Talk:Mathematical coincidence

message: Forgive the intrusion by someone who is not a proper mathematician (an economist). Here's one that may have been included-then-deleted:  
2 approx= exp((1/2)^(1/2)) 
Not that good an approximation (rhs=2.028, and I don't know what approximation it arises from) but it seems to me to be rather pleasing.  — Preceding unsigned comment added by Stephen Wright Birkbeck (talk • contribs) 18:16, 5 January 2014 (UTC)
thread_title: Another coincidence

message: A few comments. Maybe mathematical coincidence might yet be a better page name. I'm not sure what a 'theoretical explanation' would be, in all cases: but certainly in the case of exp(π√163) there is a very good if hidden reason. Perhaps the pigeonhole principle could be invoked. After all, it is because of Dirichlet's theorem on diophantine approximation, based on it, that we know that good rational approximations exist. And so on, for other kinds of relations. By the way, I added the law of small numbers link, but that really needs disambiguation since the Poisson distribution meaning is a separate thing.
Charles Matthews 16:10, 21 Jun 2004 (UTC)
replies: text: The scientific howlers list is likely to grow, slowly but surely. Dpbsmith 22:58, 21 Jun 2004 (UTC)
thread_title:  Name of article 

message: I am a mathematician who studies (among other things) topological (Nielsen) coincidence theory. The word "coincidence" has a widely accepted and recognized technical meaning: given two functions f and g, the Coincidence Set Coin(f,g) is the set of points x such that f(x) = g(x).
This is important as it is (perhaps) the most natural generalization of fixed point (mathematics) theory (where g is taken to be the identity map) and is the original setting for many results (e.g. the Lefschetz fixed-point theorem) which are now commonly misidentified as being fixed point results. (Lefschetz proved first the coincidence version of his result, and noted the fixed point version as a specific case.)
Coincidence theory also has an important reduction when the function g is taken to be a constant map- this setting is called root theory (finding points x with f(x) = c for some constant c). 
As a mathematician, I feel like a wikipedia page on coincidences should refer to the above concept. The content now described as "mathematical coincidence" would perhaps be more accurately described as "mathematical curiosity".
My $0.02.
Chris Staecker, UCLA Math Dept
:Well, we can have a page coincidence set, or coincidence (mathematics), any time you want. Charles Matthews 19:30, 26 September 2005 (UTC)
replies: text: If you ever decide to make those pages, I trust no one would object to the placement of a link to it at the top of the page instructing people on ambiguity of the title.Wrath0fb0b 14:26, 16 March 2006 (UTC)
thread_title:  From a concerned mathematician 

message: It seems to me that there's an important distinction between "coincidences" that arise out of a general theory, like the one about exp(pi sqrt 163), and ones for which no explanation of any kind is known. To take a few examples from the page as of 2005-04-10:
* e^pi ~= pi^e is true because pi is close to e and x / log x is stationary at e. Not much of a coincidence, really; the same would be just as true if 3 or sqrt(10) were used in place of pi.
* pi ~= 355/113 is a "real" coincidence, so far as I know: that is, no reason is known why pi should have so large a coefficient so early in its continued fraction.
* sqrt(2) ~= 17/12 is not much of a coincidence; there's a general theorem that says that roots of quadratic equations always have rational approximations that are at least about that good.
* exp(pi) ~= pi+20 seems to be a "real" coincidence.
* 1 mile / 1 km ~= phi is an absolute coincidence, if anything is. (Incidentally, it might be worth mentioning the Zeckendorff representation in connection with this...)
Is it worth making this distinction on the page? Gareth McCaughan 13:48, 2005 Apr 10 (UTC)
:You make an excellent point. One might as well claim that "pi ~= 3.14" is a coincidence. How about pi^4 + pi^5 ~= e^6? MrHumperdink 16:24, 7 May 2006 (UTC)
replies: text: Cooool... I'm adding this to the article.--Army1987 18:59, 7 May 2006 (UTC)
replies: text: It is cool, but many of these are not. pi ~= 22/7 is not a coincidence, it is an approximation. I'm going to be bold and go through the list, removing what do not seem to be coincidences. Obviously my point of view should be rechecked by other editors; I'll list what I take out here. MrHumperdink 00:31, 8 May 2006 (UTC)
thread_title:  Two levels of "coincidence" 

message: None of these can be classified as coincidences, except maybe 
* e^\pi\simeq\pi^e. -Hmib 02:48, 20 Jun 2005 (UTC)
replies: text: which is explained by the fact that e and pi are both close to 3. --MarSch 13:39, 28 October 2005 (UTC)
thread_title:  these are not coincidences 

