Wikipedia talk:WikiProject Mathematics/Archive/2016/Jan

Which other articles should link to Generalized structure tensor?
Which other articles should link to Generalized structure tensor? Michael Hardy (talk) 18:56, 1 January 2016 (UTC)

Trisection image
I have listed at Files for discussion/2016 January 1 an angle trisection image that added to angle trisection. Please contribute to the discussion there. —David Eppstein (talk) 05:54, 1 January 2016 (UTC)
 * 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)
 * Wow! Boris Tsirelson (talk) 19:28, 1 January 2016 (UTC)
 * 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.
 * $$ 2 \arcsin \tfrac 1 3 \sin \tfrac \theta 2 \neq \tfrac \theta 3, $$
 * But it's close. — Arthur Rubin  (talk) 18:02, 2 January 2016 (UTC)

Additive
My first thought when I see additive function is the article corresponding to Cauchy's functional equation; I think we need more links between the articles presently at additive function, additive map, and Cauchy's functional equation. I'd like to bring the matter up here, rather than at the article talk pages, to see if any of the expert Wikipedians with an interest in mathematics can provide some input, before making a formal proposal on the article talk page(s). — Arthur Rubin (talk) 06:30, 3 January 2016 (UTC)

Equivalence relation, equivalence class, and partition of a set
I don't want to propose it formally without input from people interested in mathematics, but not necessarily mathematicians. There is considerable overlap between those articles; equivalence relation has sections pointing to equivalence class, quotient set (which redirects to equivalence class), and partition of a set. Perhaps some merger of the articles would be appropriate, if we can avoid Marxist interpretations of class. — Arthur Rubin (talk) 06:27, 3 January 2016 (UTC)


 * 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)


 * 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)


 * 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.   S ławomir  Biały  20:14, 3 January 2016 (UTC)


 * 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)


 * There's also quite a bit of overlap in topic between Disjoint sets and Partition of a set. —David Eppstein (talk) 19:40, 3 January 2016 (UTC)

Semi-major axis page move proposed
Should Semi-major axis be moved to Elliptical axis? See Talk:Semi-major axis. Johnuniq (talk) 05:05, 4 January 2016 (UTC)

Draft:Microplane Model for Constitutive Laws of Materials
Hi. Could we get some input on this article over at AfC? Thanks.  Onel 5969  TT me 12:58, 4 January 2016 (UTC)

Proposed deletion of Degeneracy (mathematics)


The article Degeneracy (mathematics) has been proposed for deletion&#32; because of the following concern:
 * It lacks notability (WP:N). There is no mathematical topic of degeneracy. This article is just a small rag-bag of arbitrary and uncited examples.

While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the notice, but please explain why in your edit summary or on |the article's talk page.

Please consider improving the article to address the issues raised. Removing will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. &mdash; Cheers, Steelpillow (Talk) 14:15, 27 December 2015 (UTC)
 * PROD template removed. &mdash; Cheers, Steelpillow (Talk) 09:36, 31 December 2015 (UTC)
 * And now it's up for AfD: Articles for deletion/Degeneracy (mathematics). —David Eppstein (talk) 21:22, 6 January 2016 (UTC)

spelling issue for math theorems: s's versus s'
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).

So what are the opinions here? Everbody ok with such moves?--Kmhkmh (talk) 12:01, 3 January 2016 (UTC)


 * 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)
 * 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.   S ławomir  Biały  12:51, 3 January 2016 (UTC)
 * 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)
 * 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)

AfC submission
See Draft:Katugampola fractional operators and Draft:Thin plate energy functional. Thank you, FoCuS contribs ;  talk to me!  21:08, 7 January 2016 (UTC)
 * Also Draft:Learning data representations, that while not strictly mathematical, could use some experienced eyes. Best, FoCuS contribs ;  talk to me!  21:11, 7 January 2016 (UTC)

Are algorithms invented or discovered?
When editing a Wikipedia article are mathematical algorithms "invented", or are they "discovered"? Or maybe it doesn't matter either way? --82.132.234.81 (talk) 18:12, 7 January 2016 (UTC)


 * Oh! This is a special case of a famous philosophical question: do we invent or discover mathematical objects? No chance of consensus. See for instance Platonism. Boris Tsirelson (talk) 18:23, 7 January 2016 (UTC)


