would like to know its value to a precision equal to that of the other sub areas. Can I find that information somewhere?[[User:WFPM|WFPM]] ([[User talk:WFPM|talk]]) 01:12, 11 May 2013 (UTC)

:Yes, you most certainly can. but not here. This [[wp:notforum|isn't a forum]]. [[User:Edaham|Edaham]] ([[User talk:Edaham|talk]]) 07:06, 2 October 2017 (UTC)

== New Comment ==

I give a compass & straightedge construction using the Golden Mean which yields 3.14164 for pi at http://www.goldennumber.net/squaring-the-circle/ Ricci4.4428828 (talk) 00:58, 11 June 2013 (UTC)

I have also discovered a compass & straightedge method of squaring the circle precisely in both area & perimeter on smooth Riemannian manifolds of positive Ricci curvature; despite the transcendental nature of pi: http://www.circleissquared.com/index.html C. Ricci Ricci4.4428828Ricci4.4428828 (talk) 00:58, 11 June 2013 (UTC) <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Ricci4.4428828|Ricci4.4428828]] ([[User talk:Ricci4.4428828|talk]] • [[Special:Contributions/Ricci4.4428828|contribs]]) </span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

:See [[WP:FORUM|what Wikipedia is not]]. If you are proposing additions to the article, then what you point to above cannot be included: it violates the [[WP:NOR|no original research policy]], there are [[WP:N|problems with its notability]], and you have a [[WP:COI|conflict of interest]]. And if the above is simply meant to be calling attention to your work, then [[WP:TPG|it is also inappropriate for a talk page]]; talk pages are for discussions on improving the main article, not for discussions on the topic of the main article. That is, talk pages are not an [[internet forum]]. If your addition above is not meant to be either, then please explain what it is meant to be. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 03:25, 11 June 2013 (UTC)

::Also see [[Ferdinand von Lindemann]], which points out "Before the publication of Lindemann's proof, it was known that ''if'' ''π'' was transcendental, then it would be impossible to [[squaring the circle|square the circle]] by [[compass and straightedge]]." My calculator says that the value of π is 3.1415926, not 3.14164.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 05:11, 11 June 2013 (UTC)

:::This value for pi (3.1416)is derived from the Fibonacci numbers; a sequence of continued fractions which ultimately converge on the Golden Mean. I give a compass & straightedge construction using this ratio which yields the same value for pi at http://www.goldennumber.net/squaring-the-circle/ These results have been verified by the website host Gary Meisner, certified CPA and an MBA in Finance. [[User:Ricci4.4428828|Ricci4.4428828]] ([[User talk:Ricci4.4428828|talk]]) 11:52, 11 June 2013 (UTC)

:::It is worthy to note that this tight approximation for pi (3.1416) using the Golden Mean is mentioned on many math related sites. For example: http://mathworld.wolfram.com/PiApproximations.html. I am not sure if I referenced that correctly. [[User:Ricci4.4428828|Ricci4.4428828]] ([[User talk:Ricci4.4428828|talk]]) 12:21, 11 June 2013 (UTC)

:::: The classical problem of squaring the circle requkres the construction of a square that has the exact are as that of given circle. The '''exact''' area; so ''any'' approximation of pi, no matter how it is derived, is irrelevant. The construction must give the exact area, which requires the use of pi, not any approximation thereof. And "verifications" by a CPA/MBA are irrelevant. That's not a recognized reliable source. See [[WP:RS|Wikipedia's policies on reliable source]] for information on what is and what is not considered a reliable source. "[W]ebsite host Gary Meisner, certified CPA and an MBA in Finance" is not one. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 15:42, 11 June 2013 (UTC)

::::I think that 2 separate considerations are being confused here. The exact value of Pi has no meaning in itself. What is important is its value as a measurement of the relationship of 2 significant physical dimension values. If I create a square with an area dimension of 4, I can then say that the area within the enclosed circle is equal to the value Pi. And if I create a square with an area of 16, I can also say that the area within a 1/4th quadrant of the circle also has an area of Pi. So we are dealing with relative area relationships here, of which Pi is only 1. So these 2 different configurations of enclosed areas have the same relative size relationship, and the value of Pi is involved in the geometry of construction of the considered areas, and I have my doubts about the ability of a mathematical formula to come up with an exact numerical number for the value of Pi.[[User:WFPM|WFPM]] ([[User talk:WFPM|talk]]) 17:35, 14 June 2013 (UTC)