message: I have removed the following items from the list:
**  \sqrt{2 \pi} \simeq 5/2  to about 0.1% (one part in a thousand).
** \pi\simeq 22/7; correct to about 0.04%; \pi\simeq 355/113, correct to six places or 0.000008%.
** \pi^3\simeq31; correct to about 0.02%.
** \pi^2\simeq10; correct to about 1.3%. This coincidence was used in the design of slide rules, where the "folded" scales are folded on \pi rather than \sqrt{10}, because it is a more useful number and has the effect of folding the scales in about the same place; \pi^2\simeq 227/23, correct to 0.0004% (note 2, 227, and 23 are Chen primes).
** \pi^4\simeq 2143/22, accurate to about one part in 10^{10}; due to Srinivasa Ramanujan, who might have noticed that the continued fraction representation for \pi^4 begins [97; 2,2,3,1,16539,1,1,\ldots]. See also: Pi culture.
** \pi^5\simeq306; correct to about 0.006%.
Up to here, all of these are simply approximations. So pi is close to 3 and slightly greater... obviously if you square it you get close to 10. Similarly, one might as well call it a "coincidence" that pi ~= 314/100, as to consider 22/7 and and the other fractions.
Continued:
** 1+1/\log(10)\simeq 1/\log(2); leading to Donald Knuth's observation that, to within about 5%, \log_2(x)=\log(x)+\log_{10}(x).
*** This one I'm unsure about. I took it out because it seems too complex or contrived to qualify.
**  \pi seconds is a nanocentury (ie 10^{-7} years); correct to within about 0.5%
*** Yes, or 3, or 3.1, or... basically, nothing special about pi here.
** one attoparsec per microfortnight approximately equals 1 inch per second (the actual figure is about 1.0043 inch per second).
*** "Microfortnight"? No.
** a cubic attoparsec (a cube where each edge is one attoparsec) is within 1% of a fluid ounce.
*** Again, what's special about an attoparsec, or a microfortnight, or whatever?
**  \pi\simeq\frac{63}{25}\left(\frac{17+15\sqrt{5}}{7+15\sqrt{5}}\right); accurate to 9 decimal places (due to Ramanujan).
*** What an astounding coincidence.
** NA ≈ 279, where N is Avogadro's number; correct to about 0.4%. This means that a yobibyte is slightly more than two moles of bytes.
** The speed of light is about one foot per nanosecond (accurate to 2%) or 3×108 m/s (accurate to about 0.1%)
Well, that's it for now. I tried to look for similarities which were neither too simple (e + 0.4 is close to pi! Stop the presses!) or too complex (see Ramanujan's approximation of pi). I hope this helps... MrHumperdink 01:08, 8 May 2006 (UTC)
replies: text: Please, tell me why you consider these to be coincidences, rather than simply reverting my edit in its entirety. I have discussed each one's merits. It is your place to respond now. Approximations are not "coincidences". They can be explained. That pi^4 + pi^5 ~= e^6 is pretty hard to explain, and is relatively simple. And so on. MrHumperdink 14:50, 8 May 2006 (UTC)
replies: text: I am for removal of approximations - they are not coincidences. What so special about pi = 22/7? Is 22 somewhat special, or 7? Better mention some (not really coincidences, but amazing properties of numbers) other things, like friendly numbers: 220 equals sum of all (proper) divisors of 284 (1+2+4+71+142) , while 284 equals the sum of all (proper) divisors of 220 (1+2+4+5+10+11+20+22+44+55+110). --Alextalk 15:55, 8 May 2006 (UTC)
replies: text:  That makes two of us, then. Robinh, please state your reasons for reverting my edit. I won't start an edit war - no worries there :) - but I would like to continue the discussion. I'll leave you a message. MrHumperdink 02:20, 9 May 2006 (UTC)

text: The somewhat special thing is that pi has such a large term as 292 very early in its continued fraction, and that the first powers thereof all have big numbers quite early in their CFs, in the case of π^3 and π^5 as soon as the first denominator. --Army1987 19:58, 10 May 2006 (UTC)
thread_title:  Not-Coincidences Removed 

message: Hi.  You removed 13 points.  I disagree with 10 of these deletions (which I consider to be valid entries), and am unsure about the other 3.  Perhaps a good way forward would be to delete entries one at a time, and then we discuss each one on its merits.
best wishes, Robinh 07:23, 8 May 2006 (UTC)
replies: text: Please, tell me why you consider these to be coincidences, rather than simply reverting my edit in its entirety. I have discussed each one's merits. It is your place to respond now. Approximations are not "coincidences". They can be explained. That pi^4 + pi^5 ~= e^6 is pretty hard to explain, and is relatively simple. And so on. MrHumperdink 14:50, 8 May 2006 (UTC)
replies: text: I am for removal of approximations - they are not coincidences. What so special about pi = 22/7? Is 22 somewhat special, or 7? Better mention some (not really coincidences, but amazing properties of numbers) other things, like friendly numbers: 220 equals sum of all (proper) divisors of 284 (1+2+4+71+142) , while 284 equals the sum of all (proper) divisors of 220 (1+2+4+5+10+11+20+22+44+55+110). --Alextalk 15:55, 8 May 2006 (UTC)
replies: text:  That makes two of us, then. Robinh, please state your reasons for reverting my edit. I won't start an edit war - no worries there :) - but I would like to continue the discussion. I'll leave you a message. MrHumperdink 02:20, 9 May 2006 (UTC)

text: The somewhat special thing is that pi has such a large term as 292 very early in its continued fraction, and that the first powers thereof all have big numbers quite early in their CFs, in the case of π^3 and π^5 as soon as the first denominator. --Army1987 19:58, 10 May 2006 (UTC)
thread_title: reversion of mass delete

message: First things first. Symbol \Approx (\approx) means approximately equal and should be used when dealing with numbers (for example \pi \approx 3). Symbol \Simeq ( \simeq ) on the other hand means similar or equal, which is definitely not the case with fixed values like numbers, it is usually used with functions (for example \sin x \simeq x). I believe I am clear on this: all number relationships should use \approx instead of \simeq. When we will get to assymptotic approximations/coincidences for functions then we will use  \simeq . Ok? --Alextalk 03:09, 10 May 2006 (UTC)
replies: text: no, not okay. \approx means approximately equal and there is no reason why it couldn't be used for functions.  \simeq  means homotopic.--MarSch 15:02, 11 May 2006 (UTC)
replies: text:  You better search Wikipedia for misuse of  \simeq  then. Because I found \sin x \simeq x in one of the articles. --Alextalk 17:13, 11 May 2006 (UTC)
thread_title:  Approx vs. Simeq notation 

message: Added section on amusing equalities. Not sure it belongs to this article, but it is fun reading. --Alextalk 15:36, 10 May 2006 (UTC)
replies: text: This new section seems closest to what the article is getting at: unexpected equalities. I especially liked (1+9+6+8+3)^3=19683. That is a coincidence, I think. And, as you noted, they are actually interesting to hear.
Please, can we remove the Ramanujan one I keep mentioning? Or at least explain why it is coincidental? --MrHumperdink 22:47, 10 May 2006 (UTC)
thread_title:  Other curiosities 

