Wikipedia talk:WikiProject Mathematics

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Contents 1 Uppercasing again 2 New "undo" function 3 Continued fractions 4 Wikipedia:Release Version 0.7 5 Complete lattices (and Boolean algebras) and varieties 6 Possible vandalism in Taylor series 7 Sylvester's sequence listed as Good Article 8 Slashdot of previously deleted transreal number 9 Template:Calculus footer 10 Need advice 11 A new article about continued fractions 12 Suggested move of List of mathematics articles 13 Simple Introduction 14 Area of a disk 15 Proofs of trigonometric identities 16 User:WAREL again? 17 "Big" articles 18 Problems at exponentiation and empty product

[edit] Uppercasing again

The javascript thing is sort of nice, but not sufficient to allow different articles on Ω-logic and ω-logic, which we really ought to be able to have. I've left a note at Wikipedia:Village pump (technical)#Uppercasing of non-Latin letters (including references for the two logics that should be treated, or at least treatable, distinctively). See what you think. --Trovatore 07:32, 25 November 2006 (UTC)

We can't solve all the world's problems, including the foibles of some of the terminology used. Assuming that there are distinguishable concepts there, how do the fools who are silly enough to try to make a distinction of two concepts on the basis of the capitalization of a Greek letter used as a symbol deal with disambiguating them in speech? That might give us a clue as to whether it is a problem even worth our attention, and how to deal with it if it is. Gene Nygaard 11:53, 4 December 2006 (UTC)

[edit] New "undo" function

From Wikipedia:Wikipedia Signpost/2006-11-27/Technology report:

It is also now possible to undo edits other than the last one, provided that no intermediate changes conflict with the edit to be undone. The interface used is more akin to "manual revert" than rollback: on diff pages, an "undo" link should appear next to the "edit" link on the right-hand revision. When this link is clicked, the software will attempt to undo the change while preserving any changes since then, and will add the result to the edit box to be reviewed or saved. (Andrew Garrett, r17935–r17938, bug 6925)

There is a new button labelled "(undo)" which appears on the right under the edit summary when you look at the diff in a vandal's contributions. This allows you to remove a change without disturbing subsequent changes to the same page. I just found out about it. Have not had an occassion to try it yet. JRSpriggs 10:18, 29 November 2006 (UTC)

By the way, the author of this feature, Andrew Garrett, is perhaps better known as User:Werdna who also created User:Werdnabot. JRSpriggs 12:22, 3 December 2006 (UTC)

Correction, I should have said:

There is a new button labelled "(undo)" which appears on the right on the top line, e.g. "Revision as of 17:15, 5 December 2006 (edit) (undo)", when you look at the diff. This allows you to remove a change without disturbing subsequent changes to the same page.

I have used it now and it is very convenient. Try it out! JRSpriggs 06:36, 7 December 2006 (UTC)

[edit] Continued fractions

I want to add some new articles about particular varieties of continued fractions to Wikipedia (S-fractions, J-fractions, the continued fraction of Gauss, etc). Unfortunately the definition given in the basic article is so restrictive that the mathematical objects I want to discuss have been defined right out of existence! There are already some 250 links to the existing article, so renaming it is probably out of the question. My plan is to rewrite the existing definition and tweak the rest of the article so it's still logically consistent. Here's the definition I'm working with right now.

---

In mathematics, a continued fraction is an expression of the form

where the a_i and the b_i are numbers. The a_i are the partial numerators of the continued fraction x. The b_i are the partial denominators, and the ratios a_i / b_i are the partial quotients.

If all the partial numerators are 1 and all the partial denominators (except b₀) are positive integers, the continued fraction is a simple continued fraction, expressed in canonical form. Most of this article is devoted to simple continued fractions – see this related article for a more general discussion.

---

I'm posting this for comment. Is this definition sufficiently general? I suppose I could define a continued fraction as the composition of a (possibly infinite) sequence of Möbius transformations, but that wouldn't be very accessible, for the general reader.

Oh -- I also have a question. I'm not an expert on TeX. The ellipsis in the formula above is not quite right – it really should be replaced with three dots that descend to the right. Does anybody know the name for one of those?

Your feedback is welcome. I'll check back here regularly, or you can contact me on my talk page. DavidCBryant 16:13, 30 November 2006 (UTC)

Why don't you just add a section on Generalizations? The "absurdly narrow" definition includes all real numbers, which is broad enough to start with. Septentrionalis 17:50, 30 November 2006 (UTC)

Well, I thought of that, but then I looked at generalized continued fraction, where I read:

In mathematics, a generalized continued fraction is a generalization of the concept of continued fraction in which the numerators are allowed to differ from unity. They are useful in the theory of infinite summation of series.

A generalized continued fraction is an expression such as:

where all symbols are integers. [emphasis added]

So I can't even write about "generalized" continued fractions unless I change this definition. Opening up a "generalization of generalized continued fractions" seems like a bad idea for some reason, and if I'm stuck with cleaning up a bad definition, I might as well go whole hog.