:::::Pi has plenty of applications as a dimension-free number in mathematics. See [[Basel problem]] and [[Stirling's approximation]] for two of the most basic and important of them. My opinion is: if you have vague feelings that mathematics doesn't work, and you think it's more important to express your feelings than to understand clearly and communicate to others the consensus of published mathematics, then perhaps other topics than mathematics would be a better fit for your Wikipedia editing. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 17:56, 14 June 2013 (UTC)

::::If we roll a 1 inch diameter circle along a number line starting with a point at zero, the point will next touch the number line at the value of Pi. So it's our lack of the proper drawing tool that prevents us from drawing a straight line with a value of Pi. And I'm really not interested in exact mathematical values, and particularly in base 10 (or other base) values. Because I believe that all numerical values are merely names of relative magnitude locations along a number line and accordingly of no significance unless related to some physical article of consideration. However, I don't think that I should be disqualified for pointing out that there are other fixed relationships of areas of the circle versus that of the equal area square that might offer an idea as to the logic of those relationships.[[User:WFPM|WFPM]] ([[User talk:WFPM|talk]]) 03:39, 15 June 2013 (UTC) PS: I looked at your [[Basel problem]] reference and wish to compliment Euler for getting the value Pi squared out of a summation process related to a mathematical formula.[[User:WFPM|WFPM]] ([[User talk:WFPM|talk]]) 04:00, 15 June 2013 (UTC)

:::::You may not be disqualified from pointing out things in many places. However, insofar as you wish to point out what you term to be your "beliefs" and your "interests" (or lack thereof), they have no place in Wikipedia as they constitute [[WP:OR|original research]] and are both unverifiable (within the meaning of Wikipedia) and lack notability (again, within the meaning of Wikipedia). The comments are also out of place in talk pages, as talk pages are not fora for discussion, but rather places to discuss improvements to the articles, improvements that are supposed to be based on information that is verifiable, from reliable sources, and notable. As such, I must echo David Eppstein comments: your contributions here are out of place. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 19:37, 15 June 2013 (UTC)

:::::My Gosh!! We're talking about the square area that is equivalent to that of a circle and now it's morfed into a discussion about the value of Pi. I'm interested in the area of a square and the equal area circle and I came to here for information. And now you don't like my comments about the significance about the importance of the value of Pi. And where else on Wikipedia can I go for this information? You don't care! And you say the value of Pi is 3.1415926 and my 8 dollar Casio calculator says it's 3.141592654 so what?. What I'm interested in is that if I consider a square with area 4 then draw a circular 90 degree arc through that square which has a length of Pi and separates the area of the square into the 2 sub areas Pi and 4 - Pi. So how does that fact interact with the fact that the areas outside of the circle or the equivalent area square are equal in area? Aren't these ideas relevant to the subject matter of the squaring of the circle.[[User:WFPM|WFPM]] ([[User talk:WFPM|talk]]) 23:02, 15 June 2013 (UTC)

:::::: I don't know what it is you think you are talking about; for example, I never said the value of Pi "is 3.1415926". Nor did I say anything about my likes or dislikes, I said your comments are '''out of place''' in this talk page; and, you know what? '''They still are.''' Your interests are likewise immaterial, and your continued discussion of them here is '''out of place.''' No, your ideas are not relevant to the improvement of this article, because they continue to be [[WP:OR|original research]], unverifiable, and lack notability. And, for that matter, betray willful ignorance on your part. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 01:57, 16 June 2013 (UTC)

::::::Well Okay! I'm sorry I bothered you about any detailed information about the geometric properties of the equal area square with relation to the circle. I thought it might be relevant to the subject matter of this article.[[User:WFPM|WFPM]] ([[User talk:WFPM|talk]]) 03:29, 16 June 2013 (UTC)

== The illustration on the left is wrong==

A circle with a radius of one has an area of pi squared. A square of equivalent area has sides of length pi, not the square root of pi as the illustration shows. [[User:[e-mail]|[e-mail]]] ([[User talk:[e-mail]|talk]]) 19:17, 13 January 2015 (UTC)

:No. The [[Circle#Area_enclosed|area of a circle]] is <math>\pi r^2</math>, where <math>r</math> is the radius. For <math> r = 1 </math> the area is <math> \pi 1^2 = \pi</math>. '''''[[User:Hut 8.5|<span style="color:#FF0000;">Hut 8.5</span>]]''''' 19:38, 13 January 2015 (UTC)