message: This article does not cite any sources. No coincidence, perceived or real, can be included without them. --MarSch 15:05, 11 May 2006 (UTC)
replies: text: Do we really need them? Anybody can test them with a calculator. As WP:NOR says, it makes descriptive claims the accuracy of which is easily verifiable by any reasonable adult without specialist knowledge. --Army1987 18:39, 11 May 2006 (UTC)
replies: text: But how do you verify that any of these coincidences are noteworthy, lacking "direct theoretical explanation"? Fredrik Johansson 20:30, 13 May 2006 (UTC)
replies: text: You raise a good point - for us to rate these as interesting is POV and original research. We should probably take a leaf out of the book of inherently funny word, where the idea is to find "words considered to be inherently funny". That said, I don't really know where to look to find any authoritative source. As noted above, some people may consider certain similarities "coincidental", when they are not. (For instance, e^pi ~ pi^e, which is the case simply because e ~= pi.) I'll check Mathworld, see if they have an article there. --MrHumperdink 21:13, 13 May 2006 (UTC)
replies: text:  We are providing only examples of curious numeric facts. We don't pretend to list  all "mathematical coincidences". From that point of view any correct fact found in valid sources  that mark it as such is OK for inclusion (availability of primary source should address "original research" concern). This very discussion about merits of each individual example (in my mind) addresses NPOV concern. --Alextalk 06:40, 14 May 2006 (UTC)
thread_title:  sources 

message: I'm still rather unsure about the boundary between a coincidence which has an "explanation" and one which does not. dictionary.com defines coincidence as "The state or fact of occupying the same relative position or area in space", which seems more appropriate than the alternative definition about chance events. No mathematical coincidence is a chance event, since they are all determined precisely by the underlying axioms, with no uncertainty. I am sure that for any apparently "chance" co-incidence, someone could come up with an indirect argument why the approximation was as good as it is, rather than just doing the calculation and seeing that it is. Just because an approximation is "explained" by a large term in a continued fraction expansion is not a reason to exclude it, since good approximations will obviously tend to be associated with such continued fractions. 
There should be some role for information theory here - a coincidence could be defined as an unusually compressed form for a good approximation. For example, a certain amount of information is needed for a fraction, and this amount of information can be compared to the error in an approximation. (It may be best to just compare the information content of the denominator to the accuracy) Elroch 11:36, 15 May 2006 (UTC)
replies: text: Obviously all approximate equalities are determined and chance plays no role. But we could define a coincidence as an unexpected approximate equality. Yes, in the case of CFs with large terms, coincidences do have a reason, but an unexpected one. Nobody would expect the CF of pi^4 to have a five-digit term so early before calculating (or reading about) it. In the case of approximation of irrational number by a fraction, we could for example define a coincidence as when a term in the CF is much bigger than the denominator of the fraction obtained with the terms before it. For example, IIRC, pi = [3, 7, 15, 1, 292, 1...]; fifteen is more than twice as much as the denominator in 22/7, and two hundred and ninety-two is more than twice the denominator of 355/113. (Of course, this way many approximate equalities with integers could be deemed coincidences; but we could say that this shouldn't apply to integers, and approximate equalities with integers should be considered coincidences only when a number is within 0.02 of an integer.)
Anyway, I'm removing pi^e = e^pi. That's definitely not a coincidence, it happens with any two numbers enough close to e. For example, 2.5^3 = 3^2.5 is much more precise.
If nobody objects, I'm going to remove that one by Ramanujan with fractions and roots, and to re-add the ones about pi, pi^3, pi^4 and pi^5.--Army1987 14:52, 15 May 2006 (UTC)

text: I still don't see how they are "coincidental" rather than simply "unusual". Is there even a distinction to make? For instance, the famous e^{i*\pi} + 1 = 0 seems almost "coincidental" despite it having a logical proof. I don't know any more. I may leave this page up to you two... --MrHumperdink 23:05, 15 May 2006 (UTC)
thread_title: Defining coincidence

message: Towards the bottom of the page, it is stated that 71^3 = 357911,
which is correct. However, this number is referred to as "consecutive
primes", which is incorrect. —Preceding unsigned comment added by mstemper (talk • contribs) 
:Good call. I suppose you could say "consecutive odd numbers", but it doesn't seem much of a coincidence. Why not list a factorization of 3579? or 35791113? It's somewhat remarkable that the given number was a perfect cube, but nothing to write home about. Staecker 01:43, 27 May 2006 (UTC)
replies: text: I guess it meant three five seventy-nine eleven, but so, why are they "consecutive"? --Army1987 08:53, 27 May 2006 (UTC)

text: 357911 also consists of three primes (which is amazing since the LHS contains a third power), when written in base 111 (three ones in a row!). Pick any couple of numbers and you can make up some "coincidence" between them if you think hard enough. Entries like this one are pointless. Fredrik Johansson 09:22, 27 May 2006 (UTC)

text: You are right but there is no error.  Exp[pi * sqrt(163)] = e^40.10916999113251975535008362290414... = 262537412640768743.99999999999925... which is both a large number and close to being an integer. Meanwhile sin(666°) = −sin(54°)= −sin(3π/10 radians) = −0.80901699... = −phi/2.  At the same time  cos(6*6*6°) = cos(216°) = −cos(36°) = −sin(54°) so the same value. --Henrygb 14:45, 22 November 2006 (UTC)
thread_title: Error

message: :40 is the only number whose (English name) letters are ordered alphabetically.
This has nothing to do with mathematics - not even marginally - and everything to do with language (but only one particular language).   It is in interesting fact to bring out at trivia sessions, but it is certainly not a "coincidence" (mathematical or any other kind), and I don't see how it has any place in this article.  JackofOz 01:13, 25 July 2006 (UTC)
replies: text:  Agree --Alextalk 14:01, 25 July 2006 (UTC)
thread_title: Spelling of 40

message: It seems to me that the identity 1111111111^2 = 12345678987654321 is just a special case of 1^2 = 1, 11^2 = 121, 111^2 = 12321 and so on until the sequence terminates with the 9-digit sequence of ones listed. I propose that this interesting sequence replace the given text. —The preceding unsigned comment was added by Koalaitis (talk • contribs) 22:31, 31 January 2007 (UTC)
replies: text: You're right, I have removed this one. --KnightMove 13:57, 25 April 2007 (UTC)
thread_title:  Integer Powers of Eleven in Decimal Coincidences Section 

