When this proposed trisection technique is applied to a right angle, it yields an angle whose tangent is 1/2, where one would need an angle whose sine is 1/2. That's trivially easy to show without knowing the classic theorem that is far from trivially easy to prove. Michael Hardy (talk) 19:19, 1 January 2016 (UTC)[reply]
I believe the nominator made a mathematical mistake. If I haven't made a mistake, the construction trisects the chord, rather than the angle, making it a good approximation for small angles, although obviously not exact. I don't thinkit belongs in the article, and it certainly doesn't belong on Wikipedia under that title, but as an approximate angle trisector.
On a priori grounds (i.e., I haven't looked at any of the articles before writing this) I would think that equivalence relation and equivalence class could be a single article. But the words "set partition" suggest a particular approach and collection of results related to the combinatorics of finite sets, and these should be in a separate article. --JBL (talk) 15:10, 3 January 2016 (UTC)[reply]
After a look at the articles, I agree with JBL. Equivalence relation and equivalence class should be merged and partition of a set should stay separate. Another thing to keep in mind is that people sometimes do want to partition sets without thinking about equivalence relations. Merging partitions of a set to equivalence relation would confuse many readers. Happy Squirrel (talk) 19:18, 3 January 2016 (UTC)[reply]
This raises the question of whether there are situations where one can have an "equivalence relation" without a notion of "equivalence class". Anyone who knows more than I do about stacks and groupoids, feel free to chime in. Sławomir Biały20:14, 3 January 2016 (UTC)[reply]
I believe the only thing that categories buy you in this situation is a different language (possibly less scary? or maybe more) for discussing proper classes. Ozob (talk) 23:12, 3 January 2016 (UTC)[reply]
You may prevent the proposed deletion by removing the {{proposed deletion/dated}} notice, but please explain why in your edit summary or on the article's talk page.
User talk:Cherkash seems to systematically replace s' by s's in various math articles and move them as well. Affected articles are Pappus's hexagon theorem, Pappus's area theorem, Desargues's theorem, Pappus's centroid theorem. I don't really have strong opinion on the subject although to my knowledge the old spellings were correct (and used in math literature) and I'm always a bit wary about articles getting moved from correct version to another due to (individual) taste preferences.
Crudely speaking both versions seems to be correct with various spelling and grammar guides disagreeing or simply declaring it a matter of taste. In math literature both spelling can be found as well (a Google books test on Desargues'(s) theorem for instance yielded 15,800 hits for Desargues' theorem versus 24,500 hits for Desargues's theorem).
Just to be clear: it's not just a matter of renaming the articles – the articles text often used both versions as well (probably reflecting the stylistic preferences of different editors at different times, although most of the entries seemed to agree with s's rather than s'). So all I did was pretty much harmonize possessives' use in the articles, and brought articles names in line with the proper usage, as showcased in the body of the articles. See also MOS:POSS.
As for the reasons the 's form is always preferable to a simple apostrophe in case of singular possessives: there are usually very limited "traditional" exceptions to the use of 's for singular possessives even when the noun ends with "s". Jesus seems to be one case where most style guides and grammar books agree on "Jesus' " as being acceptable (although Jesus's is still quite correct, Jesus' is an acceptable form). As for the rest, even if noun ends in "s", for as long as it's a singular noun, the 's should be added, not simply an apostrophe. See again MOS:POSS, as well as more detailed treatment here and here.