 * 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)

Links to Egorychev method
Which other articles should link to Egorychev method? Michael Hardy (talk) 01:52, 8 January 2016 (UTC)

No-retraction theorem
No-retraction theorem is only indirectly mentioned in "Brouwer fixed-point theorem"; no article, not even redirect, why? Boris Tsirelson (talk) 17:52, 23 December 2015 (UTC)


 * 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)


 * 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)
 * A redirect, for now. Boris Tsirelson (talk) 12:45, 8 January 2016 (UTC)

Numerals vs. numeral systems
There is a discussion at Talk:Arabic numerals that readers of this page might wish to join. Paul August &#9742; 15:04, 10 January 2016 (UTC)

Jacobian Conjecture article
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,

L.Andrew Campbell (talk) 02:28, 13 January 2016 (UTC)

Local cosine tree
If the new article titled Local cosine tree is worth keeping, it needs some cleanup and other work. Michael Hardy (talk) 03:50, 5 January 2016 (UTC)
 * 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)

Renaming Graph (mathematics)
There is a discussion here about renaming the article Graph (mathematics). There appears to be consensus in favor of a new name (at least among the small number of editors who have commented), but not about whether the target should be Graph (graph theory) or Graph (discrete mathematics). Additional input is welcome. --JBL (talk) 15:49, 13 January 2016 (UTC)

AfC help - again
Hi all. Could someone take a look at Draft:Lattice Delay Networks and offer an informed opinion as to the veracity and state of the article. Please ping me if and when you do. Thanks.  Onel 5969  TT me 12:57, 14 January 2016 (UTC)


 * Is it math? Rather, Electronic engineering. Boris Tsirelson (talk) 18:59, 14 January 2016 (UTC)

MWException in maths expression
I noticed an internal error [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)


 * Yup, see it too, but only with MathML. The fix looks acceptable. I vaguely recall that PigTex (our "LaTeX") hates \substack. YohanN7 (talk) 13:55, 17 December 2015 (UTC)


 * I've added a bug report: https://phabricator.wikimedia.org/T121762. It looks like its a bug in the code so its best to go straight to the bug system rather that use VP:T. --Salix alba (talk): 14:24, 17 December 2015 (UTC)
 * Thank you! I also figured that reporting this is what I should do, so it is also at T121763. I hope I have merged the tasks correctly. —Kusma (t·c) 14:29, 17 December 2015 (UTC)


 * The issue has been fully solved and everything is back to normal now :) Thank you for raising the issue. Marko Obrovac, Wikimedia Foundation (talk) 00:03, 18 December 2015 (UTC)


 * Screenshot_from_Heisenberg_group_with_broken_MathML.png Now it looks like all of the vertical spacing in mathml is broken. See the screenshot of Heisenberg group.  Can anyone else confirm this?  I've noticed it only in Firefox.  It looks normal in Chrome.   S ławomir  Biały  12:18, 22 December 2015 (UTC)
 * https://www.dropbox.com/s/eg8hj8oh0umrfck/Screenshot%202016-01-06%2019.12.13.png?dl=0 that's how it looks for me. Which FF version are you using? --Physikerwelt (talk) 18:14, 6 January 2016 (UTC)
 * Version 43.0.4. According to the Mozilla web site, this is the latest version.   S ławomir  Biały  12:20, 15 January 2016 (UTC)

Category:Benedictine mathematicians
Category:Benedictine mathematicians, which is within the scope of this WikiProject, has been nominated for deletion. If you would like to participate in the discussion, you are invited to add your comments at the category's entry on the Categories for discussion page. Thank you. RevelationDirect (talk) 04:35, 16 January 2016 (UTC)

Prerequisite hatnotes
Re: the "incomprehensibility" problem discussed at Wikipedia Signpost/2016-01-06/In the media: what would you think of putting WP:Hatnotes at the top of technical articles, along the lines of

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)


 * 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)


 * 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 space regardless of what kinds of hatnotes we chose to decorate it with.  <span style="display:inline-block;vertical-align:-.3em;line-height:.8em;text-align:right;text-shadow:black 1pt 1pt 1pt"> S ławomir  Biały  21:25, 20 January 2016 (UTC)

For many articles simple honesty would require that one should say "an understanding of WHATEVER is needed" rather than "...is recommended". Michael Hardy (talk) 19:52, 20 January 2016 (UTC)

