User talk:David Eppstein

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Speedy Keep

Your speedy keep here [1] claimed that the arguments were the same. The argument in the current AfD is that while the academic may be notable there is a complete lack of sources with which to create an article, from the responses in the AfD it can be seen that there is a complete lack of reliable independent sources to create an article with. This was not addressed in the first AfD. IRWolfie- (talk) 15:21, 4 April 2012 (UTC)

Are you going to address my concerns or do I need to take it to DRV? IRWolfie- (talk) 17:27, 4 April 2012 (UTC)

DRV seems appropriate if you are still not convinced by the two AfDs. —David Eppstein (talk) 18:47, 4 April 2012 (UTC)

The first AfD was closed properly, your close was inappropriate because the issues raised were different than the first AfD yet you closed it stating that the arguments were the same. Please point where the issue of the non-existence of sources to use in the article was raised in the first AfD. IRWolfie- (talk) 18:53, 4 April 2012 (UTC)

You reverted my revert of a bold addition on the article but you have not commented on the talk page, I suggest you do so per WP:BRD. IRWolfie- (talk) 17:17, 4 April 2012 (UTC)

I left an edit summary that says all I care to say about the matter. —David Eppstein (talk) 17:19, 4 April 2012 (UTC)

Dispute resolution survey

Dispute Resolution – Survey Invite Hello David Eppstein. I am currently conducting a study on the dispute resolution processes on the English Wikipedia, in the hope that the results will help improve these processes in the future. Whether you have used dispute resolution a little or a lot, now we need to know about your experience. The survey takes around five minutes, and the information you provide will not be shared with third parties other than to assist in analyzing the results of the survey. No personally identifiable information will be released. Please click HERE to participate. Many thanks in advance for your comments and thoughts. You are receiving this invitation because you have had some activity in dispute resolution over the past year. For more information, please see the associated research page. Steven Zhang DR goes to Wikimania! 02:23, 6 April 2012 (UTC)

Re 24968_Chernyakhovsky

Hi, please leave the article alone. There are literally hundreds of these added from the ISEF winnings, it is unfair to delete just this one. Thanks. 18.96.6.177 (talk) 04:31, 12 April 2012 (UTC)

Please see WP:WAX. —David Eppstein (talk) 04:33, 12 April 2012 (UTC)

Excuse me, but there are *hundreds* of these, and they weren't making anyone mad until Alexander Chernyakhovsky appeared. These are separate issues. Please do no pick on on article just because of your opinion on another. If you are going to do so, you have to delete 24977 Tongzhan and 24549 Jaredgoodman and all the rest like it.18.96.6.177 (talk) 04:38, 12 April 2012 (UTC)

It's true that I only do stuff to pages that I find out about — who can do otherwise? I'll be happy to prod those other two or as many others like them as you find but maybe at this point we should wait to see how the AfD goes. —David Eppstein (talk) 04:41, 12 April 2012 (UTC)

Then I am confused why you care about this one.18.96.6.177 (talk) 04:51, 12 April 2012 (UTC)

Because I found out about this one. —David Eppstein (talk) 04:52, 12 April 2012 (UTC)

Then why did you say something like "And delete his little dog", is that supposed to be funny?04:57, 12 April 2012 (UTC) — Preceding unsigned comment added by 18.96.6.177 (talk)

You never watched The Wizard of Oz? —David Eppstein (talk) 05:11, 12 April 2012 (UTC)

Apparently not.18.96.6.177 (talk) 05:23, 12 April 2012 (UTC)

R. W. H. T. Hudson

Prof. Eppstein, thank you for moving correctly Ronald Hudson's article. Giftlite (talk) 17:00, 12 April 2012 (UTC)

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DYK for Emanuels Grīnbergs

Casliber (talk · contribs) 00:04, 14 April 2012 (UTC)