Also, in case of French names (like Desargues) where the ending "s" is silent (pronounced "desarg"), it's an especially compelling case since most all English speakers actually say "desargs" for the possessive, and it should be clear that this extra "s" sound comes from the proper use of 's as the singular possessive's ending. Again, per MOS:POSS, this is a more clear case where 's should be added, based on the pronunciation. cherkash (talk) 12:35, 3 January 2016 (UTC)[reply]
I agree with applying the 's to Desargues, for the stated reason. This is something that bothered me about our spelling at that article in the past. I am neutral regarding the spelling of Pappus' versus Pappus's, since the extra s is silent there. As long as the article is consistent, I don't see a problem. Sławomir Biały12:51, 3 January 2016 (UTC)[reply]
Actually, I don't agree that the extra s in Pappus's is silent. In my personal usage, I would be more likely to write Pappus's and pronounce it with three syllables. If I heard someone pronounce the possessive with two syllables, I would transcribe it as Pappus'. --Trovatore (talk) 19:11, 7 January 2016 (UTC)[reply]
Well while the article on Desargues's theorem did indeed have a somewhat inconsistent spelling, the theorems by Pappus did not as far as I can tell, so the claimed harmonizing argument doesn't really apply here. Also while the arguments above are correct for Desargues in particular with regard to the silent s, they don't apply to Pappus either. In fact Pappus seems exactly a case like Jesus and the linked WP article even gives fellow Greek Socrates as another example for s' case. In fact it even claims (though without citation) that the French names with a silent s can be spelled either way and gives Descartes and Dumas as examples.--Kmhkmh (talk) 13:48, 3 January 2016 (UTC)[reply]
I agree no chance of ever settling that one in satisfactory way. In doubt just leave the choice of words here to main contributor(s) of the article in question.--Kmhkmh (talk) 01:23, 8 January 2016 (UTC)[reply]
Since no one else is replying, I will go out on a limb and guess it is because no one has been BOLD enough to create it. It is definately notable. Do you want to create it? Happy Squirrel (talk) 04:28, 2 January 2016 (UTC)[reply]
Rather far from my interests. I'd prefer it created by someone closer to topology than me. Someone who knows better the history of that theorem, its influence etc. Boris Tsirelson (talk) 20:04, 6 January 2016 (UTC)[reply]
I have proposed a change to the JC article on the JC talk page in the section titled 'Symmetric Case'. I need someone to implement it who has better editing skills than I do. Thank you,
It was at its foundation plagiarized from a published book, as was another recently created article by the same editor, Cohen's Class. I have deleted both articles, but if someone thinks they should be re-created using original rather than copied text I won't complain. —David Eppstein (talk) 02:39, 13 January 2016 (UTC)[reply]
[cc7bc57d] 2015-12-17 13:38:05: Fatal exception of type "MWException"
here. Not having a \binom in a \limits subscript appears to have fixed it. I assume correct LaTex would be to use something like \substack, but in any case I am a bit worried that I get thrown an exception instead of a helpful error message. Does anybody have an idea or should I post this to WP:VPT instead? —Kusma (t·c) 13:42, 17 December 2015 (UTC)[reply]
To fully understand this article, an understanding of measures, rings, and σ-algebras is recommended.
I would find this very helpful. I often go to look up a math topic I've heard of, and wade through several paragraphs before I realize how badly unprepared I am (I'm a first-year undergraduate). Math gives very little context besides the definition; it's much easier for a nonspecialist to understand what Battle of Towton is about than Carathéodory's extension theorem. Math books list prerequisites in Chapter 0, but Wikipedia has no Chapter 0, so it's easy to get out of one's depth with no idea how to retreat. There might be OR concerns, but I think it would usually be fairly obvious. FourViolas (talk) 22:53, 7 January 2016 (UTC)[reply]
This is in the FAQs: Any article with this problem could be written better by weaving its prerequisites into its exposition. Sadly, we have far too many poorly written articles. If you can point out particular articles, then I'm sure you can find interested editors to help you improve them. Ozob (talk) 00:30, 8 January 2016 (UTC)[reply]
I agree it's in the FAQ. The example of Reproducing kernel Hilbert space is rather funny. I assume it would never occur to a reader of that article that they would first need to know what a Hilbert space is. How is this any different from an article like Microcell-mediated chromosome transfer, where one needs to know what a cell is, what a chromosome is, etc.? One can get most "prerequisites" just by following links. There's no need to bash readers over the head with this. If a reader isn't intelligent enough to figure this out, chances are they wouldn't get much out of the article Reproducing kernel Hilbert spaceregardless of what kinds of hatnotes we chose to decorate it with. Sławomir Biały21:25, 20 January 2016 (UTC)[reply]
A quote from the Signpost article linked in the beginning of this discussion (see "Reproducing kernel (impenetrable science)" there):
Indeed, you have to know what is a vector space, then an Hilbert space, then a linear kernel before to understand the circumstances that allows an Hilbert space to possess a kernel that has the reproducing property. This is not a cabal to intimidate anyone, this is the fact that floor and walls should precede roof. Maybe this constraint is the reason why there are not only books, but also teachers and Universities. What a marvelous discovery! Pldx1 (talk) 09:28, 7 January 2016 (UTC)
I think this Wall-Sun-Sun article section for the existence of such primes, could be a little more balanced to mention Wall's original hypothesis of non-existence, and consequently his open question that these primes may, or may not exist after all.