message: This is hardly a decimal coincidence, for it this completely expected in all integers squares if not for the limitations of the decimal system.
For example, consider (2x+y)^2=4x^2+4xy+y^2. Substituting in x=10, y=1 will automatically give a decimal expansion and no further computations, and thus we can easily switch the values to also switch the digits of the outcome. This is why 12^2=144 and 21^2 = 441. But consider (5x+y)^2=25x^2+10xy+y^2. Substituting x=10, y=1 will not be the reverse of x=1, y=10. Why? Because 25 is not a digit and thus these substitutions will not automatically form a decimal expansion. This so-called "coincidence" that only 12^2 = 144, 21^2 = 441 produce such a result (which is incorrect, as 13^2 = 169, 31^2 = 961 is also similar) is a result of the limitations of the decimal system, not by mere chance. As another example, consider the number base 26. In base 26, 25 is a digit and thus substituting x=26, y=1 will automatically give a base number expansion in (5x+y)^2=25x^2+10xy+y^2, and thus x=1, y=26 will produce a reverse:
(15_{26})^2=1AP_{26} and (51_{26})^2=PA1_{26}  
—75.176.165.18 01:41, 24 August 2007 (UTC)
thread_title: "As 12² = 144, 21² = 441."

message: In addition to the mentioned case of 5^2 + 2 = 3^3, I recall reading that 2^3 and 3^2 are the only non-trivial natural powers with a difference of 1, and 5^3 and 2^7 the only with a difference of 3. I dunno what exactly happens with larger numbers; you can just start picking up power pairs at semi-random (3^3 + 5 = 2^6; 11^2 + 7 = 2^7; 10^3 + 24 = 2^10; 3^5 + 100 = 7^3...) but I haven't found any number cropping up twice, between different powers at least (square differences can account for just about anything non-prime, and cubes a lot too). Not that I've looked very hard. I digress tho; my points being:
* is anyone able to verify that for n = 1, 3, there are no other solutions either?
** for that matter, a citation for the case mentioned in the article might be nice too, as it's not exactly a trivial claim.
* is anyone able to provide examples of multiple cases of some difference between differing powers?
** or cite a theorem or hypothesis on their non-existence?
BTW, I don't think approximations such as pi^2 = 10 should have no place in here, mostly because it's not even very good an approximation. How about setting a threshold of accuracy before something can count as a "co-incidence"?
--Tropylium 11:53, 27 September 2007 (UTC)
thread_title: Only powers that differ by  ''n''

message: 7^7/8^6  in octal, 3.110367 vs pi 3.110375524210, is the best appromimation of pi in 'humble' numbers (primes less than 10), in numbers less than 1e8.
256/81 is the ancient Egyptian version of pi, derived from subtracting 1/9 of the diameter, and squaring to get the area.  
1521/484 is a very good appromimation to pi in square numbers.  A square of edge 44 inches, has the same area as a circle of diameter 39 inches.
20*sqrt(2)/9.  An ancient value of pi, which equates a quadrant arc of 10, where the inscribed circle is 9.  --Wendy.krieger 07:49, 1 October 2007 (UTC)
thread_title: Pi Appromimates

message: 6^phi = phi^6 ~ 18.  One can start a multiplicitive fibbonacci-series, from 2,3 which passes through 6, 18, 108, 1944 etc.
ln 17 = 17/6.  This makes log_17 of e = 0.6000 base 17.
US dry bushel = 14-inch cylinder [cylinder 14 inches high, diameter] (actually 2738 cyl inch, not 2744), is inscribed in a 14 inch cube, representing the heaped bushel (2744 cu in, vs actual 2747.715 in).  Also, the wine tun (252 US gallons), is very close to a 42-inch cylinder (exact for pi=22/7) 1 tun = 58212 cyl in, 42 inch cylinder =  58188.6 cu inches.
One hoppus foot = 36 litres, [= 36.054128], 1 kilolitre = 45 cylinder feet (eg cylinder 3 ft diam * 5 ft high), makes pi = 20.sqrt(2)/9. 
--Wendy.krieger 08:02, 1 October 2007 (UTC)
thread_title: Some Curios

message: That the Joule is an SI unit, is indeed a cooincidence.  We know this, because the Joule is part of an older system (Volt-Ohm-Second), where the unit of energy happened to be equal to the then unfashionable "mecahnical" definition of energy, when using the already MKS units.  
We see that the Volt-Ohm-second system was used with any measure (eg V/ft, V/cm), the units being an arbitary unit not derived from Length, Mass, Time.  Gustav Mie proposed a system V, Ohm, s, cm (mass = dekatonne), and Giorgi suggested V, Ohm, s, m, (mass = kg).  This allowed MKS units to be used as a scientific measure, rather than the technological units).
Wendy.krieger 07:19, 5 October 2007 (UTC)
thread_title: Joule

message: I've tagged both the article and this talk page with cleanup, since there is a ton of unsourced trivia and other stuff that needs to be either sourced or removed.  Not every numerical coincidence is noteworthy enough to be in an encyclopedia; only those that have been discussed as such in reliable sources should be here. Dicklyon (talk) 22:13, 28 December 2007 (UTC)
thread_title: Cleanup tag

message: Dicklyon,
I am wondering why you totally removed my contribution regarding the fact that that 25 ET semitones almost exactly equals Phi^3, without discussion, but then returned this information to the page in your own words.
I would have been open to discussion, and agreeable to stating the coincidence in a concise manner. Prof.rick (talk) 02:51, 15 January 2008 (UTC)
replies: text: Are we a bit forgetful?  See the section #Repeated reverts of "Music: Phi and semitone" above.  My compromise was to allow a brief mention in the new section where it fit, but even that probably doesn't belong, based on WP:NOR. Dicklyon (talk) 03:54, 15 January 2008 (UTC)
replies: text: Are we a bit sarcastic? I don't have to review the facts...you know them. Yes, you "compromised"...a very polite way of describing your actions. I have nothing to add at this point, but await discussion by other editors.  Prof.rick (talk) 05:16, 15 January 2008 (UTC)
thread_title:  Phi and semitone 