== Huh? ==

Like an increasing number of scientific or technical articles on Wikipedia, this seems to have been written by experts to trigger discussions between their colleagues and would-be experts. Meanwhile, many people who want to know what "squaring the circle" actually means have to look elsewhere. "...the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge." means what exactly? We can't measure the area of the circle? When "constructing" squares (from wood?) it's tricky getting the edges straight? And why would you use compasses to "construct" a square? An article this obscure is worthless, unless it helps a math student who was assigned to write it to get a good grade.

:To understand the that sentence see [[Compass-and-straightedge construction]]. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 16:26, 7 March 2015 (UTC)

== Circularity? ==

I read the discussion above because I found the article unclear about one step -- not the one discussed so much above, but rather: *Why* it is impossible to "construct" an irrational value from a rational one? I make my living doing other sorts of applied math, but had not encountered the formal term "a constructible number" (minimal extension of the field *R* such that...). Given a typical reader's likely intuitive idea of "constructible", the question arises: "Why doesn't setting a compass to some given size (say, 1), and then merely using it to draw a circle, amount to "constructing" a transcendental number (2pi) from a non-transcendental (1)?" Doing so obviously "constructs" a locus of (virtual graphite) points whose length is a transcendental multiple of 1 -- but the intuitive meaning of "construct with compass and straightedge" differs subtly (but crucially) from the formal definition you need here. When you try to figure it out by reading [[constructible numbers]], it's clear that the notion "constructible" originates from "constructible with compass and straightedge" (it does give a field-oriented definition as well, but the equivalence is not trivial/obvious). So the current explanation boils down to "You can't square a circle with compass and straightedge, because pi is not a constructible number. What's a constructible number? One that can't be constructed with compass and straightedge." That seems to beg for a fix. <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Sderose|Sderose]] ([[User talk:Sderose|talk]] • [[Special:Contributions/Sderose|contribs]]) 16:35, 29 October 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

:After selecting an arbitrary length to be considered the unit (value 1), we say that a positive number ''a'' is constructible if we can mark two points ''p'' and ''q'' on a straight line, using only compass and straightedge and the given unit value, such that the distance between ''p'' and ''q'' is exactly ''a'' times the unit. The fact that the length of the circle is 2pi does not actually yield a construction of a ''straight line segment'' of length 2pi. The actual explanation does not, however, boil down to what you claim it does. The actual argument is: We can square the circle if and only if we can construct the number <math>\sqrt{\pi}</math>. '''If''' we could construct that number, then we would also be able to construct <math>\pi</math>. However, <math>\pi</math> is '''transcendental''', and no transcendental number is constructible. Since <math>\pi</math> is not constructible, neither is its square root, and since its square root is not constructible, we cannot square the circle. The argument does not rest on "pi is not constructible", it rests on "pi is transcendental." [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 17:18, 29 October 2015 (UTC)

== Deleted in article: "Will a fraction constructed on a ray..." ==

Pardon, I did not want anyone bewilder with my post or with my english (Google Translater + school a long time ago). I have full understanding for the deletion of my contribution by the user Magidin.

I try the description of my proposal with essential facts.

* An application example is the fraction

:<math>\frac{245 850 922}{78 256 779} = 3.14159265358979316028\dots</math>

* Construction of the '''fraction''', '''that corresponds an approximation of the number pi''', with use the method [[Intercept_theorem#The_construction_of_a_decimal_number|Intercept theorem, The construction of a decimal number]]. See also [https://commons.wikimedia.org/wiki/File:01-_Strahlensatz,_Anwendung.svg Commons: Decimal number 8.639]</small>

* Reference fraction: [[Johann Heinrich Lambert]] in his book "Beyträge zum Gebrauche der Mathematik und deren Anwendung" [https://books.google.de/books?id=fKhEAAAAcAAJ&pg=PA157&dq=78256779%3A245850922&f=false#v=onepage&q=78256779%3A245850922&f=false "Beyträge zum Gebrauche der Mathematik und deren Anwendung"] Quadratur des Circuls, p. 157

* Reference application: Brechtel, Udo [https://udo-brechtel.de/index.php?s=quadratur "Quadratur des Kreises?"]