WP:COPYVIO

In the AFD Wikipedia:Articles for deletion/Joachim Weickert you stated that you "didn't see much evidence of copyvio". Please cast your eye upon Talk:Joachim Weickert. If you don't see a problem, then please read Wikipedia:Copyright violations. You might also wish to read the information page Wikipedia:Copy-paste Much of the content of the article at the time of the AFD nomination was a violation of the Wikipedia terms of use. Thanks. Edison (talk) 05:12, 19 April 2012 (UTC)

Well, I agree that the comparison on the talk page looks too closely paraphrased for my taste, but there are only so many ways one can write "he got degrees X and Y and worked at universities Z and W." —David Eppstein (talk) 05:18, 19 April 2012 (UTC)

DYK for Mictyris guinotae

Materialscientist (talk) 16:10, 20 April 2012 (UTC)

DYK for Danièle Guinot

Materialscientist (talk) 16:10, 20 April 2012 (UTC)

º vs °

I considered users who type the degree sign as $\circ$ as lamers, but only before spotting your "180º rotation"[2]. Incnis Mrsi (talk) 09:47, 23 April 2012 (UTC)

Sorry, but ° and º look too similar to each other and are right next to each other on the keyboard (option-shift-8 vs option-0); it's hard to remember which is which. —David Eppstein (talk) 15:24, 23 April 2012 (UTC)

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Stupid bot, that one was deliberate, as indicated by the dab needed tag. —David Eppstein (talk) 15:22, 23 April 2012 (UTC)

DYK for Telephone number (mathematics)

Orlady (talk) 16:09, 26 April 2012 (UTC)

Maximum weighted average

Thought it might amuse you that after considerable discussion about a question on the Math Reference Desk today, User:Modocc found a 1995 paper of yours that answers it: Wikipedia:Reference desk/Mathematics#Calculating the 3 marks that drag a weighted average down the most. Regards, Qwfp (talk) 21:45, 30 April 2012 (UTC)

Thanks for letting me know. That's one of my more obscure ones... —David Eppstein (talk) 21:49, 30 April 2012 (UTC)

This is for you. Listen carefully.

http://www.youtube.com/watch?v=gfebdiErvDo — Preceding unsigned comment added by 86.24.46.135 (talk) 22:59, 2 May 2012 (UTC)

Dead link in article 'Rule 184'

Hi. The article 'Rule 184' has a dead link that could not be repaired automatically. Can you help fix it?

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This link is marked with {{Dead link}} in the article. Please take a look at that article and fix what you can. Thank you!

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 Done. Thanks for the heads-up. —David Eppstein (talk) 06:30, 6 May 2012 (UTC)

DYK for Tina Mion

Graeme Bartlett (talk) 00:04, 11 May 2012 (UTC)

Your continuing subversive anti-Western and anti-Ukrainian edits and reverts

David Eppstein, you serve your anti-Western and anti-Ukrainian Russian master, Vlad Putine, very well.

Your continuing anti-Ukrainian edits and reverts cannot be ignored.

Please familiarize yourself with Wikipedia policies before resorting again to your disruptive and subversive editing of Ukraine-related Wikipedia articles. Wikipedia policies may seem difficult for you to understand and to comply with, David Eppstein. However, believe me, this is just in the beginning. Please do not hesitate to ask other editors, including myself, if you need any explanations or clarifications. I would also recommend to you to use talk pages of pro-Western Ukrainian editors, asking questions and getting answers about Ukraine, BEFORE attempting to contribute the Ukraine-related Wikipedia articles.

Please do not resort again to your past habit of biased anti-Western edits about the Ukrainian matters.

. — Preceding unsigned comment added by 76.102.173.102 (talk) 06:12, 12 May 2012 (UTC)

Please make it stop! Kiefer.Wolfowitz 21:35, 17 July 2012 (UTC)

Courcelle's

Thank you. The logical statement does, however, run over the edge on my browser. I think it needs to have line breaks between the conjuncts and disjuncts but not knowing the math syntax, I should leave that to you. History2007 (talk) 22:20, 13 May 2012 (UTC)

A barnstar for you!

