Talk:Root rectangle

This stub appears to be utter nonsense
I quote the article's bullet points, with my comments on each:


 * The root 2 rectangle, is called harmonic rectangle. When you divide it in half, the two resulting figures keep the root 2 proportion.


 * COMMENT: Depending on which way you divide a 1 : √2 rectangle, the ratio of sides of the resulting 2 identical rectangles will either be 1 : √2/2 or 1/2 : √2; neither ratio equals 1 : √2 (one is double, the other is half).


 * The root 3 rectangle's short side is equivalent to the side of an hexagon while the longer is equivalent to it's ratio.


 * COMMENT: What does this mean? Any length, therefore any side of any rectangle, can be the length of a hexagon's side, or, for that matter, the side of anything. What is the "it" in "it's ratio"?


 * The root 4 rectangle has a proportion 1:2, which means it's equivalent to two perfect squares put together.


 * COMMENT: Any rectangle with sides of ratio 1:i, where i is any integer, is like putting i squares side by side. It has nothing to do with 2 being √4: every number is the square root of its square. So, to generalize, you could call every 1:i rectangle a root 1:i2 rectangle, but you would not be saying anything; it is a tautology. And in geometry, what makes any square more perfect than any other? All squares are equilateral.


 * The root 5 rectangle is related to the golden proportion. The longer side is equal to 1, plus two times the middle reason of phi.


 * COMMENT: Why do say this is related to the golden proportion, a non-existent article, when what you mean is called the golden ratio on Wikipedia and most everywhere else. You were the one who started the golden ratio project, so you already know this. Saying phi is meaningless without a link or definition. And what in the world is "the middle reason of phi"?

Please learn how to cite a source. Please read WP:CITE.

The word it's is the contraction of it is; the possessive of it is its. One of your it's is the correct meaning, but is too casual for an encyclopedia: to be grammatically correct, it should be replaced by "that it is". Your other it's is just a blunder (you mean the possessive).

Dude, it really is not fair to the rest of us for you to make messes on Wikipedia, in especially in article space, for others to clean up. That is what you were doing awhile ago with your sudden interest in the golden (or, as you would have it, auric) ratio, and now this. Please! Finell (Talk) 09:44, 19 May 2008 (UTC)

Yeah, please, be careful with your tone and comments. learn how to... yadda yadda is both rude and annoying. Stating the article need more sources and adding the tag would be fear and enough.

Your comment about its is right on the spot.

Your comment on root two rectangle is just wrong. Check your math again. The one about root 5 is just annoying, golden ratio, section and proportion are synonyms.

Please, reduce your criticism to the necesary. In general, your posting here was very productive, but it's hard to take you seriously, when you start making moot points. You don't have to criticize every single thing.--20-dude (talk) 21:11, 19 May 2008 (UTC)


 * I second Finell's sentiment that "it really is not fair to the rest of us for you to make messes on Wikipedia, in especially in article space, for others to clean up." If you would listen to why he is annoyed by your editing, and make an effort to improve, that would be more productive than getting all defensive.  The article really is pretty unintelligible as it stands. Dicklyon (talk) 02:38, 20 May 2008 (UTC)


 * Sorry. Deal with it. You don't have to do all the clean up, but so far, you're very good at

the dealing. Nobody is forcing anybody to clean up. As you can see, I did all of it myself.

The funny thing is that somebody messed up after my cleaning up. The Properties part, as I wrote it was all supported by the same author. By modiffying it, somebody made it look as if the author was supporting other stuff. Besides, every root rectangle has particular properties that would be a shame not to write down. Every single property I mentioned is fully supported by my (academic and reliable) source and easy to prove by anyone with a functioning, regular brain.--20-dude (talk) 05:10, 20 May 2008 (UTC)


 * I did a bit of cleanup myself. It's possible I messed up the citations; it was hard to interpret many of those points sensibly, so hard to believe that they could be supported by a reliable source; and your source is not readily available.  If I messed it up, please do set it right, or let me know and I'll work on it.  There are many sources readily available by Google book search, so you might want to use some of those, too, to arrive at sensible things to say. Dicklyon (talk) 06:11, 20 May 2008 (UTC)


 * By the way, some of those books are pre-1923, public domain, fully available online, and have some good illustrations. You should add some of those and make the text more intelligible. Dicklyon (talk) 06:34, 20 May 2008 (UTC)


 * Kickass observations. However, you lost me at the "hard to believe the points could be supported by a reliable source" part... To me the points are kind of obvious. Perhaps the fact that I can use AutoCAD to reproduce and prove the geometry in my computer makes this difference of perception. Considering you're quite a math enthusiast, you should get a copy of that software. Needless to mention, I'd NEVER base any point on the results of my experimentation. In this case, I strictly used sources.