Is the topic generally suitable for the article? Greetings --[[User:Petrus3743|Petrus3743]] ([[User talk:Petrus3743|talk]]) 16:48, 11 July 2016 (UTC)

:I couldn't really understand this due to the fractured English. Pi cannot be expressed as a fraction as it is a [[transcendental number]], and fractions will be an approximation. This needs a clearer explanation of why it is suitable for the article.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 17:01, 11 July 2016 (UTC)

::See also my addendums in my entry --[[User:Petrus3743|Petrus3743]] ([[User talk:Petrus3743|talk]]) 17:41, 11 July 2016 (UTC)

:::It is still unclear to me. The section is about modern constructions that give an approximation to pi. You start by saying "An application example". "Application" of what? Not the prior paragraph, which just describes a particular approximation. "Example" of what? The link you give, which is to your own addition to the article in question, is also rather hard to parse (and may constitute [[WP:OR|original research]]); you can't avoid the problem of original research (or conflict of interest) by adding OR to one article, have it pass unnoticed or unchallenged, and then refering to that OR. It is also unclear what your citation is for; the Lambert link goes to a page of the work that lists a number of rations, which presumably approximate pi. But it is not a proper citation for the construction, or for a "modern" construction (I'm guessing, based on the typeface; your citation is pretty useless given that it lacks several important items, such as date of publication). The second citation is to a webpage; absent proper justification, webpages are not generally considered [[WP:RS|reliable sources]]. In short, I do not understand what it is you are trying to add, why you are trying to add it, or what your reliable, verifiable sources are to justify that addition. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 18:44, 11 July 2016 (UTC)

::::@[[User:Magidin|Magidin]],<br />

::::thank you for your hints. I understand your arguments, you are right. My suggestion also includes own research and is therefore not suitable as a supplement for the article. Greetings from Munich --[[User:Petrus3743|Petrus3743]] ([[User talk:Petrus3743|talk]]) 20:51, 11 July 2016 (UTC)

== Anonymous edit and reverts on lede ==

User 95.145.130.35 made changes to the lead, calling the previous text a "waffle". This was reverted by two different editors, and the user reverted back claiming the wording made things "less precise". At this point, we are treading close to [[WP:3rr|the three revert rule]]. Two different editors have disagreed with the edit; rather than revert yet again, it should have gone to the [[Talk:Squaring the circle|talk page]]. IP user's first edit claimed that specifically mentioning that this is a construct within Euclidean geometry and what the Euclidean axioms allow was a "waffle"; it's hardly an waffle to expand on what "constructing" means within Euclidean geometry. Removing the preface that indicates that this is an explanation, and leaving only "it" makes the sentence read as if this is an ''alternative'' and optional interpretation of the problem, which it is not. It is a more precise description of what "construction with straightedge and compass" means. I have left the main text of this comment on IP user's talk page. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 22:27, 8 December 2016 (UTC)

:I would not consider this clause a "waffle", but on the other hand I do have problems with the entire sentence, which has been in the lead for several years. There is a hint here of a relationship with the axioms of Euclidean geometry, but this is not expounded on in the article, with the closest approach being some ambiguous remarks concerning hyperbolic geometry. I consider the sentence a red herring. It talks of the axioms giving existence of lines and circles (the basis of straightedge and compass constructions to be sure) and posits whether or not they suffice for the existence of the squares coming from the a putative construction. Well, they aren't&ndash;since the construction is impossible, but the squares certainly exist in Euclidean geometry. One needs more axioms to prove this, above and beyond Euclid's five (in particular, the Archimedean axiom is necessary). So, what I am saying is that the situation is more complex than what is hinted at by the sentence and it should either be expanded on or removed. I am not sure that this is the right article for an expanded treatment, so I think that the sentence should be removed or reworked. --[[User:Wcherowi|Bill Cherowitzo ]] ([[User talk:Wcherowi|talk]]) 06:09, 9 December 2016 (UTC)

::If what the sentence needs is rewriting, that's fine. I found the edit and edit summary to be at best unhelpful, hence this discussion. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 07:19, 9 December 2016 (UTC)

::I think it should be removed. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 11:27, 9 December 2016 (UTC)

:::Firstly, User:Magidin should note that "a waffle" is a thing made of potato or dough which can be fried and is tasty, while "waffle" is verbose text which doesn't add any substance to the article. I claimed that the text I removed was "waffle", not "a waffle". I judge that you are not a fluent English speaker, and suggest that you should be accordingly careful with language issues.