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)

Boris Tsirelson (talk) 21:03, 20 January 2016 (UTC)

Thoughts on an edit
Thoughts on this edit to Geodesic are welcome. I've started a discussion on the talk page. <span style="display:inline-block;vertical-align:-.3em;line-height:.8em;text-align:right;text-shadow:black 1pt 1pt 1pt"> S ławomir Biały  15:30, 23 January 2016 (UTC)

D. D. Wall's open question
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 $$F_{u_{p^1}}$$, be the smallest Fibonacci number divisible by the prime $$p$$.
 * Let $$F_{u_{p^2}}$$, be the smallest Fibonacci number divisible by $$p^2$$.
 * Let $$\prod_{1}^{n\ge 1}$$ be the quotient of primitive(characteristic) prime factor(s), ie factors that have not occurred in any earlier Fibonacci numbers.


 * $$\left \lbrace {n \mid m}\ \text{iff}\ {F_n \mid F_m} \right \rbrace\, n \ge 3$$


 * $$p^2 \mid F_{u_{p^1}}\ \text{iff}\ F_{p^2} \mid F_{F_{u_{p^1}}}$$


 * If an integer $$i$$, has prime factorization, $$p_{1}^{e_{1}}\cdot\ p_{2}^{e_{2}}...p_{n}^{e_{n}}$$ then the entry point of $$i$$ equals, $$\left \lbrace u_{i} = \operatorname{lcm}({ u_{p_{1}^{e_{1}}}, u_{p_{2}^{e_{2}}}, ... u_{p_{n}^{e_{n}}}}) \right \rbrace$$.


 * $$\text{If}\ i=F_{F_{u_{p^1}}}\ \text{then}\ F_{p^2} \nmid\! F_{F_{u_{p^1}}}\ \left \lbrace F_{F_{u_{p^1}}}\neq F_{F_{u_{p^2}}} \right \rbrace$$.


 * $$\text{Abstract example, }p_{1}=p,\ e_{1}\ge 2$$
 * $$\text{If }i=(F_{p_{1}^2}\ \cdot\ F_{p_{2}^{e_{2}}}\ \cdot\ ...\ F_{p_{n}^{e_{n}}}\ \cdot\ \prod{})=F_{F_{u_{p^1}}}\ \text{then does i's entry point }u_{(F_{F_{u_{p^1}}})}=F_{u_{p^1}}\ \text{still?}$$
 * $$\text{No, since any extra powers of p produce a later entry point, }u_i=\operatorname{lcm}(p_{1}^{2},\ p_{2}^{e_{2}},\ ...\ p_{n}^{e_{n}},\ F_{u_{p^1}})\neq F_{u_{p^1}}=F_{pu_{p^1}}.$$
 * $$\text{While the factor, }j=(F_{p_{1}^1}\ \cdot\ F_{p_{2}^{e_{2}}}\ \cdot\ ...\ F_{p_{n}^{e_{n}}}\ \cdot\ \prod{})\text{ always has an entry point of, }u_j=\operatorname{lcm}(p_{1}^1,\ p_{2}^{e_{2}},\ ...\ p_{n}^{e_{n}},\ F_{u_{p^1}})=F_{u_{p^1}}.$$


 * $${F_{u_{p^1}}}\neq {F_{u_{p^2}}}$$
 * $$\neq $$
 * $$p^2 \nmid\! F_{u_{p^1}}$$
 * $$p^2 \nmid\! F_{u_{p^1}}$$


 * Preceding post either is a copy or is very similar to the post by the same author at Talk:Wall–Sun–Sun prime, and the first sentence refers apparently to Wall–Sun–Sun prime. D.Lazard (talk) 20:39, 25 December 2015 (UTC)

One should not write this:
 * $$p^2 | F_{u_{p^1}} \, $$

but rather this:
 * $$p^2 \mid F_{u_{p^1}} \, $$

Likewise "lcm" should use \operatorname{lcm}, and it is horribly vulgar to use an asterisk for ordinary multiplication in a TeX-like setting. Michael Hardy (talk) 20:52, 27 December 2015 (UTC)
 * Thank you.Primedivine (talk) 03:47, 28 December 2015 (UTC)