Call me cranky if you like, but the existing definition of a cf on Wikipedia does not reflect the way mathematicians use this term. DavidCBryant 18:18, 30 November 2006 (UTC)

It seems to me like the correct thing to do would be to modify the generalized continued fraction article to fit your definition and discuss the various special cases there. The definition given at continued fraction seems to be the most common one and should probably remain the same. -- Fropuff 19:00, 30 November 2006 (UTC)

And why stop at numbers? There are extremely useful continued fractions where the coefficients are functions; most of the useful generalizations are proven by evaluating these. But do please leave the basic definition at the head of continued fractions; the urge to plunge into the greatest possible generality immediately should be resisted for the sake of comprehensibility. Septentrionalis 20:17, 30 November 2006 (UTC)

I proposed stopping at numbers because that's what most people think of when they think of addition and multiplication. I do understand that continued fractions of functions can be formed. And it's certainly possible to define continued fractions with differential operators, and with a whole lot of other objects that are the elements of a field, or even of a division ring. I'm not sure how useful such things would be ... that kind of stuff is not my bag. Anyway, I'm clearly a minority of one at the moment ... I read some other talk pages where others raised similar concerns, but they've apparently been driven away from Wikipedia. One poor guy named q analogue apparently tried to work on this before I did, without much success. Another guy, Hillman, apparently took some abuse from somebody -- I can't tell easily because his user page has been protected.

Arithmonic is apparently still around, but he seems to be keeping a low profile at the moment. I looked at his web site; he has written a book about generalized continued fractions and claims to have found periodic representations of cubic irrationalities. That's a pretty amazing advance, if he's right. LaGrange proved the bit about periodic continued fractions and quadratic irrationals about 200 years ago. So here's a guy who maybe made this huge advance in number theory, and you guys apparently don't even want to talk to him. "Original research", I suppose. (This is part of a message signed by User:DavidCBryant 01:07, 6 December 2006 (UTC) -- the original signature appears below, after some interpolated comments.)

No, sheer fantasy, like most "original research" around here; all periodic continued fractions are quadratic. The proof is in Hardy and Wright; briefly, if x is the value of the whole continued fraction, and r the value of the tail.

and by comparing this equation for n and m a period apart, and solving each for r, we get a quadratic equation for x. Septentrionalis 03:10, 6 December 2006 (UTC)

I'm familiar with the proof that an infinite periodic continued fraction in the traditional form (where each element of the cf is just a complex number) converges to a root of some quadratic polynomial if it converges at all. Not every infinite periodic cf is going to converge, though ... it's pretty easy to build [0; z, z, z, z, ...] and see that it's divergent for certain complex z, all of which lie on an open segment of the imaginary axis from −2i to 2i. For instance, just plugging in i for z generates a periodic sequence of convergents with a period of 3, and every third convergent is the point at infinity. You can get similar "orbits" of any length by plugging in other (pure imaginary) values of z. That's not what Arithmonic is talking about on his web site.

Arithmonic has devised a generalized continued fraction (a "fractal fraction") in which each partial numerator and partial denominator is itself a ratio between a finite continued fraction and one of those Engel expansion things. He has a whole lot of "1"s appearing as numerators, and positive integers as denominators. Anyway, his doodad looks sort of like a Christmas tree of integers arranged in a very complicated pattern, so it's only a "continued fraction" in a very general sense. I really don't think the proof mentioned above applies to Arithmonic's Christmas tree, because the recurrence relations he mentions involve the preceding 3 convergents, not just the previous 2. You _can_ get a third-degree polynomial out of a longer recurrence relation like that.

I haven't really figured out how that Christmas-tree-like structure works. But I did see his claim, which is that when you plug a "3" into this thing -- that's it, just a "3" everywhere a denominator occurs -- it converges to the (real) cube root of 2. I can't really say if he's right or not ... the web site doesn't provide enough detail for me to follow exactly what's going on. And I'm not ready to buy his book and try to plow through it right now. But I'm not ready to dismiss his claim as "sheer fantasy". I've looked at his stuff closely enough to understand that there just might be something unusual hidden inside the "fractal fractions" he's talking about. DavidCBryant 17:10, 6 December 2006 (UTC)

Anyway, I know when I'm licked. If you want to read any more about what I really think, try this link. DavidCBryant 01:07, 6 December 2006 (UTC)

What DCB really thinks is that

• We should include

in continued fraction

• That we are preventing this by advising him to leave the definition there as that of "simple continued fractions".

He never said this; I'm going to surprise him. I agree that we should include it; I disagree that we need to fiddle with the definition. Septentrionalis 03:19, 6 December 2006 (UTC)

Well, thanks for reading my rant, PMA. That's nice of you. I do appreciate it. But your solution doesn't make a lot of sense to me, because now you've displayed an object in the article that is not one of the objects the article defines at the outset. I think some readers might find it confusing, the way it stands. But hey, what's a little inconsistency here or there? After all, the article about complex analysis says that a function of a complex number is itself a real number. Set of all sets, here we come! (Or was that "Bertrand Russell, here we come!" I forget now.)