:::Secondly it appears that User:Magidin did not fully understand my edit. I did not claim that specifically mentioning Euclidean geometry and axioms was waffle. I claimed it of the words I removed, which were "More abstractly and more precisely,". "Abstract" and "precise" are mutually contradictory properties.

:::And thirdly, after my initial edit was undone without any explanation, User:Magidin restored just the "More precisely, ". If it were true that it really was more precise, then one should just give the more precise explanation. An imprecise and a precise explanation of the same thing is not a service to readers. However, it is in no way true that the statements about Euclidean axioms are a more precise statement of the problem than the initial clear statement of the problem.

:::It seems to me that the sentence itself is of some interest though probably not significant enough to merit being in the first paragraph of the lead section. If it were removed from the lead, perhaps a place could be found for it in the article. But whatever its merits, it seems to me that people undoing other people's work should be careful when doing so and always a) understand what the edit was doing and b) explain why they think it needs to be undone. That didn't happen here and that's disappointing. [[Special:Contributions/95.145.130.35|95.145.130.35]] ([[User talk:95.145.130.35|talk]]) 20:40, 11 December 2016 (UTC)

::::Firstly, thank you for your expanded explanation. Secondly, keep your language snarks out of an attempt at reasonable discussion. While English is not my first or second or third language, I do know the difference here and your first paragraph is little more than an ad hominem. Given that the only word in quotation marks was "waffle", not as you imply the words "a waffle", you know perfectly well what was meant, so you are contributing nothing there but only trying to dismiss disagreement on the basis of who is making the counterclaim. [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 23:02, 11 December 2016 (UTC)

:::::I did not appreciate your undoing of my edits, and I do not appreciate your tone policing. I am not perceiving much in the way of a desire to make the article better from you. Do you, in fact, desire that? [[Special:Contributions/95.145.130.35|95.145.130.35]] ([[User talk:95.145.130.35|talk]]) 00:34, 12 December 2016 (UTC)

::::::I was not the only (or even the first) person to undo your edit; you complain about undoing edits with no comments, but that is what you did to that revert (which I did not make).

:::::: The very fact that I asked you and others to weigh in on how to deal with that sentence demonstrates a desire to find consensus to make the article better. It does not mean it will end up in my prefered wording; it also need not mean it will end in your prefered wording, and asking that it be discussed is not an insult thrown your way.

::::::I disagree that "abstract" and "precise" are mutually contradictory; the antonym of "abstract" is not "precise", it's "concrete". A more abstract description can in fact be a more precise one; it is certainly possible that the version at issue did not in fact provide more precision, but that is not a problem of allegedly mutually contradictory words. The wording left makes it appear that understanding the problem as asking something about Euclidean geometry within the context of the axiom is an ''optional'' way of understanding the problem; that is not the case: it is the ''intended'' way of understanding the problem. Simply eliminating words that signal that the problem is being described differently opens up potential serious misunderstanding: that while one ''could'' interpret the problem as one of constructibility within Euclidean geometry and its usual axioms, one need ''not'' do so, and instead may understand the problem differently; in which case, the next paragraph asserting a proof of impossibility would be incorrect (as that only refers to constructibility within Euclidean geometry and its usual axioms). So the remaining wording, which currently stand as your edit, is in my opinion problematical.

::::::Finally: if you do not appreciate being called on an ad hominem (and instead dismiss this as "tone policing"), then don't be a rude ass; or was the equivalent of a spelling flame really your leading argument? [[User:Magidin|Magidin]] ([[User talk:Magidin|talk]]) 01:18, 12 December 2016 (UTC)

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== Espen Gaarder Haug ==

Re [https://en.wikipedia.org/w/index.php?title=Squaring_the_circle&curid=201359&diff=957948636&oldid=957945798 this edit]: I'm beginning to wonder if there is a [[WP:COI|conflict of interest]] here. Is {{u|MetricoGeo}} in some way linked to the author of the paper?--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 09:16, 21 May 2020 (UTC)

:Who wrote the new section on squaring the circle? It was not me (MetricoGeo)! This I am sure someone can investigate.