	The Teamwork Barnstar
	Thank you for the re-write and reformatting of the article Albert Brahms which was formally proposed for deleltion. TeamWork is Wikipedian. Stephenwanjau (talk) 03:28, 14 May 2012 (UTC)

Thanks! Glad I could help. —David Eppstein (talk) 03:28, 14 May 2012 (UTC)

TB

Hello, David Eppstein. You have new messages at Talk:Lattice gas automaton.
Message added 20:38, 18 May 2012 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

benzband (talk) 20:38, 18 May 2012 (UTC)

Notability of Academics

I replied to your comments on the talk page of WP:PROF. NJ Wine (talk) 02:28, 23 May 2012 (UTC)

Invitation

	Great American Wikinic at Pan-Pacific Park
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DYK for Albert Brahms

Graeme Bartlett (talk) 08:04, 25 May 2012 (UTC)

proof outline

It is possible to write down this formula:

$\sum _{k=0}^{n}k^{2}=\sum _{k=0}^{n-1}\sum _{i=k+1}^{n}i$

This is an alternative way to group the sum of the squares: to quote an example, we assume n=5:

$0^{2}+1^{2}+2^{2}+3^{2}+4^{2}+5^{2}=$

$1+2+3+4+5+$

$2+3+4+5+$

$3+4+5+$

$4+5+$

$5$

In this representation the number five is summed 5 times, the number 4 is summed 4 times, and so on, until zero. After that, it is possible to use this result to solve the summation:

$\sum _{i=k}^{n}i={\frac {n(n+1)}{2}}-{\frac {k(k-1)}{2}}$

The main formula is equivalent to

$\sum _{k=0}^{n}k^{2}=\sum _{k=0}^{n-1}[{\frac {n(n+1)}{2}}-{\frac {k(k+1)}{2}}]$

After some agebraic manipulation it is possible to obtain:

${\frac {3}{2}}\sum _{k=0}^{n}k^{2}={\frac {n^{2}(n+1)}{2}}-{\frac {n(n-1)}{4}}+{\frac {n^{2}}{2}}$

This is equivalent to the desired formula.

86.24.46.135 (talk) 18:47, 29 May 2012 (UTC)

File:Steinhaus-Johnson-Trotter-Permutohedron.svg

With permutation labels from the permutohedron

Hi David. I don't really get your illustration of the Steinhaus–Johnson–Trotter algorithm. You have labelled your graph with the permutations from the Cayley graph and not with those from the permutohedron . Is this really what you have intended? I created the file on the right because that's how I understand "Hamiltonian path in the permutohedron". Lipedia (talk) 17:05, 30 May 2012 (UTC)

The algorithm works by swapping the values of elements in adjacent positions of the permutation, so we need the vertices of the graph to be labeled in such a way that this kind of swap corresponds to an edge. The Cayley graph has that property; the permutohedron doesn't. But the graphs are isomorphic (related to each other by inverting the labels) so the algorithm does indeed also find a Hamiltonian path in a graph isomorphic to the permutohedron. —David Eppstein (talk) 17:21, 30 May 2012 (UTC)

Indeed, your illustration is correct. To me the sentence

"Consecutive permutations in the sequence generated by the Steinhaus–Johnson–Trotter algorithm have numbers of inversions that differ by one, forming a Gray code for the factorial number system."

was misleading, because the path in the permutohedron is a textbook example of a "Gray code for the factorial number system" - but I wouln't say that about the path in the Cayley graph. There is e.g. a change from inversion vector (0,0,0,2) to (0,0,1,0). Is that a change in a Gray code?! See my change. Lipedia (talk) 12:36, 31 May 2012 (UTC)

Block me!

You can block me whenever you want. When the block will expire I will post my proof again. Forever. If you block me forever, I will ask somebody also to post my proof for me. Forever.