Let , be the smallest Fibonacci number divisible by the prime .
Let , be the smallest Fibonacci number divisible by .
Let be the quotient of primitive(characteristic) prime factor(s), ie factors that have not occurred in any earlier Fibonacci numbers.
Please take a look at the conclusion of Zhi-Zong-Sun and Zhi-Wei-Sun's paper, pages 386 .
It states what I've stated above, although less elegantly. Why, has everyone overlooked this part of their paper?
Z. H. Sun and Z. W. Sun, Fibonacci numbers and Fermat's last theorem, Acta Arithmetica, Vol. 60, No. 4 (1992), 371-388
I suggest that we come up with an update for the article, that is balanced to reflect this previously unrecognized viewpoint, ie , where means exactly divides, .Primedivine (talk) 18:37, 3 January 2016 (UTC)[reply]
If it is truly a "previously unrecognized viewpoint", then Wikipedia is not the place to publish it. Indeed, presumably you should be able to write something up and submit it for peer review if you feel strongly about it. Sławomir Biały19:06, 3 January 2016 (UTC)[reply]
EDIT The abstract example above clarifies the proof by contradiction.
The problem named as, "The non-existence of Wall–Sun–Sun primes", as shown at OEIS. I have seen this referenced in several papers, where the original viewpoint or consensus was that they do not exist. Primedivine (talk) 14:47, 24 January 2016 (UTC)[reply]
I've been working a lot today on the Hand-waving article (which is much broader and more general than just the maths usage, and also includes, barely, nose-following). I'm having difficulty finding a clear definition of nose-following in a RS. The best I can come up with (as I used at the Follow one's nose disambiguation page) "a mathematics publishing and pedagogical term meaning to pursue a mathematical solution by mechanistically applying one's already-understood concepts without learning or applying anything new". I'm not certain this is properly nuanced (especially since I ran into two seemingly positive uses: "the ... enlightened nose-following that mark mathematical exploration" and "they did not yet know the 'follow your nose' proof tactic which I learned in my first upper division math class in college", plus contextually neutral ones like "The thing about nose-following proofs is that they are not very interesting. They need to be taught to students, of course" and "A student needs a tremendous amount of experience before they are ready to do math by simply following their nose."), and I'd like to have a source before putting it in the article (all these come from blogs and forums). Worse, the article says nose-following is the opposite of hand-waving, but what I've been able to glean of the meaning of nose-following, the two concepts are totally tangential, and certainly not antonyms. This suggests either our article is saying something wrong, a bunch of people are wrong on the Internet (I know that's hard to believe), or I have way too little information to grok with fullness what "opposite" relationship is meant.
That maths section at the article badly needs work. After I reworked a lot of it, I discovered the entire thing was copy-pasted from a Quora post, making it both OR and COPYVIO. Maybe enough of it's been altered by subsequent edits to not be a copyvio (and the Q poster's name is very familiar, so he might be 'a Pedian who wouldn't object anyway), but it looks to me like a lot of the assertions are opinional, and one was already flagged as iffy.
Also, the term "nose proofs" sometimes hyphenated at "nose-proofs" (plus "nose-proofing", etc.) appear to be directly related and should be covered in the same section. — SMcCandlish ☺☏¢ ≽ʌⱷ҅ᴥⱷʌ≼ 14:20, 26 January 2016 (UTC)[reply]
I read an article recently by Raoul Bott who said Rene Thom was apparently famous for "[doing] mathematics with his fingers and his hands". Quoting Bott (1988) "Morse theory indomitable", Publ IHES, 68:99-114:
"I still recall the motions of his hands as he taught me that for manifolds with boundary, only half of the critical points of the boundary really 'counted'."