message: Dick,
I would like to leave both this and YOUR entry above it open to discussion by other editors.  Is this reasonable?
My most recent addition to the article is a "mathematically evident" fact (such as "0.333 approximately equals 1/3"). I have found, in working on other articles with other editors and administrators, self-evident facts do NOT require a published source of reference.  The argument is not that we must cite a published source for every single word or figure we enter into Wikipedia, but that the material we present is VERIFIABLE. If you, or anyone, does the very simply math of my recent entry, you will realize that it is unquestionably self-verifying. (This is hardly "original research".)
If we leave these matters open to discussion, I am certain an agreement and/or concensus can be reached, one way or the other. If not, then we can eventually ask for arbitration.  (Give the process time!)
With patience, and in continuing dedication to Wikipedia,  Prof.rick (talk) 05:09, 15 January 2008 (UTC)
replies: text: Sure, discussion is what we're here for.  In the context of "coincidences", I think what we want for "verifiability" is not the checking of the arithmetic, but the verification that something is a "coincidence" in the sense that it is interesting enough to have been remarked on.  If we open the article up to all true mathematical relations that anyone wants to claim is a coincidence, it will be out of control.  Much of the discussion above has been about trying to get back some control over the creeping content, and it seems to me that one obvious filter we want is that we only include content that has a source.  I realize that not everyone shares that view. Dicklyon (talk) 05:24, 15 January 2008 (UTC)

text: In the new item you added the "Phi" was a new name and symbol for the "phi" in the item above it, but meant the same number as opposed to the conjugage golden ratio that it looked like.  And there was no explanation of what it was, or why you thought it was a coincidence, or how it fit in that section.  But basically it was another bit of your original research, as far as I can see; if there's a source for it as a coincidence, cite that and it will be OK.  As to discussion, yes, I am often very brief in edit comments when reverting junk, but always willing to talk it over as needed; see WP:BRD.   Dicklyon (talk) 06:54, 15 January 2008 (UTC)
thread_title:  Discussion: (Phi^3)/4 

message: I went ahead and took out the item on the fourth, since it follows trivially from the one on the fifth (since a fourth is an octave minus a fifth).  And it was just a magnet for elaboration that had nothing to do with mathematical coincidence, as we saw. Dicklyon (talk) 00:59, 16 January 2008 (UTC)
thread_title: Fourth

message: Dicklyon comments, "Simple numerology is not mathematic coincidence." However, if one omits the relation between 8! and the number of minutes in a month, then one would also omit the relation between 10! and the number of seconds in 6 weeks, for the same reason. --Robert Munafo (talk) 01:13, 9 February 2008 (UTC)
replies: text: Yes, I agree.  I'll take it out. Dicklyon (talk) 07:19, 9 February 2008 (UTC)

text: Yes, I think so.  This article is a magnet for numerology, which detracts from the topic. Dicklyon (talk) 19:07, 9 February 2008 (UTC)
replies: text: How is that one numerology? It's easy to verify but it does not seem trivially apparent to me that there should exist x, y, z so that x! * y! = z!. (Any larger examples? Doesn't look likely because you'll need to include an equal amount of all primes on both sides.) Additionally, there's no symbolism of extra-mathematical significance used in there... I'm not convinced it's necessarily a coincidence but it seems like an interesting factoid nevertheless. --Tropylium (talk) 12:36, 17 June 2008 (UTC)

text: Some of my stuff is being rejected as original research.  Consider the esthetics of 13!=2^10*3^5*5^2*7*11*13=100100*(250+6)*(250-7)=6227020800, and of the related pair A) (365+1/4)^2=3^7*61+9/16 and B) (365+1/4)^4=17797577732+7^2/2^8.Julzes (talk) 02:27, 25 May 2009 (UTC)
replies: text: (10^5+10^2)*(10^3/4+6)*(10^3/4+7) isn't really that big a deal. Given four arbitrary powers of ten and three~four single-digit integers, you can represent a whole lot of numbers really. That (a/d)^2 coincides next to a multiple of a large power of 3 is somewhat interesting, but not all that much; and I'm afraid don't see at all what's special about the last? --Trɔpʏliʊm • blah 10:00, 25 May 2009 (UTC)
replies: text: I'm sorry, but it is primarily the coincidence of seven 7s and the connection to A (where likely the most symmetrical transformation of the first six digits as a mixed fraction raised to a power (of 2408 possibilities according to my effort)) that makes B appealing.  There are other things, but they are not the result of pure inspection.  The fact that the sum of the digits of both numerator and denominator of B are 13 and that numbers congruent to 13 modulo 32 in place of 365 will produce the same fractional part struck me at least.  I am currently doing research on an even stronger coincidence problem related to B that may settle the issue, if an issue exists.  But, as I said, I am just looking at what can be seen of the pairing of A and B by inspection for possible inclusion in the article.  As I see it, the article's introduction could include discussion of it at some later date, before going on to all of the other reasonably neat observations.  I don't judge the first as spectacular as far as coincidences go.  It's a nice way to get from thirteen-factorial to its value--as a semi-mental calculation--with a little additional appeal is all.Julzes (talk) 22:34, 25 May 2009 (UTC)
thread_title: Simple Numerology

message: For the record, 987654321/123456789 ~ 8 is not a coincidence, it works in any base.  —Preceding unsigned comment added by 99.226.91.117 (talk) 03:59, 21 March 2008 (UTC)
thread_title: 987654321

message: "This can be told humorously as: Take the number "1234", transpose the first two digits and the last two digits, so the number becomes "2143". Divide that number by "two-two" (22, so 2143/22 = 97.40909...). Take the two-squaredth root (4th root) of this number. The final outcome is remarkably close to π (within about one part in a billion)." (My bold). In what way is this even slightly humourous? If someone tried to tell me a joke like that at a party I'd have to try remarkably hard not to punch them in the face. El Pollo Diablo (Talk) 13:01, 23 October 2008 (UTC)
thread_title: Humourous? ''Really?''