I think it's not fair what you did on "square pyramidal number page". Do you think it's fair to make a content remove only because you decided that it's not interesting? A civilized person would discuss it in the discussion page. I'm not dropping this. — Preceding unsigned comment added by 86.24.46.135 (talk) 15:48, 1 June 2012 (UTC)

I've taken this to WP:ANI. —David Eppstein (talk) 16:10, 1 June 2012 (UTC)

I think 86.24.46.135 is asking for a permanent ban. And I hope he gets one. Maproom (talk) 19:25, 2 June 2012 (UTC)

Indian mathematics

Hello, I am a user very active in the Good Article nominating system. I often look and scout for articles that could pass as GAs. I was sifting through WikiProject Mathematics, and found this article. You seem to be the editor who has has the most recent edits done, and I was wondering, do think the article is ready to go under a GA review. If so, Great! If not, what could be done to improve it. I am really exuberant when an article I nominate becomes a GA, and would like for this one to. Please, help this article become a GA. Thanks mate! Oakley77 (talk) 16:45, 3 June 2012 (UTC)

I don't think I'm really the right person to ask about that article — my edits haven't been very major in comparison to some others, and I think others such as Fowler&fowler (talk · contribs) are more knowledgeable. But the biggest problem with that article is that it's a politically contentious subject — you will run into a three-way conflict between proponents of India who wish to puff up their (significant) accomplishments even further, others who wish to diminish them, and others who wish to strive for an accurate portrayal without political bias.

Talkback

Hello, David Eppstein. You have new messages at Rehevkor's talk page.
Message added 01:19, 12 June 2012 (UTC). You can remove this notice at any time by removing the {{Talkback}} or {{Tb}} template.

Яehevkor ✉ 01:19, 12 June 2012 (UTC)

Travis Turner

Hi David,

Regarding Travis Turner, I see he still does not have a page and I am a big fan of his films/music and want to see a proper page created for him...I am not sure how to create the article properly myself is there a possibility of you creating it?, or helping me get it created? As The Princess For Christmas is notable.

I have no idea who Turner is, so I think it would helpful to find someone to help who does know of him. But I think the most important thing is to start with reliable sources (e.g. newspaper stories about Turner found in Google news search), cite them properly, and only put into the article the information you've found in those sources. That way it should be obvious to other editors that he's notable. —David Eppstein (talk) 23:42, 13 June 2012 (UTC)

Acyclic graph

If the only difference between the kinds of graphs that can be called acyclic is the direction of the graphs and cycles, prehaps this is a suitable topic for a short article delineating these distinctions and explaining why all of these types are nonetheless "acyclic" graphs. This would also resolve the current disambig link to this title at Fat tree. Cheers! bd2412 T 17:25, 15 June 2012 (UTC)

Those three classes of graphs are not very similar to each other. I think a disambiguation page is a reasonable solution. As for the fat tree link, it is clearly about the undirected case. —David Eppstein (talk) 18:00, 15 June 2012 (UTC)

If they are suitably distinct that incoming links can be kept clear, then I have no objection to continued disambiguation. Nevertheless, as a non-expert in the area, they seem to be variations on a theme. After all, what is it that makes them all "acyclic graphs"? Just a thought. bd2412 T 18:56, 15 June 2012 (UTC)

They all have forbidden graph characterizations where the forbidden subgraph is something that can be called a cycle. But those are not the only ways of characterizing these graphs, and the details of what that something is makes them quite different from each other. —David Eppstein (talk) 19:02, 15 June 2012 (UTC)

It's all Greek to me, but I trust your judgment in the field. Cheers again! bd2412 T 19:11, 15 June 2012 (UTC)

DYK for Wall poems in Leiden

Casliber (talk · contribs) 16:02, 16 June 2012 (UTC)

Zemgus Girgensons

Would it be possible to unsalt the Zemgus Girgensons article, as in three days the 2012 NHL Entry Draft will take place, and Girgensons is more than likely to be selected in the first round, thus passing the WP:NHOCKEY criteria. Surely there will be contributors willing to add some information on his article straight afterwards. Gragox (talk) 13:50, 19 June 2012 (UTC)