Anyway, I'm tired of arguing about the difference between a "continued fraction" and a "simple" or "regular" continued fraction. I'm going to concentrate on some other topics for a while. DavidCBryant 17:10, 6 December 2006 (UTC)

I've just added the continued fraction for π given above to the List of formulae involving π (so I hope it's correct!). Michael Hardy 00:36, 8 December 2006 (UTC)

Thanks, Michael. The formula is already in the article about Pi, in the "Continued Fractions" subheading. So you're not on the hook, if it's wrong. It is correct, though. It doesn't converge very quickly ... it's reminiscent of Wallis' continued product for Pi, in a quaint sort of way. Anyway, just to allay any concerns you may have, the first 12 convergents are 3/1, 19/6, 141/45, 1321/420, 14835/4725, 196011/62370, 2971101/945945, 50952465/16216200, 974212515/310134825, 20570537475/6547290750, 475113942765/151242416325, and 11922290683065/3794809718700. (I know that numerical evidence does not constitute a proof. But at least you can see that this thing is tending in the right direction ... 3, 3.167, 3.133, 3.14524, 3.13968, 3.1427, 3.14088, 3.14207, 3.14125, 3.14184, 3.14141, 3.14174, ...) DavidCBryant 03:55, 8 December 2006 (UTC)

[edit] Wikipedia:Release Version 0.7

The next round of nominations for the Wikipedia:Release Version is now open, these are articles which are to go on a CD-release of wikipedia. I've nominated 19 new mathematics articles.

Number - Pythagorean theorem - Eigenvalue, eigenvector and eigenspace - Fermat's Last Theorem - Polar coordinate system - Euclidean geometry - Derivative - Integral - Regular polytope - Cartesian coordinate system - Chaos theory - Circle - Real number - Complex number - Decimal - Infinity - Polynomial - Statistics - Gottfried Leibniz

which are generally our higher importance topics and of at least B+ status. I guess most of these could do with some a bit of love and care. There may be other articles I've missed which others think should also be nominated. --Salix alba (talk) 11:09, 2 December 2006 (UTC)

I'm curious, what work do you think the derivative page needs? It's already a GA. --King Bee 22:33, 4 December 2006 (UTC)

So good that someone just vandalized it to say that the derivative is "defined as the poopie of a cow." Isn't anonymous public editing fun! For as appalling as such vandalism is, I have to tell the truth and say that this particular expression got a chuckle out of that corner of my brain where my junior high self still lives. (BTW, how does one go about reverting a change without messing up other edits that have taken place later? I was hesitant to try it myself since I figure someone out there knows how to do it better than I do. But I'd really like to know if there's some fancy trick for it.) VectorPosse 23:09, 4 December 2006 (UTC)

Never mind. I figured it out. This new "undo" feature is the bomb! VectorPosse 23:23, 4 December 2006 (UTC)

Actually, that is kind of funny that you checked it right after my comment. =) --King Bee 00:18, 5 December 2006 (UTC)

As you asked, compare the German version de:Differentialrechnung which is an FA. History is very brief, the critical points min/max could do with an illustration, only one application, taylors theorem could do with expansion, week on functions which fails to be continuous, no mention of C-infinity fuctions. Newton-Raphson methods missing (as an example of why derivatives are useful). The generisations section is written at too high a level, using a lot of technical terms the lay reader would not understand, a simple example of a function of more than one variable would help. Week on referencing. Differential equations could do with a mention. Generally OK as a how-to for single valued case, but peters out towards the end. Theres some more comments on Talk:Derivative#GA_Review and Wikipedia:Good_articles/Disputes/Archive_7#Derivative. --Salix alba (talk) 20:35, 6 December 2006 (UTC)

[edit] Complete lattices (and Boolean algebras) and varieties

This comprises a few questions related to the concept of κ-complete lattices and Boolean algebras (where κ is an arbitrary cardinal number), and universal algebras with infinitary (or proper class) signatures.

1. Where should statements about κ-complete lattices appear? -complete lattice? A section of complete lattice? A section of lattice (order)? Something else?
2. In my Ph.D. thesis, I note that κ-complete Boolean algebras can be looked as as a variety (universal algebra) with respect to an infinitary signature. (I know of no other source, but I've never been contacted to say that it was in error. A reference in my thesis does apply universal algebra to infinitary algebras, but I don't know if I kept a copy of the reference.) Where (and if) should this information appear in Wikipedia. (I'll have to go over my thesis to see if I mentioned κ-complete lattices. I think it's in there, although it may only be for κ-complete κ-distributive lattices.)
3. Also in my thesis, I noted that complete Boolean algebras can be thought of as a variety with the signature being a proper class. (I'm almost certain no one else has dealt with that, but not absolutely certain).
4. Also in my thesis, I extended the concept of free algebra to those with a proper class of operations, and noting that the free complete Boolean algebra on an infinite set of generators does exist in that sense, but is a proper class.