It's curious that Bott appears to mean the metaphor both in its colloquial sense (of our article), and in the literal sense. Later on, he says:
"At infinity, his hands and fingers seemed to take over."
What should become of the article titled Trillium theorem? Deletion is proposed on the ground that no theorem by that name can be found in the Civilized part of the Universe, but might it be known by some other name and otherwise worthy of inclusion? Michael Hardy (talk) 01:45, 25 January 2016 (UTC)[reply]
I think it's fairly clear. It depends on what references are found. If the result can be sourced, and it can be established that trillium theorem is the standard name, then it should be kept (or possibly merged somewhere). If the result can be sourced, but not under that name, then it should be given the standard name, if there is one, or possibly merged somewhere. If the result cannot be sourced, then the article should be deleted without prejudice to recreation with good sources. --Trovatore (talk) 02:10, 25 January 2016 (UTC)[reply]
I asked about this over on my Google account and got a link to a document in Russian that looks relevant: http://www.geometry.ru/persons/kushnir/9pointcircle.pdf — I don't read Russian but if someone else does and can use it to source this article, please do. I also got a response from a Polish mathematician who writes that this is indeed well-known folklore, especially in Olympiad circles, and that the "trillium theorem" name (in its Polish form) is uncommon but not unknown. —David Eppstein (talk) 00:33, 26 January 2016 (UTC)[reply]
In case that it is simply one of those "well known but unnamed theorems" and no appropriate Russian source can be found there is also the option of moving its content to another article (like circumcircle or triangle) before deleting it.--Kmhkmh (talk) 00:52, 26 January 2016 (UTC)[reply]
The picture which goes with the article is potentially misleading because in it the given triangle appears to be isosceles rather than a general scalene triangle. Consequently, the midpoint of AC, the intersection of AC with BI, and the point where AC is tangent to the inscribed circle all appear to be the same point which they should not be. JRSpriggs (talk) 01:37, 26 January 2016 (UTC)[reply]
If "trillium" is rare even in Polish, perhaps we should use a (literal) translation of the best Polish (or Russian) name. In the absence of that, we should use MathWorld's made-up name, or perhaps make up our own. I think "trident" would be the best choice, rather than naming it after a local (to the source of the theorem) three-lobed plant. — Arthur Rubin(talk)16:51, 26 January 2016 (UTC)[reply]
That is strictly speaking a slightly different theorem as it uses the perpendicular bisector (of a side) rather than the angle bisector. However the angle bisector and the perpendicular bisector of the opposing side do intersects the circumcircle in the same point thus yirld the same conclusion.--Kmhkmh (talk) 20:26, 26 January 2016 (UTC)[reply]
Does Mathworld have theorem with a name attached to it? If that is the case I'd see that as a sufficient source for now and to close the deletion request.--Kmhkmh (talk) 17:51, 26 January 2016 (UTC)[reply]
I don't know if this helps the discussion or not, but I have found the result (without a name) written as the justification of a construction problem in Aref and Wernick's Problems and Solutions in Euclidean Geometry, Dover, 1968, page 68. The problem was to construct a triangle given a vertex, the circumcircle and the center of the incircle. Bill Cherowitzo (talk) 18:29, 26 January 2016 (UTC)[reply]
The article mentioned above actually contains the result on page 34 under name 'Теорема трилистника'. Added it and two more Russian sources. Stannic (talk) 03:47, 27 January 2016 (UTC)[reply]
I'd just like to make a couple points:
If it doesn't have a standard name, we can't give it a name. I don't agree with Arthur's idea of making up our own. Creating neologisms is a fun game, but Wikipedia makes it too easy and takes all the sport out of it, so it has to be disallowed for that purpose.
Mathworld doesn't count. Mathworld loves to make up names, but unless these gain actual traction in the wider community, we shouldn't copy them.
Even if there's no standard name, that doesn't mean the content shouldn't stay, but it does mean it probably shouldn't have a standalone article. Actually I think that's true anyway. This is a non-obvious result, but it's also not obvious that it's very important. If there's no obvious place to merge it, then maybe someone can make a "list"-type page for little geometric facts like this (assuming it's true, which I haven't checked, but no one seems to have raised any doubts).