Ok, done. —David Eppstein (talk) 15:12, 19 June 2012 (UTC)

David Eppstein article

I saw you removed Category:American Jews from your biography article on the grounds that it was unsourced and untrue. Not that you are obligated to provide any, but do you have any reason to believe it is not true? Genetic test or something? Forgive me if it is a rude question, it seemed an obvious conclusion from the surname and photograph, but I did not mean to insert a libelous or offensive label. On a related matter I see that you link your personal page and blog from your user page. If someone in industry were editing their own biography article, discussing their profession, and linking more detailed off-wiki pages about themselves and places of employment, would this be considered less appropriate than for someone in academia? It seems ok to me; I am not objecting. Thanks for your time. Obotlig ☣ ^interrogate 07:55, 20 June 2012 (UTC)

Jewish descent runs through the mother's line and my mother's ancesters were all Christian. I was baptised shortly after birth. My marriage ceremony was in a Unitarian church. I could go on. In any case, it is inappropriate to add religion categories to biographical articles when there is no evidence that religion is important to the subject; see WP:CAT/R. —David Eppstein (talk) 14:05, 20 June 2012 (UTC)

I believe the category is an ethnic description. There is nothing at WP:CAT/R and I couldn't quickly find the relevant policy or guideline article. What the Jewish culture or religion considers to convey membership in the race, ethnic group or religion is not relevant to someone being substantially of an ethnic background and obviously so, by the normal standards of English readers, western anthropologists, etc. At any rate, thanks for the information. It seems to me if someone has a "Jewish" surname and visually appears to be an Ashkenazi Jew they should be classified as such, and would be by the overwhelming majority of native English speakers. But it's more important what you consider an offensive label. Obotlig ☣ ^interrogate 14:29, 20 June 2012 (UTC)

I believe the same rules about sourcing apply as well to ethnicity as to religion. And I'm all for people celebrating the accomplishments of their own ancestors but I find the idea of imposing an ethnicity on other people, especially by stereotypes of looks or names, rather repugnant. —David Eppstein (talk) 15:11, 20 June 2012 (UTC)

So you feel that we should only label the ethnicity (versus nationality or citizenship) of a person if they themselves apply the label, rather than using sourced information about their parents or other ancestors? I guess this is an important question toward the right of a person to define themselves to the world and opens up questions in a number of fields of study and thought. It does seem a fundamental problem for Wikipedia, which as you indicate would just go by reliable sources, but where there does seem to be some wiggle room in BLP articles. Thanks again for taking the time to respond. Obotlig ☣ ^interrogate 15:23, 20 June 2012 (UTC)

I'm sorry that I didn't see this before. I took your page and hundreds of others off my watchlist following a block.

Of course, having a concern about antisemitism and trying to remove antisemitism from articles was one of the charges in my RfC/U complaint.

I suppose that it's best just to ignore or delete such stuff.

Kiefer.Wolfowitz 21:32, 17 July 2012 (UTC)

Thanks

Mea Culpa! I jumped on the Dilworth's Theorem edit without thinking it through. Thanks for fixing my mistake. Bill Cherowitzo (talk) 17:41, 22 June 2012 (UTC)

No problem. —David Eppstein (talk) 17:48, 22 June 2012 (UTC)

DYK for Double bubble conjecture

Graeme Bartlett (talk) 16:03, 9 July 2012 (UTC)

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Taxicab geometry

David,

I wanted to discuss the change I made and you undid on the Taxicab geometry page. You said, in your update comment, that my change "misses the point". I disagree or maybe I just don't understand what you meant.

The caption to the picture is clearly incorrect. It says "Taxicab geometry versus Euclidean distance: In taxicab geometry all four pictured lines have the same length (12) for the same route. In Euclidean geometry, the green line has length 6×√2 ≈ 8.48, and is the unique shortest path." [emphasis added].