What to do, what to do? I don't want to violate WP:OR or the extension of WP:AUTO to my work, but my thesis is a WP:RS, I suppose. — Arthur Rubin | (talk) 15:56, 4 December 2006 (UTC)

It's an important principal point. The WP:OR sums up Articles may not contain any unpublished arguments, ideas, data, or theories; or any unpublished analysis or synthesis of published arguments, ideas, data, or theories that serves to advance a position.; and in the fuller explanations states This policy does not prohibit editors with specialist knowledge from adding their knowledge to Wikipedia, but it does prohibit them from drawing on their personal knowledge without citing their sources. If an editor has published the results of his or her research in a reliable publication, then s/he may cite that source while writing in the third person and complying with our NPOV policy. I do not at all this excludes you from citing your own thesis; or any other to write about their own work (if it does fulfil the WP:RS guidelines and is of encyclopedian intetrest). Perhaps, we should be a little extra careful about our own work, because (a) we may risk to exaggerate its general interest, and (b) we may underestimate the troubles for others to follow the exposition of ideas. Apart from that, I find the 'who do you think you are' attitude extremely distasteful, and rather counterproductive. (I noticed you've had an attac of that kind on your talk page; you have my deepest sympathy and support in this matter.) The researchers also often do have experience of explaining their ideas to wider auditoria, and putting them into context. IMO, it would be an extremely stupid waste not to accept contributions of this kind.

Concretely, if you are asking 'Is κ-completeness of sufficient interest for the WP?', my personal answer is yes. However, I'd not like it to be written as parts of articles such as Complete lattice, since as far as I understand a complete lattice is κ-complete for 'each' κ (excuse my usage of 'naïve set theory'), not the other way around; and since I think at least one important result is not extendable from the theory of complete lattices to the κ-complete ones. (Namely, a complete semilattice is a lattice; but does this hold for e.g. -complete semilattices?) So, I'd prefer separate articles. I also think giving the basic definitions and a few main properties should be enough; and sensible links and categorisations.--JoergenB 18:41, 4 December 2006 (UTC)

Technical point; it's clear that an ℵ₁-complete semilattice is not necessarily an ℵ₁-complete lattice, even if it is a lattice. But there's still the naming problem to deal with. There is a PlanetMath article at κ-complete, but that's just wrong for a name. (Being ℵ₀ complete is trivial, under those definitions, which I believe are standard.

[edit] Possible vandalism in Taylor series

This article contains the text

Third, the (truncated) series can be used to compute function values approximately (often by recasting the polynomial into the Chlemloid's form and evaluating it with the Chlemshaw's algorithm).

I cannot find any Google hits for Chlemloid's form or Chlemshaw's algorithm anywhere but in this article or its mirrors. Could this be sneaky vandalism? -- 80.168.226.41 02:45, 6 December 2006 (UTC)

Zipping back many, many edits finds an older version of this text:

Third, the (truncated) series can be used to compute function values approximately (often by recasting in the polynomial into the Chebyshev form and evaluating it with the Clenshaw algorithm).

I've reverted to this version of that sentence: it looks at least plausible, given the context. -- 80.168.226.41 02:50, 6 December 2006 (UTC)

[edit] Sylvester's sequence listed as Good Article

Sylvester's sequence has been listed as a Good Article, thanks to a proposal by User:Anton Mravcek and a review by User:Twinxor. I'm a little surprised, given its low density of inline citations and our recent experiences with GA reviews, but pleasantly surprised. —David Eppstein 16:32, 6 December 2006 (UTC)

Happy news. Light and reason have pushed back dark and chaos, at least for a day. Another positive sign is that Wikipedia:Scientific citation guidelines has elevated status.

I'm sure the illustration helps. (People like pretty pictures, even if they don't understand them.) The topic will be unfamiliar to almost all readers; curiously, that can help. (Every day or so our geometry article is vandalized.)

One weakness that catches my eye is the lack of ISBNs. For the second edition of Concrete Mathematics, we should have

• ISBN-10: 0-201-55802-5; ISBN-13: 978-0-201-55802-9; Published: 1994-02-28.

(I don't know if the exercise cited has changed from the first edition.) For Computational Recreations in Mathematica, we should have

• ISBN-10: 0-201-52989-0; ISBN-13: 978-0-201-52989-0; Published: April 1991.

A reminder: We are but three weeks away from the big ISBN switch. From ISBN.org:

On January 1, 2007, the book industry will begin using 13 digit ISBNs to identify all books in supply chain.

However, any ISBN is better than none. (The online converter is handy for hyphenation, validation, and conversion.) A quick way to find a number if the book is not in front of you is to do a web search with the title in double quotation marks and 'ISBN'. Example: '"Concrete Mathematics" ISBN' (without the single quotation marks). Usually the top hits are Amazon and AbeBooks; often the ISBN is visible in the list of search results without clicking further.

We could also use ISSN ids. These are harder to find, but an AMS site can help with this, and with expanding abbreviated journal names. Thus we find

• Acta Arith. is Acta Arithmetica; Polish Acad. Sci., Warsaw; ISSN 0065-1036.
• Amer. J. Math. is American Journal of Mathematics; Johns Hopkins Univ. Press, Baltimore, MD; ISSN 0002-9327.
• Enseign. Math. is Enseignement des Mathématiques (The Teaching of Mathematics); Masson, Paris; ISSN 1269-7842.
• Enseign. Math. (2) is L'Enseignement Mathématique. Revue Internationale. IIe Série.; Enseignement Math., Geneva; ISSN 0013-8584.

I'm guessing that the second series is intended for the Erdős and Graham article.