If we're keeping the content, then we don't want to deletetrillium theorem; it should be made a redirect, so as to preserve the history. I don't think there's anything else by that name, so the redirect is harmless. --Trovatore (talk) 22:23, 26 January 2016 (UTC)[reply]
I've added some sources but none give it a name as a theorem. I suggest moving to Incenter–excenter circle following MathWorld [1] as this at least gets two (low quality) hits in Google scholar. Spinning the article to be more about the circle and less about the theorem shouldn't be difficult. —David Eppstein (talk) 00:53, 27 January 2016 (UTC)[reply]
incenter excenter
Some general comments:
I agree with Trovatore that we cannot make up names for theorem on our own as that would be a violation WP:OR (names can be seen as a special of external facts, hence the name need to exist in an (published) external source. One (accepted) workaround or exception here would be to pick a purely descriptive name (that approach is often used for important current events having no established name yet). Another one might be to pick the original foreign name (assuming a foreign source for it exists) or maybe a literal translation of it.
I disagree with Trovatore however that we can't use a name from Mathworld. Yes, WP cannot neologisms on its own because of the WP:OR aspect and of course if would highly problematic anyway if we start to establish names for the mathematical community, but we can however use or report "neologism" published on other sources. Mathworld can after all be seen as a published source and whether we personally like or not a name in Mathworld has in doubt more impact than a name that shows up in 1 or 2 rarely read mathbooks. We do usually accept the latter (absent of better sources for a name), so I see no reason not accept Mathworld here.
I disagree with Trovatore as well with regards to the redirect. Redirects are usually used for established alternative names and should be mentioned explicitly in the target article (otherwise the purpose of the redirect is unclear to the reader). If we conclude however that there is no established name, then is exactly what we can't do and we would need to delete the entry without redirect.
If we go for the suggested incenter-excenter circle approach we may have to drop the other language WPs as they are clearly about the theorem and not that circle. Going this way is imho basically a variation of deleting the original entry but saving its content by moving to a different entry where the content can seen be seen as appropriate and just not having its own article. We'd also a slightly different drawing bring the excenter into the picture. I provided one above, that could be used.
Um, no, we can't use a neologism just because somebody uses it. We can report that Mathworld uses it, but we should not follow Mathworld, which is an utterly terrible source for names. Really really really bad. Just never never never follow Mathworld for names, ever. --Trovatore (talk) 04:07, 27 January 2016 (UTC)[reply]
On the redirect question, we can and do have redirects from all sorts of problematic names, even ones that are seriously POV. As long as they're unambiguous, there's not too much of a problem. --Trovatore (talk) 04:10, 27 January 2016 (UTC)[reply]
I'm aware of your utter dislike of Mathworld, I don't quite share it though. Mathworld does more or less fulfill the formal criteria we require from an external source (not to mention that we use it all over WP for more than a decade anyhow).
Yes, we have redirects for all sort of problematic or inofficial names, they are however (at least to my knowledge) usually established in the sense that they are used in external sources. And unless it is directly obvious from the name they are usually mentioned explicitly in the target article, because otherwise the reader doesn't understand why and for what exactly he got redirected.
My dislike of Mathworld is mostly about naming. The math itself is usually fine. But Mathworld uncritically gives names that do not have any actual currency in the mathematical community. We ought to base our names on currency in the community, not the formal point that it can be found in a published source. (Especially a tertiary source.)
The point about giving notice to users as to how they arrived at a given article is a good one, albeit its importance is proportional to the chance that they would enter that search term in the first place, which I suspect is fairly low for this term. However, in any case, we can certainly report the name that Mathworld gives it. I don't object to that. That isn't a use; it's a mention. We shouldn't use the name. --Trovatore (talk) 04:26, 27 January 2016 (UTC)[reply]
Suppose the article titled Giraffe began like this:
well Basicly, a girrafFe is a term used by zoolooloogists to refer to when an animal has a long neck living in the planes of eastern and Southern Africa, which eats leafs.