Note that the green line in the picture clearly is not length 12. Note also that the green line is not the "same length" as the other three lines. This is made clear by the final sentence of the caption which says that the green line is length 8.48, showing that the Euclidean distance is shorter than the Taxicab distance.

I would also draw your attention to the default description of the graphic which says "Figure illustrating Manhattan verses Euclidean distance. The red, blue, and yellow lines all have the same length (12), whereas the green line has length ${\sqrt {72}}\approx 8.4853$." This again makes the distinction between the three lines of equal length (red, blue, yellow) and the green line that is shorter.

I believe that my original edit was correct in amending the caption to reflect the fact the three of the lines are of length 12 while one line, the green one, is shorter. Please help me understand how this is incorrect or misses the point.

Thanks,

- James

James (talk) 19:34, 13 July 2012 (UTC)

The green line has length 12 in taxicab geometry. If you do not understand this then you do not understand the subject of the article and should not be editing it. —David Eppstein (talk) 19:43, 13 July 2012 (UTC)

I don't disagree that I don't fully understand the subject, that's why I was reading the page in the first place. Given that the article, in theory, should be directed at those who don't understand the subject, I would argue that my misunderstanding of the caption should be evidence that the article itself needs to be rewritten or expanded to explain to us (who don't understand, including the author of the graphic apparently) why a line of length 8.48 is actually a line of length 12. --James (talk) 19:59, 13 July 2012 (UTC)

Because the whole point of taxicab geometry is that it's a different way of measuring distances. —David Eppstein (talk) 02:55, 14 July 2012 (UTC)

So, what you intended to say, as I interpret it, is that the taxicab distance between two points is always the same. The red, yellow, and blue lines demonstrate that no matter how you 'drive' from point A to point B, it will be the same distance (the sum of the absolute value of the difference in the point coordinates: $abs(Ax-Bx)+abs(Ay-By)$). The original author of the graph you are using was trying to illustrate that the taxicab distance is longer than the Euclidean distance (represented by the green line). Therefore, I would maintain that while the taxicab distance between the two points in the graph is indeed always 12, the length of the green line is, in fact, 8.48 and represents the Euclidean distance. The green line clearly violates the axioms of taxicab geometry because it is not orthogonal to the coordinate axis. Therefore, it cannot be thought of as graphically representing the taxicab distance between the two points. Other sites I've looked at seem to share this view of such graphs (e.g. http://jwilson.coe.uga.edu/EMAT6680Fa06/Sexton/GeoFinalProject/Taxicab/Distance.html, http://mathworld.wolfram.com/TaxicabMetric.html, http://library.thinkquest.org/06aug/02430/, http://www.taxicabgeometry.net/general/basics.html, http://www.newyorkgeek.com/2011/08/pre-boarding-manhattan-distance-and-graph-theory/, etc.). I fact, I've not found a single site that considers the equivalent of the green line in the drawing to represent the taxicab distance. If you can find another site that does so, I'd love to see it. --James (talk) 18:04, 16 July 2012 (UTC)

Not quite. It is true that as long as your path doesn't double back on itself in either the east-west direction or the north-south direction then its length is equal to the taxicab distance. But really, what I meant is that the length of a curve needs to be defined carefully (as is done in arc length) and when you do this careful definition using taxicab distance you find that the length of the green curve is 12. —David Eppstein (talk) 18:11, 16 July 2012 (UTC)

Re: "as long as your path doesn't double back on itself" ... good clarification. But, back to the point of the original post, I think that the current caption for the graph is, at best, misleading. The apparent graphical length of the green line does not represent the Manhattan distance of 12. Instead, it represents the Euclidean distance and was clearly intended by the original author to demonstrate the difference between the two measurement methods. I think the caption should reflect this reality. I don't think that the current caption helps people reading the article understand the subject better (in fact, it makes it more confusing). If we can't come to agreement, how do we resolve this? Public discussion? Arbitration? Being a new contributor to Wikipedia, I'm unfamiliar with the appropriate resolution protocol. --James (talk) 19:22, 16 July 2012 (UTC)