Quibbles aside, it's nice to see a small technical article appreciated. --KSmrq^T 08:09, 7 December 2006 (UTC)

Good to see the guidelines have a greater status. I've now started a thread on Wikipedia talk:What is a good article? discussing the issue. At least some of the GA people are quite supportive of changing the criteia as soons as the agidelines have been accepted.

Nice to see Sylvester's sequence get through. The one point I'd make is that the caption could be expanded. I'd probably turn it round by 90 degrees and add a labels for 0 and 1, so its more obvious that the things are summing to 1. --Salix alba (talk) 14:02, 7 December 2006 (UTC)

Thanks for the quibbles; I added the ISBN-10's and a longer caption. To my mind ISSN's do not belong on individual article references but rather the reference should wikilink the journal name (as the ones in this article already do) and the ISSN should go into the article about the journal. If I had a DOI link I'd include that, though. —David Eppstein 16:19, 7 December 2006 (UTC)

[edit] Slashdot of previously deleted transreal number

FYI, slashdot.org has evoked transreal number which is a recreate of a previously deleted article. I think its an prime example of mathematical illiteracy. Oh well. Afd, fix or delete. linas 19:46, 7 December 2006 (UTC)

For the morbidly curious, the Slashdot article is here. Perspex machine has been AFDed, too; I prodded James Anderson (mathematician). Lunch 23:30, 7 December 2006 (UTC)

[edit] Template:Calculus footer

A new {{Calculus footer}} has been created. A discussion about it is going on at Talk:Calculus#Re: Addition of Template:Calculus footer. Oleg Alexandrov (talk) 17:30, 9 December 2006 (UTC)

[edit] Need advice

I need an advice on how to group entries in List of operators. Any thoughts?--Planemo 13:26, 10 December 2006 (UTC)

This is a little out of my area, but I feel that you need more explanation of these transformations. What do the variables mean? What is the transformation used for? It is good that you have pointers to articles for some of them, but every one of them should have a pointer (even if it is a red-link). You described them as "This list includes the most widespread transformations of analytical functions of one argument.". In what sense are they "analytical"? If you mean that they are defined on the complex plane and have complex derivatives everywhere, then you should put them in a category that deals with complex numbers. JRSpriggs 04:56, 11 December 2006 (UTC)

I added some boilerplate and various links that perhaps addresses JRSpriggs' comments. A merge with list of transforms might be contemplated. There are some generic transforms that don't easily fit in this list. linas 06:44, 11 December 2006 (UTC)

I would strongly recommend the merge. List of operators is where I would look for unary and binary operators (+,- *,/, absolute value). Septentrionalis PMAnderson 16:00, 11 December 2006 (UTC)

They are functions, not operators and already covered in "left composition" entry ()--Planemo 17:32, 11 December 2006 (UTC)

And these are functionals; so? Septentrionalis PMAnderson 18:48, 11 December 2006 (UTC)

No they all are particular cases of left composition operator.--Planemo 18:52, 11 December 2006 (UTC)

The question is how to group the entries better: by properties (i.e. linearity) or by branch of mathematics where they are used? But where to place such operators as composition or derivative then? Should the functionals be separated or not? Or to create a special section for binary operations such as composition, convolution and inner product? Or maybe group by type of coordinates/parametrization?--Planemo 11:39, 11 December 2006 (UTC)

IMHO, having such a "list" is not that good an idea. the term "operator" is used in a hell of a lotta places in mathematics, making a comprehensive listing difficult and somewhat pointless. and having an incomplete list, as that article is right now, is misleading, unless one is very specific about the context and what is meant by an "operator". right now it looks rather like an ungainly collection. for instance, an operator theorist would find few items on that list to be of interest; in any case, they are well-covered elsewhere. i am sure such examples abound from other fields, say the boundary operator from homology. also, some entries in the list seem rather funny, e.g. taking the inverse of a function is listed, so is the arc-length of a curve and the L^2 norm. sure one can use whatever terminology one wants, but calling every trivial thing an "operator" doesn't help the credibility or the utility of the "list". Mct mht 18:25, 11 December 2006 (UTC)

I agree the term is too broad, but the list is dedicated to the certain meaning. And what's wrong with arc-length or inverse function? Maybe that they are not liner while most "specialists in operators" work with linear ones?--Planemo 18:47, 11 December 2006 (UTC)

What's wrong with the non-linear operators is that there are just about zero operator-theoretic results, theorems or facts about them. Taking some random thing and calling it "an operator" seems pointless to me, as it does not suddenly offer new insight, nor does it allow some general theorem to be applied to obtain new results. By contrast, the linear opers have a rich theory and many general theorems that can be applied. Thus, I'd recommend discarding the entire non-linear section. But perhaps this discussion should be taken to the article talk page. linas 03:24, 14 December 2006 (UTC)

[edit] A new article about continued fractions

Hi, all!

I just put a new article out in the big namespace. Please take a look at it and tell me what you think -- either here, or on my user talk page.