message: I want to highlight a particular item recently deleted: sqrt(2)+sqrt(3)~=pi.  I think it needs to be in such an article.Julzes (talk) 22:59, 29 May 2009 (UTC)
replies: text: Have you seen it somewhere else? Two decimal places precision in pi is quite low considering the complexity of the expression. Dmcq (talk) 09:41, 31 May 2009 (UTC)
replies: text: No I haven't, and I was surprised to find it was accurate to about THREE significant figures for the first time myself here, since I was one of the best competitive math students in the country in high school.  You're not picking on the fact that it technically rounds up to 3.15, are you?Julzes (talk) 11:07, 31 May 2009 (UTC)

text: Your reading of the sum of the first two non-trivial square-roots as complex is a bit mystifying.Julzes (talk) 11:22, 31 May 2009 (UTC)
replies: text: Two decimal places is the number of correct digits after the decimal point. I also find the approximation unimpressive and don't support it without a good source. The article looks like an  and I think we should work towards only having sourced examples. PrimeHunter (talk) 11:25, 31 May 2009 (UTC)
replies: text: Well, I do tend to agree in general that it's the example-farm you suggest.  I personally think it should be part of a larger article and paired down to the best examples with reference to outside for more.  I did not say the case in question was impressive, but I also contest its complexity.  It doesn't get too much simpler.Julzes (talk) 11:34, 31 May 2009 (UTC)

text: 0.15% is the quality of it as an approximation, but it's one that I can't say I see as useful.Julzes (talk) 11:43, 31 May 2009 (UTC)

text: What about simple facts that aren't here?  Most everyone you or I know knows about the first ten digits of e, but that doesn't mean it doesn't deserve mention, and the common logarithm of 2 is inaccurately handled in the article.Julzes (talk) 11:47, 31 May 2009 (UTC)

text: An easy estimation of its complexity is given by how many keys you'd have to punch on a simple calculator -  2 root 3 root plus to cut it down using reverse polish. There's 16 keys so that's a 5 digit hexadecimal number whereas the value got had only 3 significant decimal digits. Seems pretty poor to me. I'm sure doing things in binary and using an arithmetic code would make it considerably better but it isn't exactly outstanding. Dmcq (talk) 12:03, 31 May 2009 (UTC)

text: I'm not going to argue with that.Julzes (talk) 12:15, 31 May 2009 (UTC)

text: I'd say my way of looking at it is that the three irrational numbers concerned are apt to be memorized to several digits by many children, yet they might only see the relationship if it's pointed out.  It's not critical.Julzes (talk) 12:18, 31 May 2009 (UTC)

text: Has anybody found good textual justification for this article's existence in a single place?  There was, in my earlier reading of material that no longer resides in the article, a webpage by a Californis Institute of Technology Ph.D. dealing with the matter.  But if that's about as deep as it goes, it seems almost as though there is no known source justification for the article's existence at all.  No single one, at least.  I certainly am not suggesting this for AfD, but it does almost seem that I and other participants here are making some kind of exception with it.  I have no doubt that this material belongs here in some form, but a recent modification to slightly improve the definition in the lead (by me), which is just a 'common sense' application of what 'mathematical coincidence' means (by including a type in addition to near-integer reals, where a large integer is found to satisfy two relatively simple and not related criteria) should be in any 'real literature' on the subject.  Also, should a mathematics coincidence to a non-mathematical object be considered mathematical?  This is part of the current content, but for something to be coincidental it has to have contact with mathematics to achieve notability. Even if it is a unit-measurement coincidence with no clear reason, it would seem that it is a coincidence but not a mathematical one.  I wish I had a lot of time to devote now to fixing this (these) issue(s) myself, and others, but I do not.  I have made some sort of commitment to wikipedia in other languages that may dovetail, but I don't have any expectations it will.Julzes (talk) 15:28, 18 June 2012 (UTC)
thread_title:  Simplicity vs. Precision 

message: There are a number of the coincidences which are listed in MathWorld, e.g.
: \left(1+\frac{1}{6400}\right) \sum_{k=1}^8 \frac{1}{k} \approx e.
in , and the attributions there are to personal communications. Is a reference to the Mathworld articles ok or should the items just be removed and this article just point to the Mathworld articles as see external sites? Dmcq (talk) 09:25, 31 May 2009 (UTC)
replies: text: Any citation is better than none.  Let's get what we can done.Julzes (talk) 11:19, 31 May 2009 (UTC)
replies: text: I think would be best to go to the sources cited in Mathworld where they exist.  As you point out, some are unsourced technically ("personal communication").Julzes (talk) 12:30, 31 May 2009 (UTC)

text: The very first item in your article choice is an example of a "coincidence" I would add.  That's pretty neat.Julzes (talk) 12:33, 31 May 2009 (UTC)

text: It's a "simple" application of (1+1/n)^n-->e.  It's sort of sourced.Julzes (talk) 12:41, 31 May 2009 (UTC)
thread_title:  Coincidences in MathWorld 

message: I'm not spending a lot of time on this today, but this article needs a major prose infusion.  I would put a few paragraphs together for the introduction, do something about distinguishing between mathematically meaningful coincidences and those which are quite apparently not of that nature, and say something about Pythagoreanism and about distinguishing between data-mining quasi-results and everything else.  I would suggest, or will write myself, an introduction that includes a paragraph combining the second through fifth coincidences currently listed.  Nowhere does the fact that e=2.718281828... appear, and this would be highlighted in what needs to be said to get this article right.  The decision to attack things that smack of numerology in the history of this article is certainly somewhat incorrect.  There were once, before I came here, a whole host of supposed coincidences in units.  I have not analyzed that material, but I have reasonably good grounds to take another look at it.  I'll be back to spend more time on this article periodically (It's not top priority for me).Julzes (talk) 23:43, 3 January 2010 (UTC)
replies: text: I though the main reason things had been removed was that no reliable sources could be found for the removed stuff. It had become a list of peoples own calculations. Dmcq (talk) 00:14, 4 January 2010 (UTC)