My guess at an appropriate resolution for this would be: find references on and add material to the article concerning how one goes about calculating arc length in taxicab geometry, so that the correctness of the existing caption would become more obvious to readers of the article. —David Eppstein (talk) 20:09, 16 July 2012 (UTC)

Since you don't want to take the time to explain your position or site any references (and I can't find any that support your position), and you obviously don't intend to allow me to make any significant edits to the page to correct the misleading caption perhaps you would consider altering the article to make it more clear. I found the following description in the talk page for the article in question in the Biangles section. "You can visualize why the green line has length twelve by imagining that it zig-zags like the blue line, and then mentally decreasing the size of the zig-zags and seeing how it gets closer and closer to the path of the line without changing its length. However, the actual line doesn't zig-zag. It is a unique straight line connecting the points, but has a length defined on metric that behaves as if it were composed of microscopic zig-zags." I think something along this line would help people to better understand what you are intending with your caption. --James (talk) 23:02, 16 July 2012 (UTC)

It's not that I don't want to take the time; it's that the explanation I would give you is essentially already present in arc length. I don't like the talk page description because you could apply the same thought experiment in Euclidean geometry but it gives the wrong answer there. This and this look like they might also be relevant as references. —David Eppstein (talk) 23:36, 16 July 2012 (UTC)

Wikipedia:Articles for deletion/Dan Martin (academic)

Hi David, I made a discovery that Dan Martin has recently been given a named chair and the permanent position as CMU's Dean of the Faculty of Fine Arts (it's a college deanship equivalent to Vice Provost most places since there are five schools the report, with departments inside them). I wonder if you'd consider at least the named chair to satisfy PROF#C5? Thanks, -- Michael Scott Cuthbert (talk) 19:44, 15 July 2012 (UTC)

Will the Circle Be Unbroken

In modern music, the twelve notes of the octave are equally space around the chromatic circle. This circle thus circumscribes four equilateral triangles with vertices among the notes. Each such triangle specifies the successive open-strings of a major-thirds tuning.

Hi David!

You did nice work on this graphic. I've used it on 3 articles so far: guitar tunings, major-thirds tuning, and augmented-fourths tuning.

(I might use it on minor-thirds tuning, but that seems to have been used by only William Sethares's guide on alternative tunings. Sethares's BLP could use work.)

Best regards, Kiefer.Wolfowitz 21:11, 17 July 2012 (UTC)

Thanks, glad to hear it's being useful. The actual design was from an earlier image, File:Pitchclassspace.png, though — all I did was redraw it with some cosmetic changes. —David Eppstein (talk) 21:17, 17 July 2012 (UTC)

proof outline

It is possible to write down this formula:

$\sum _{k=0}^{n}k^{2}=\sum _{k=0}^{n-1}\sum _{i=k+1}^{n}i$

This is an alternative way to group the sum of the squares: to quote an example, we assume n=5:

$0^{2}+1^{2}+2^{2}+3^{2}+4^{2}+5^{2}=$

$1+2+3+4+5+$

$2+3+4+5+$

$3+4+5+$

$4+5+$

$5$

In this representation the number five is summed 5 times, the number 4 is summed 4 times, and so on, until zero. After that, it is possible to use this result to solve the summation:

$\sum _{i=k}^{n}i={\frac {n(n+1)}{2}}-{\frac {k(k-1)}{2}}$

The main formula is equivalent to

$\sum _{k=0}^{n}k^{2}=\sum _{k=0}^{n-1}[{\frac {n(n+1)}{2}}-{\frac {k(k+1)}{2}}]$

After some agebraic manipulation it is possible to obtain:

${\frac {3}{2}}\sum _{k=0}^{n}k^{2}={\frac {n^{2}(n+1)}{2}}-{\frac {n(n-1)}{4}}+{\frac {n^{2}}{2}}$

This is equivalent to the desired formula.

86.24.46.135 (talk) 22:41, 23 July 2012 (UTC)