Thanks! DavidCBryant 02:10, 12 December 2006 (UTC)

Or the article talk page. Septentrionalis PMAnderson 04:03, 13 December 2006 (UTC)

[edit] Suggested move of List of mathematics articles

I came across the page List of mathematics articles and am concerned about the self-references in it. Outside of the {{MathTopicTOC}} template, the entire page is written as if the reader is an editor of Wikipedia. This would cause confusion if the page were reused outside of Wikipedia. After discussing this with User:Oleg Alexandrov, it was suggested that the page could be moved to Wikipedia:List of mathematics articles. I would support such a move, but he opposed it on the grounds that the page would be difficult to move and that it belongs in the main namespace. I am seeking further input. Thanks. Khatru2 04:18, 12 December 2006 (UTC)

what do other subject areas do? it appears there's a list of physics articles with a similar structure (with exception of a reference to the wikiphysics project). Lunch 04:29, 12 December 2006 (UTC)

Here's how I see it. The article you mention presently serves 3 purposes:

1. A header page to our index of all mathematical articles

   This is clearly valid in the main namespace, so some portion of the page should remain in place to continue in that role.

2. A pointer to this Wikiproject for new mathematics editors

   This is perhaps no longer needed. Portal:Mathematics now serves as the "main page" for mathematics on Wikipedia and it contains the necessary links to this project.

3. A way for editors to monitor changes to the mathematics articles

   This material should probably be moved to somewhere within the Wikipedia namespace (if, in fact, there are editors who still require it).

-- Fropuff 05:36, 12 December 2006 (UTC)

I suggest that the article be split into two articles: (1) one article with the current name which has been stripped of references to Wikipedia stuff; and (2) a new article in Wikipedia space which has the other stuff which was stripped out of the first article, PLUS it include the current article by referrence using the template {{:List of mathematics articles}}. That inclusion would have an effect like the following. JRSpriggs 10:23, 12 December 2006 (UTC)

{{:List of mathematics articles}}

I really think all this is not worth the trouble. Yes, the list of mathematics articles has a dual purpose, both for editors and for readers. Theoretically speaking a split or a move to the Wikipedia namespace would be the right thing to do. Practically speaking it would be an inconvenience, and I really think that keeping things the way they are outweighs any advantages of separating the two. Let the readers read the first part in that article, the actual lists, and let the editors or potential editors wonder about the wikiproject link and the changes to the list. That's what I'd think, at least. Oleg Alexandrov (talk) 15:53, 12 December 2006 (UTC)

The self-references to the Wikipedia Math Project have to go. If we wish to reference the project we can do so by a portal box which would be perfectly appropriate, but talking about the project in the text makes the article reak of vanity and is completely unencyclopedic.--Jersey Devil 23:18, 12 December 2006 (UTC)

[edit] Simple Introduction

Some science articles are starting to produce introductory versions of themselves to make them more accessible to the average encyclopedia reader. You can see what has been done so far at special relativity, general relativity and evolution, all of which now have special introduction articles. These are intermediate between the very simple articles on Simple Wikipedia and the regular encyclopedia articles. They serve a valuable function in producing something that is useful for getting someone up to speed so that they can then tackle the real article. Those who want even simpler explanations can drop down to Simple Wikipedia. What do you think?--Filll 22:55, 12 December 2006 (UTC)

I am completely sympathetic with the need to have good pedagogical material. At the same time these articles seem out of place in what is supposed to be an encyclopedia. An encyclopedia should be a reference work that provides a succinct overview of a given topic, not a textbook from which to learn. It also seems detrimental to divide the effort of editors amongst multiple articles on the same topic. In my view it would be more appropriate to move the introductions you mention and others like them to Wikibooks. We can and should provide links to that material from Wikipedia. -- Fropuff 04:17, 13 December 2006 (UTC)

I find the introductory versions for the physics articles refreshing and worthwhile. I can agree with many of the points made by Fropuff, especially about dividing up editors' efforts, but I do believe there is a place in an encyclopedia for such material. I have expressed the opinion here in this forum before--and perhaps I am in a minority here--that we ought to be flexible about what is "allowed" or "disallowed" instead of being too dogmatic about what is "encyclopedic". In other words, I believe good pedagogy can be a guiding principle and not a secondary consideration. VectorPosse 05:19, 13 December 2006 (UTC)

I can appreciate the need not to divide the efforts of a few editors. However, I have a few comments:

• this is not a zero sum game. There are more editors joining all the time. There are roughly 30,000 editors now on Wikipedia and more will come if things continue
• providing accessible materials will actually enable more editors to contribute in areas in which they are not specialists but can come up to speed, increasing the number of available editors
• Encyclopediae are only useful if they can be used with a minimum of hassle. If I look in some subject I am not an expert in and it is too much trouble to even read the introduction/lead of the article, I will probably give up and look someplace else
• Encyclopedia Britannica provides something of a gold standard in encyclopedias. Encyclopedia Britannica has multiple articles on many subjects at different levels of sophistication:
  • "Britannica Discovery Library" for preschool children
  • "My First Britannica" encyclopedia for 6 to 12 year olds
  • the single volume Britannica Concise Encyclopædia
  • macropedia
  • micropedia
  • ready reference volumes

and this does not include the propedia. So Britannica might have 6 or more articles at different levels aimed at different audiences. I am not suggesting that Wikipedia attempt to equal their efforts, but 2 or 3 does not seem excessive when the most famous competitor has recognized the need for 6 or more. And the criteria they have is utility, because if it is not useful, they cannot sell encyclopediae.