text: A good leader is always an excellent advantage for an article. As to the expansion of e I'm sure there probably is some citation for that if one can find it. In most maths articles one can get away with sticking something fairly obvious like that in but I think this one has to be careful with strong entrance criteria or it'll just degenerate into rubbish. Dmcq (talk) 14:44, 4 January 2010 (UTC)
thread_title:  Re-writing and re-organizing and other things needed 

message: A recent diff  stuck in stuff I would never have imagined would have made it into a book I was surprised when told they were in the book "Prime Curios!: The Dictionary of Prime Number Trivia". Could someone who has access to the book verify that and say if it really is full of that sort of stuff thanks as I'm finding it hard to believe anyone would pay good money for that sort of thing.
The main point though is shouldn't there be some better selection criteria if there are books full of trivia like that? The book is entitled trivia and I really don't see that Wikipedia should duplicate its contents. Dmcq (talk) 15:35, 14 June 2012 (UTC)
replies: text: Both those were contributed to the Prime Curios website by 'Merickel' as far as I can make out and the contributor index for the book can be looked at from  and it doesn't have Merickel listed. They may have a different name there or some mistake but yes I really would like someone to check now thnks. Dmcq (talk) 15:44, 14 June 2012 (UTC)
replies: text: This article is still a mess.  I apologize for raising your hopes, if I did.Julzes (talk) 22:28, 25 June 2012 (UTC)
replies: text: The book is older than Merickel's first website contribution.Julzes (talk) 18:59, 29 January 2013 (UTC)
thread_title:  Prime curios 

message: Re-assessed to C-class.--Gilderien Chat|List of good deeds 14:08, 14 July 2012 (UTC)
thread_title: Assess

message: All over the page! HotdogPi 03:13, 8 September 2012 (UTC)
thread_title:  FAILED TO PARSE 

message: *To convert meters/second to miles/hour, multiply by \sqrt{5} :  correct to 0.04%
*Doubling a  power quantity is an increase of 3 dB; doubling a  field quantity is an increase of 6 dB :  both correct to 0.3%
M-1 (talk) 00:25, 5 October 2012 (UTC)
thread_title:  a couple of physics coincidences 

message: According to a recent edit: "The circumference of the earth is equal to forty thousand kilometers, to within 0.2%." 
This is correct but it is not a coincidence. The kilometre was originally defined to be 1/10,000 of the distance from the equator to the pole -- see History_of_the_metric_system. Nick Levine (talk) 13:19, 8 November 2013 (UTC)
thread_title:  Earth's circumference 

message: cos e + sin e = about -0.5? Is that an example?  — Preceding unsigned comment added by JDiala (talk • contribs) 07:44, 30 January 2014 (UTC)
thread_title:  cos e + sin e 

message: The eighth root of ten is very close to four-thirds.  — Preceding unsigned comment added by 72.77.58.127 (talk) 18:57, 29 April 2014 (UTC)
thread_title:  Eighth root of ten 

message: The section "speed of light" says
:Another coincidence is that one lunar year (354 days) of acceleration with 1g gives speed of light: 9.8×354×24×3600=299,738,880.
That doesn't make any sense. You could accelerate forever at 1g and not reach the speed of light. Loraof (talk) 14:44, 9 October 2015 (UTC)
replies: text: True, I made a small note to point that out. Maybe we should remove the whole sentence but let's wait for more input. Gap9551 (talk) 16:32, 9 October 2015 (UTC)
replies: text: I removed it now, because further down in the subsection 'Gravitational acceleration', it is mentioned that g is close to 1 lightyear/year^2, which is physically fully correct and captures the same coincidence. Gap9551 (talk) 18:46, 6 April 2016 (UTC)
thread_title:  Speed of light 

message: The square of the number of seconds in a leap year is close to a power of 10: (366 \times 86400)^2 \approx 10^{15} (±0.002%). --MizardX (talk) 15:39, 22 June 2016 (UTC)
thread_title:  366 days squared 

message: 2 + 4 + 8 = 14;
1 + 2 + 4 = 7;
21 + 42 + 84 = 147;
Let's swap digits in numbers: 21, 42, 84 to make 12, 24, 48 - another geometrical sequence. 
Then subtract "second" numbers from first ones:
21 - 12 = 9;
42 - 24 = 18;
84 - 48 = 36;
9, 18, 36 - it is also a geometrical sequence. 
Subtracting "third" numbers from second ones:
12 - 9 = 3;
24 - 18 = 6;
48 - 36 = 12;
"Fourth" numbers (3, 6, 12) also form a geometrical sequence.
Subtract "fourth" numbers from "third" ones:
9 - 3 = 6;
18 - 6 = 12;
36 - 12 = 24;
"Fifth" numbers also form a geometrical sequence: (6, 12, 24).
Subtract "fifth" numbers from "fourth" ones:
3 - 6 = -3
6 - 12 = -6
12 - 24 - -12
"Sixth" numbers also form a geometrical sequence: ((-3), (-6), (-12)).
Subtract "sixth" numbers from "fifth" ones:
6 - (-3) = 9;
12 - (-6) = 18;
24 - (-12) = 36;
"Seventh" numbers also form a geometrical sequence: (9, 18, 36). 
We can make that iteration any number of times and we would always receive a geometrical sequence.  — Preceding unsigned comment added by Rabbitsquirrelcat (talk • contribs) 18:28, 14 September 2016 (UTC)
thread_title:  21 42 84 - interesting geometrical sequence 

message: 3*1013*1669*211317915670188235207471*917594864466917047064519*349052954223539065525171338860405905128439 = 10000*(1092738277*314158989541307472007949836495783819190879794835648629101616910339200019752591795513)+101 (something about 'C-O-N-G' as a transliteration). OR, so not.  — Preceding unsigned comment added by 96.83.240.59 (talk) 13:16, 22 February 2017 (UTC)
replies: text: Note: 84-digit, two 24-digit primes, leading digits of pi, 3 years after Hanoi's being named capital of Vietnam, Room 101 in 1984 by G. Orwell who's understood to have chosen title by inverting final pair.  So, a mix.  Notable for page, highly NO! Inexplicable historical baggage.Julzes (talk) 20:43, 22 February 2017 (UTC)
replies: text: Result out 13 hours and 16 minutes ago.Julzes (talk) 21:43, 22 February 2017 (UTC)
thread_title:  Text too 