:So why did David Eppstein delete it? The Squaring the circle page has a series of references to even books and popular science and non-peer reviewed web-cites. As asked before, how many peer reviewed papers on Squaring the Circle has been published in the last 20 years (in decent journals)? Whoever put in the new section (unknown to me) also seems to have put it under the right section. It is not a section that endorse it. It is simply a section made on the Squaring the Circle page long time ago that simply state "Other modern claims". And under this section two non-peer review books are mentioned. But a peer reviewed paper, that claim to give new light on the problem and also do not hide that it "We could argue that this is bending the rules and moving the problem of transcendental ⇡ into a transcendental velocity between the reference frames, rather than directly into the construction of the Circle and the Square. Still, one could just as well argue that the previous attempts to Square the Circle have not taken into account that observations of space and time are a↵ected by motion, and that space and time are closely connected." https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1514&context=tme is deleted by Eppstein. [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 10:32, 21 May 2020 (UTC)

:Ahaha, I wondered about this deletion, then investigated a bit further. Eppstein that quickly deleted what someone referring this this paper had put on the Squaring the Circle wiki page, is the same guy (active on wikipedia for years) that deleted Haug's wikipedia page some years ago. A wikipedia page that had been there for more than 10 years. Eppstein is clearly allergic to Haug's work, and he want to delete as much of references to Haug's work as possible? The conflict seems to be about Eppstein do not like Haug's view on physics? Who should declare conflict of interest here, do we need to dig up the old wikipedia archives of deletion and debate? Could Eppstein be slightly biased here??? I am just asking! I am not going to edit or write a single world on the Squaring of Circle page, this I leave up to the very Objective types such as Eppstein. Very objective to have series of references to very popular stuff and delete references to work in good journals (if he do not like that person). I suspect it will be deleted, more and more pages of wiki are dominated by science-activists. These are often highly educated scientist, but with very biased view the do not even want to see problems from other angels than their own biased view. (UTC) [[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 11:46, 21 May 2020 (UTC)

*Sorry - why is this claim important? The "Other modern claims" section isn't meant to be a list of everybody who's claimed to have squared the circle, just a few of the most important ones. The [[Indiana Pi Bill]], for example, is notorious. Why is this paper from a mathematics education journal considered important enough? Furthermore presenting phrases like "presented an practical way of squaring the circle" is likely to mislead the reader. '''''[[User:Hut 8.5|<span style="color:#FF0000;">Hut 8.5</span>]]''''' 12:42, 21 May 2020 (UTC)

** Yes, "accelerate the train to a speed relative to the embankment of <math>c\sqrt{1-\frac{1}{\pi^2}}</math>" (roughly 2.84 &times; 10⁸ meters per second) is not exactly "practical". [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:12, 21 May 2020 (UTC)

"The "Other modern claims" section isn't meant to be a list of everybody who's claimed to have squared the circle,". It should naturally be limited to peer reviewed work published in scientific journals and for non-peer reviewed claims only too well known historical disputes that are well documented, such as yes for example The Indiana Pi Bill. How many well known, well documented historical disputes on Squaring the Circle (in modern times, last few hundred years) of any magnitude exist? A handfull at most! This should be minimum requirement for anything on the whole page? Or is the wiki-page an opinion page now where wiki editors can bring in links to work (even non peer reviewed) they just like, and then delete what they dont like, or references to work form people they dont like for whatever reason? But from what I see here now, it clearly looks like what was deleted will be deleted, we now understand why Eppstein deleted it so quickly! His argument for deletion was clearly just something he came up with that made it sound reasonable, but that the writer of the new section was looking straight through (see recent history on the page and arguments). People spending lots of time editing on wiki have likely high status among other active wiki editors, backing each other, so yes I think we know how this ends. Can someone list all the references given on the page and rank them roughly, based on scientific validity and quality, documentation etc., grope into peer-reviewed and non peer reviewed etc.? [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 13:03, 21 May 2020 (UTC)

:Squaring the circle is based on achieving it with a finite number of steps with compass and straightedge. This is known to be impossible. The [https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1514&context=tme paper] introduces all sorts of concepts from the Theory of Relativity and non-Euclidean geometry which are at best speculative.--'''''[[User:ianmacm|<span style="background:#88b;color:#cff;font-variant:small-caps">♦Ian<span style="background:#99c">Ma<span style="background:#aad">c</span></span>M♦</span>]] ^{[[User_talk:ianmacm|(talk to me)]]}''''' 13:57, 21 May 2020 (UTC)