• I have no objection to Wikibooks, but that seems like the wrong format for shorter articles that are somewhat focused.
• The lead parts of many articles on Wikipedia are completely unhelpful to nonspecialists. In real print encyclopediae, I do not find this to be the case. They pay more attention to accessibility, and we should too. An introductory article is just an extended lead article, or primer that can be used as an aid to reading the regular article.
• Succinct and terse is a great goal, but it is not one I have noticed being met here on Wikipedia often enough. That still does not preclude the requirement of the material being accessible.--Filll 05:47, 13 December 2006 (UTC)

I don't know if I agree that simple intro articles are out of place. But I do think the concern of dividing up effort is a very valid one. I would agree that editing is not a "zero sum game", but I think that's the wrong thing to bring up. I think what Fropuff was referring to is the dividing up of expertise. Sure there are editors joining everyday, and if somebody puts in less effort, people will join who will pick up the slack. Unfortunately, that doesn't really address expertise. When one person, expert on a particular topic, stops editing, progress in that area may stop for a very long time (and errors start creeping in). It's not like there's a uniform distribution of experts joining, let alone a uniform distribution of expertise in the different areas.

I find it doubtful that even doing an incredible job would significantly increase the expertise level of editors. To really gain significant expertise takes considerable effort and dedication. People with that desire will want to study the material out of books. What Wikipedia offers is a useful synthesis of materials. I don't think a scenario where someone learns exclusively off Wikipedia is viable, even assuming a radical improvement.

One thing I want to point out about Brittanica and paper encyclopedias is that they really do a careful job of selection. By doing so, they can focus on fewer articles and ones in which it is much simpler to write well. Wikipedia does not have this advantage. Its strength is in large coverage. So it's really unfair and unrealistic to compare.

Since I got on this soapbox, I do want to say one thing about accessibility however. A common refrain is "Only a specialist can understand it and why would he or she need to read this?" This is wrong. The mistaken assumption is that because the reader did not understand it, the article is esoteric and cannot be understood by anyone other than an "expert". This leads to the tagging of numerous mathematical articles as being too technical. Of course, in reality, there are many people and many levels of expertise and many levels of mathematical maturity. A person adept in one technical subject can often learn something in another because of a high degree of maturity and understanding of how to cull the main ideas out.

Being too technical is an issue that we should be concerned about, but probably if there was less of what I just described, math editors would probably take these concerns more seriously. We try nonetheless.

Having said that, this concern has been raised before, again and again. There's been more of a focus on improving what we have, rather than extending it. People, with the desire, have improved articles such as mathematics and manifold. It took a great deal of effort and time. Right now I've been working on a rewrite of knot theory. It's taking a lot of time, and I certainly can't put in that much time regularly. There are also a few things I promised, but never got done. So the spirit is willing, but the flesh, as usual, is often weak. --Chan-Ho (Talk) 18:57, 13 December 2006 (UTC)

Chan-Ho raises some good points about how best to split our time, the sheare quantity of mathematical articles can be intimidating. levels of expertise can also be intermidating, when an undergraduate user joins the project, he is greated with a big list of very experiences mathematicians, which may give the feeling of "what can I contribute". The answer is plenty, we have a lot of articles which don't require PhD's to edit, indeed these are often our most visited articles.

Its just occured to me that it might be worthwhile to set up a /High school mathematics work group and /Degree level mathematics workgroup where those with those levels of qualifications could congrigate. The workgroups could have their own list of articles to work on and possible participants lists. It might help in setting up some sub communities where people feel more able to contribute.

Also Wikipedia:WikiProject Mathematics/Participants could do with a prune. Many of the people who are listed there are no longer active. I had a start at this at User:Salix alba/Sandbox2, moving those who had not contributed in the last three months to a hall of fame section.

We do have a good recruiting oportunity at the moment, the Wikipedia:Articles for deletion/Transreal number‎ and related debates have seen a lot of new people, maybe some of these could be encouraged to work on some of the mathematics article. --Salix alba (talk) 20:02, 13 December 2006 (UTC)

Things like knot theory and category theory are not places for amateurs. I would agree completely with that. However, if you do have a lot of editors with lower skill levels, I hope you can employ them in constructive ways.

Another value of having things as accessible as possible is that many scientists actually visit Wikipedia as one of their starting places when doing research on an unfamiliar topic. And many people interested in applications regularly try to mine mathematics for ideas and machinery to use in applied disciplines. These people might have an impressive level of sophistication in some other area, but need a helping hand or even a guide to the literature to help them get started. This is a function that Wikipedia can fill. --Filll 20:25, 13 December 2006 (UTC)

I've now created a Hall of Fame section in /Participants for users how have not editted in the last three months. There were some who had not edited since 2004. A reasuring number on the participants list are still active editors which is encouraging. --Salix alba (talk) 23:32, 13 December 2006 (UTC)

Actually, I think knot theory is a good field for amateurs. That's why I picked knot theory to improve, since I expect it's an article that can be widely read and digested. Mentioning it in the same breath as category theory is kind of misleading, although of course, some very advanced aspects of knot theory are very abstract and even category theoretical. There have been several editors with an "amateur" interest in knot theory that have made big contributions to the knot theory portion of Wikipedia. But some left, one passed away, and it's difficult to replace dedicated editors in general.