This section starts by saying this:
 * I think this article section could be

WHICH section of WHICH article?? Michael Hardy (talk) 20:37, 29 December 2015 (UTC)
 * The Wall-Sun-Sun article section for the existence of such primes. I edited it above.
 * Perhaps the consensus is leaning toward Wall-Sun-Sun primes existing. May I ask if there is any problem with the restatement of D. Wells form, ie


 * $$F_n \mid F_m\ \text{iff}\ n \mid m, n \ge 3$$
 * Is this statement equivalent and true?
 * $$ n \mid m\ \text{iff}\ F_n \mid F_m, n \ge 3$$
 * Considering, $$n=p^2, m=F_{u_{p^{1}}}$$ as indices.
 * The integer $$F_{F_{u_{p^1}}}$$ is to be divisible by $$F_{p^2}$$, and $$F_{p}$$ correct? Primedivine (talk) 23:43, 29 December 2015 (UTC)

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?
 * Sun-Sun

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 $$p\mid \mid F_{u_{p^1}}$$, where $$\mid \mid$$ means exactly divides, $$u_{p^1}\neq u_{p^2}$$.Primedivine (talk) 18:37, 3 January 2016 (UTC)


 * 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.  <span style="display:inline-block;vertical-align:-.3em;line-height:.8em;text-align:right;text-shadow:black 1pt 1pt 1pt"> S ławomir  Biały  19:06, 3 January 2016 (UTC)
 * I meant previously unrecognized by editors, not unrecognized by reliable sources. Primedivine (talk) 20:53, 3 January 2016 (UTC)

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)

Nose-following and hand-waving
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)


 * 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."
 * I'm not sure this worth adding to the article, but I found Bott's candid descriptions of Thom to be rather beautiful. <span style="display:inline-block;vertical-align:-.3em;line-height:.8em;text-align:right;text-shadow:black 1pt 1pt 1pt"> S ławomir  Biały  14:26, 26 January 2016 (UTC)

History of numbers
History of numbers is currently almost the most vacuous article that can be imagined. Michael Hardy (talk) 03:16, 25 January 2016 (UTC)
 * I'm sure a more vacuous article can be imagined, although, I admit, I've never seen one. — Arthur Rubin  (talk) 17:24, 26 January 2016 (UTC)

Trillium theorem
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)
 * 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)
 * It might be a good idea to search for the Russian name in the article. Perhaps google.ru?  — Arthur Rubin  (talk) 03:38, 25 January 2016 (UTC)
 * The theorem looks vaguely like something I saw at the Intel Science and Engineering Faire last spring, from a Russian student. — Arthur Rubin  (talk) 03:41, 25 January 2016 (UTC)
 * 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)

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)


 * 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)
 * Well that can be quickly fix with a replacement drawing assuming we keep the content.--Kmhkmh (talk) 15:22, 26 January 2016 (UTC)
 * I switched the article to use Kmhkmh's drawing. Thanks! —David Eppstein (talk) 17:07, 26 January 2016 (UTC)
 * 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)
 * It's called the "trident theorem" on p.8 of http://spotidoc.com/doc/1237477/xi-geometrical-olympiad-in-honour-of-ifsharygin-the — I'm not sure whether that counts as a reliable source. —David Eppstein (talk) 19:15, 26 January 2016 (UTC)
 * 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)
 * It looks vaguely like the polar of the 9-point circle. The Russian article pointed to above is titled "9-point circle", and seems to be about the 9-point circle. — Arthur Rubin  (talk) 17:14, 26 January 2016 (UTC)
 * 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)
 * 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)
 * 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)
 * 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 delete trillium 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)

I've added some sources but none give it a name as a theorem. I suggest moving to Incenter–excenter circle following MathWorld 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)

Some general comments: --Kmhkmh (talk) 03:23, 27 January 2016 (UTC)
 * 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)
 * 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)
 * 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.
 * --Kmhkmh (talk) 04:17, 27 January 2016 (UTC)
 * 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)

History of numbers
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.

That is the level at which the article titled History of numbers currently stands. Michael Hardy (talk) 19:04, 26 January 2016 (UTC)


 * . . . and now I've brought the article to a slightly less uncivilized level. Michael Hardy (talk) 22:29, 26 January 2016 (UTC)
 * lmao 137.124.161.12 (talk) 23:53, 28 January 2016 (UTC)