:Wikipedia is not the place to promote work that has not attracted attention and interest from the scholarly community, whether or not that work is technically correct. Including Espen Gaarder Haug's paper is not appropriate, and this has nothing to do with any supposed personal animosity against Espen Gaarder Haug. (I doubt there is any such animosity; [[Wikipedia:WikiProject Deletion sorting/Academics and educators/archive 2|deleting articles on non-notable academic types is commonplace]].) [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:07, 21 May 2020 (UTC)

"** Yes, "accelerate the train to a speed relative to the embankment of <math>c\sqrt{1-\frac{1}{\pi^2}}</math>" (roughly 2.84 &times; 10⁸ meters per second) is not exactly "practical". [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:12, 21 May 2020 (UTC)" XOR'easter is here searching for arguments to delete the reference to the paper. Had XOR'easter read the whole paper would he have seen that this is only one of the special solutions and that even a printer head moving at v>0 as stated in the paper will do. So his indication that one need to move so fast as it is not practical even close to possible is totally false.

Further XOR'easter writes "is not the place to promote work that has not attracted attention and interest from the scholarly community, whether or not that work is technically correct.". I cannot see how any author of any paper has written anything about own paper on Squaring the Circle page and thereby doing self promotion. The paper is one of the very few peer review papers published on Squaring the Circle the last 20 years. And this despute I think will get interesting in the coming months and years, far outside wiki !! XOR'easter are you in any way part of Eppsteins circle? Where you part of working and voting for deleting the wiki page about Haug years back? [[User:MetricoGeo|MetricoGeo]] ([[User talk:MetricoGeo|talk]]) 14:23, 21 May 2020 (UTC)

:The "printer head" proposal is still a [[thought experiment]] involving lasers and synchronized clocks, not a practical method. Promotion is not limited to ''self''-promotion. And with [https://en.wikipedia.org/w/index.php?title=Squaring_the_circle&type=revision&diff=957974186&oldid=957962457 this edit], you crossed the [[WP:3RR|3RR]] line, meaning that you could already have been blocked (and willy-nilly casting aspersions upon the character of those who disagree with you is [[WP:NPA|not likely to earn you friends]]). [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 14:31, 21 May 2020 (UTC)

Interesting. So XOR'easter want to change that one sentence to theoretical solution rather than practical, do anyone have problems with this, I doubt that the dispute has anything to do with this? Is any other discussed solution to the Squaring of the Circle more practical as they exclude 100 years + last discovery on Minkowski Space-Time?

While I think this article successfully explains why it is not possible to square the circle, it completely ignores the question of why anyone would ''want'' to. The "squaring" of various objects was far more important to ancient mathematicians than modern readers would normally be aware of. It seems this article would be greatly improved with one or two paragraphs explaining the concept of squaring, and perhaps a simple example using the triangle. [[User:Maury Markowitz|Maury Markowitz]] ([[User talk:Maury Markowitz|talk]]) 10:35, 10 June 2022 (UTC)

I am looking up old wiki archives now. So Eppstein was as stated earlier one of the persons active on wiki that bashed Haug on wiki talk pages for his lack of qualifications years ago and successfully got the 10+ year wikipge about him deleted, with the help of vote from? XOR'easter surprisingly was one of the others bashing Haug for his physics in 2018 and working hard to delete the wikipedia page about him. A wiki page that had been there long over 10 years was attacked by XOR'easter and Eppstein. Did Eppstein call you XOR'easter for support also here, I am just asking you XOR'easter if this is what happened now? Do you think you and Eppstein think the past here could make you the slightest biased? Is this how wikipedia work these days? Has it become corrupted with circles of people spending much time here, becoming buddies defending each others editing rather than trying to get the best out of wikipedia? Just asking, please explain to us non frequent visitors how this now will work. Eppstein and XOR'easter and a few others in the Eppstein-circle will now vote for deletion and show how democratic and fair wiki editing is? Yes we know the result of this dispute (for the year being) [[User:QuantitativeGeometry|QuantitativeGeometry]] ([[User talk:QuantitativeGeometry|talk]]) 15:01, 21 May 2020 (UTC)

:I added a couple of lines on this to the second paragraph of the history section. But although the source for the quote I added, [[Proclus]], was in the tradition of Greek mathematics, he was far later than the origins of the problem and the theory he gives is speculative. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 16:31, 10 June 2022 (UTC)