The goal of accessibility is a good one, and I hope some of Richard's proposed mechanisms will help that along. More direction would be beneficial, I think. ---Chan-Ho (Talk) 04:52, 14 December 2006 (UTC)

[edit] Area of a disk

The article area of a disk could use some work. It may be the only Wikipedia article justifying the familiar πr² expression, so it wouldn't hurt to bring it up to civilized standards. Michael Hardy 01:09, 13 December 2006 (UTC)

I've reproduced the proof by Archimedes on the talk page. (But without the obvious figures.) The article page scares me! Maybe later. --KSmrq^T 00:22, 14 December 2006 (UTC)

[edit] Proofs of trigonometric identities

Proofs of trigonometric identities is, in its present form, a horrible mess. Please help clean it up. Michael Hardy 19:12, 13 December 2006 (UTC)

I slapped it into Category:Article proofs, which, by definition, only allows messy, horrible articles. :-) linas 02:55, 14 December 2006 (UTC)

[edit] User:WAREL again?

this change at Perfect number by Chikushi (talk • contribs) looks a lot like User:WAREL. It's his first edit, and the formula is byte-for-byte identical to this edit by MIYAJ (talk • contribs), blocked as a sock puppet of User:WAREL. Did I do right in reverting it? — Arthur Rubin | (talk) 20:41, 13 December 2006 (UTC)

Definately. Well spotted! :-) Tompw (talk) 01:01, 15 December 2006 (UTC)

[edit] "Big" articles

I'm encountering some concern about the size of the article Areas of mathematics. I saw a reference to a 64K (= 65,536 byte) limit in somebody's message (Oleg's?) recently.

Anyway, I want to learn more about that. Does anyone know where to look it up? Does the limit apply to the wiki markup file that an author/editor can access? Or does it apply to the XML file (sans images) that the server serves up? I'm certain the 64K limit doesn't count graphics ... I tried to load the Mandelbrot set article the other day, and my poor little box choked on it somewhere between 1.0 and 2.0 Mbytes.  :(

Thanks for the help! DavidCBryant 20:53, 13 December 2006 (UTC)

Wikipedia:Article size is the relavant guideline. AoM is less than 64K, so I think its probably OK. As this is a list type article much of the guideline is not really relavant, and the problems with older browsers has mostly disapeared. Mandelbrot is one if the most image rich pages about, but I am suprised that your prowser chocked. You must have quite an old machine. --Salix alba (talk) 22:18, 13 December 2006 (UTC)

AMD K6, 300 MHz. Dial-up connection. I paid $50 for it, OS and all. I'm a Neanderthal.  ;^> Thanks for the reference! DavidCBryant 11:45, 14 December 2006 (UTC)

I agree that AoM is not a place to enforce teh article size rule, unless it gets truley huge, and its very nature should make that avoidable. (I have a Cerelon 333, an even worse processor. However, even with broadband, info arrives at the computer slow enough for my ancient computer to deal with it... internet connections are far slower than internal data transfer - even the original IDE standard from 1994 ran at 3.3MB/sec = 26.4Mb/sec, over three times faster than the most turbo-charged broadband around in the UK today) Tompw (talk) 13:30, 14 December 2006 (UTC)

[edit] Problems at exponentiation and empty product

Yes, it's the infamous 0⁰ debate again, and from many aspects I regret that I stepped in it, because it's really kind of a silly argument that doesn't matter much. However it does matter, at least a little, that the two mentioned articles asserted a consensus that does not exist.

(Precis of my position, which is not really the point, but just so you know where I'm coming from: The arguments for 0⁰=1 make perfect sense for exponentiation as defined on the naturals, or even when the base is ineterpreted as a real and the exponent as a natural, because then we are indeed discussing an empty product. However they cease to convince in the context of real-number-to-real-number exponentiation. The natural number 0 and the real number 0.0 are distinct kinds of thing, and there is no reason 0.0^0.0 must be defined, merely because 0⁰ is.)

Anyway as I say my position is beside the point. The point is that there are editors (well, one in particular, a difficult fellow whom some of you have encountered in the past) who want to preserve the articles in a state where they assert a consensus that does not in fact exist among mathematicians. I think you'll all agree that's wrong, whatever your views on the underlying "issue", if we can dignify it with that name. Please come and work on a broader-based approach. --Trovatore 17:06, 15 December 2006 (UTC)

Isn't 0⁰ an indeterminate form; i.e., I can make it equal to whatever I like if it shows up in a limit? How does it make sense to define 0⁰ = 1? --King Bee 17:20, 15 December 2006 (UTC)

Please, let's take discussion on the merits somewhere else -- this talk page would quickly become unusable. (See talk:empty product, for example -- my fault, I concede, but let's not repeat the problem here.) --Trovatore 17:25, 15 December 2006 (UTC)

Agreed. --King Bee 17:32, 15 December 2006 (UTC)