message: The prime factorization of 13532385396179 is equal to 13×532×3853×96179 which uses the same digits and ordering as the number itself. I don't know if this is considered a coincidence or not.  — Preceding unsigned comment added by 71.179.19.89 (talk) 23:03, 14 December 2017 (UTC)
replies: text: Indeed; added to the Decimal coincidences section. Renerpho (talk) 15:27, 15 April 2024 (UTC)
thread_title:  Conway's climb to a prime 

message: 2^2^3^2^-1 = 2^2^√3 = 10.000478217... ~= 10.
e^11^3 begins with four 1s
7^3^6 and 2^2^11 are close in magnitude?
6^2^7 almost a googol?
2^2^666 ~= 10^10^200 (actual value 10^10^199.96458...), involves number of the beast
71.179.19.89 (talk) 23:27, 14 December 2017 (UTC)
thread_title:  Power towers? 

message: √(62) inches ≈ 20 centimeters, with an error of 0.0001% (0.2 microns). A more accurate value is 19.999979999989999989999987499982... centimeters. Note that most of the digits in the first 32 digits are nines. 71.179.21.46 (talk) 19:33, 27 August 2018 (UTC)
replies: text: Gap9551 (talk) 19:38, 6 September 2018 (UTC)
thread_title:  Square root of 62 inches to centimeters 

message: Something useless I noticed one day, but is strangely interesting.
--Skintigh (talk) 02:49, 17 January 2019 (UTC)
thread_title:  100 decimal = 64 hexadecimal, 100 octal = 64 decimal. 

message: The 13th Mersenne prime is 2^{521}-1, and \sqrt[13]{521}\approx\frac{1+\sqrt{5}}{2}. In addition, 521 is the 13th Lucas number. 
The last nine digits of the 43rd Mersenne prime, 2^{30402457}-1, contain each digit from 1 to 9 exactly once: 652943871.
—Jencie Nasino (talk) 02:10, 22 July 2019 (UTC)
thread_title:  Coincidences regarding Mersenne primes 

message: perhaps this is a dumb question, but why is 163 a category? is it very fundamental or something, or do i just not get some reference Ajlee2006 (talk) 13:20, 23 August 2020 (UTC)
replies: text: No, not really. I've removed two of the three examples under it and combined the last entry into the previous subsection. –Deacon Vorbis (carbon • videos) 13:31, 23 August 2020 (UTC)
thread_title:  why 163? 

message: *\sqrt[\pi]{4}\approx e^{W(\ln2)}. Correct to about .317%.
*The error's error is about 1.024*π‰.Alfa-ketosav (talk) 20:10, 22 September 2020 (UTC)
thread_title: Another coincidence

message: Gatomon sequence (aka Tailmon sequence) - ascending or descending arithmetic progression or geometrical sequence formed by additive prime numbers which all have the same sum of digits which is also an additive prime number. 
5, 23, 41 and 191, 227, 263 are (examples of) Gatomon sequences (Tailmon sequences). I may think that suggested names are "cool" and "funny" because they commemorate cute catlike creature from Digimon franchise by naming such sequences as "Gatomon sequences" ("Tailmon sequences"). It is rather not surprising that I do not know if there are any other Gatomon sequences, even in decimal system.
5 = 5; 2+3 = 5; 4+1 = 5.
5 - an additive prime number.
5, 23, 41 - common difference is 18.
1+9+1 = 11; 2+2+7 = 11; 2+6+3 = 11.
11 - an additive prime number (1+1 = 2).
191, 227, 263 - common difference is 36.
--Rabbitsquirrelcat (talk) 20:08, 18 December 2021 (UTC)
thread_title:  Something which I nicknamed "Gatomon sequence" (it is associated with additive prime numbers) 

message: 987654321 / 123456789 ≈ 8.0000000729 ≈ 8 180.244.139.139 (talk) 16:12, 10 March 2024 (UTC)
replies: text: That could be done in any non-tiny base and follows from how bases work so it's not a coincidence. In base 10: 123456789×8 = 123456789×(10-1-1) = 1234567890 - 123456789 - 123456789 = 1111111101 - 123456789 = 987654312. PrimeHunter (talk) 22:52, 10 March 2024 (UTC)
thread_title:  Another coincidence? 

message: Quote from article: 
<< \,7^{510}\approx10^{431}. This is equivalent to {\log7}\approx\frac{431}{510} >>
What is the significance of this fact? Of course you can approximate \lg 7 by infinitely many rational numbers p/q which will lead to approximations 7^q \sim 10^p. Any pair of non-zero non-unit natural numbers (and not only) have the same approximate equialities. One can agree that 2^{10}\sim 10^3 is interesting because exponents are small and precision is quite impressive, but 510 and 431 are large enough to be interesting.  — Preceding unsigned comment added by 46.39.51.110 (talk) 11:37, 13 April 2024 (UTC)
replies: text:  The same question for << 6^9 = 10077696, which is close to 10^7 = 10000000. Also, 6^9 - 10(6^5) = 9999936, which is even closer to 10^7 = 10000000 >>and << \,7^6 = 117649\approx\frac{10^7}{85} = 117647.0588 >>.
Removed, per the above, and because no citations were given that would demonstrate how this was notable. Renerpho (talk) 15:13, 15 April 2024 (UTC)
thread_title:  Coincidence about 7^q = 10^p 

message: (See section "Planet Earth", added recently about pi*10^7 )
Again, there is no significance in that, no specific of pi there, just about "3" or "3.15", etc. See also discussions above in the current talk page (sections "Not-Coincidences Removed" and "nanocentury"). Please, remove it. 46.39.51.121 (talk) 14:24, 24 April 2024 (UTC)
thread_title:  Earth solar orbit