 * BTW, the root-phi rectangle, called penton, is one of the 12 dynamic rectangles I mentioned to you (Dicklyon), in your talk page. Everything seems to indicate they are very real, as you can see some like the sixton, the auron, the biauron, the diagon and the hemidiagon can be found in academic sources; but the trion, the quadriagon, the hemiolion (a simple 2:3 rectangle!) and the bipenton appear only on regular unsourced sites. --20-dude (talk) 07:14, 20 May 2008 (UTC)

Question
Why did you changed the order of my references? I've been using the classic method (LASTNAME, Name. Title of the book in cursive. Editorial. Year. Page.), but you (Dicklyon) don't seem to care much for it. Why is that? Is there some relevant guideline I've been missing, or is it just matter of preference?--20-dude (talk) 08:38, 20 May 2008 (UTC)

Excuse my ignorance, but why is the page separated from the editorial only by a colon? That doesn't make much sense to me. I't not like you'll find anything on, say, the page 193 of Oxford Press.--20-dude (talk) 08:49, 20 May 2008 (UTC)


 * I was trying to move toward consistency with the style established broadin in wikipedia by the template:cite book. It would be best to just use the template, as I did in the new ref that I added. Dicklyon (talk) 14:39, 20 May 2008 (UTC)


 * I'll follow that format from now on.--20-dude (talk) 08:53, 21 May 2008 (UTC)

Citing
The citing is now fine. I liked the last Dicklyon contribs a lot.

Finell, read WP:CITE. You have to learn to tie the source/author with the statement. Each cite works for specific statements, not for all of them. Sorry if I came too strong on you when I noticed, but the irony made me momentarely mad.

By the way, Dick: it's very possible Matila was relying on Jay, so it might be ok, but I think it was Ghyka who stated the stuf about root-6 and on not being found often in art. We have to confirm that data. --20-dude (talk) 01:27, 25 May 2008 (UTC)

Dynamic rectangle: etymology
In the 1920s, Jay Hambidge used the term dynamic rectangle in writing about his theory of dynamic symmetry. Can anyone cite an earlier usage of this term? Dude? Finell (Talk) 03:33, 26 May 2008 (UTC)

Root 2 rectangle
Dear Dude:

The stub you wrote included the following statement:

The root 2 rectangle, is called harmonic rectangle. When you divide it in half, the two resulting figures keep the root 2 proportion.

I wrote the following on this Talk page:

COMMENT: Depending on which way you divide a 1 : √2 rectangle, the ratio of sides of the resulting 2 identical rectangles will either be 1 : √2/2 or 1/2 : √2; neither ratio equals 1 : √2 (one is double, the other is half).

You replied:

Your comment on root two rectangle is just wrong. Check your math again.

Dude, please tell me exactly, and clearly, what is wrong with the math in my comment? Thank you. Finell (Talk) 03:52, 26 May 2008 (UTC)


 * Finell, that's why we need an illustration. I replaced that section with the more general one on root-N rectangles divided into N identical pieces.  From 1 : √N you get 1 : 1√N, which is the same aspect ratio if you interchange lengths to get short : long.  So it was not wrong, just unclear and un-general. See this book for illustration. Dicklyon (talk) 04:09, 26 May 2008 (UTC)

Root 5 rectangle
Dear Dude:

The stub you wrote included the following statement:

The root 5 rectangle is related to the golden proportion. The longer side is equal to 1, plus two times the middle reason of phi.

I wrote the following on this Talk page:

COMMENT: Why do say this is related to the golden proportion, a non-existent article, when what you mean is called the golden ratio on Wikipedia and most everywhere else. You were the one who started the golden ratio project, so you already know this. Saying phi is meaningless without a link or definition. And what in the world is "the middle reason of phi"?

You replied:

Your comment ... about root 5 is just annoying, golden ratio, section and proportion are synonyms.

Dude, the problem that you created was making a red link for golden proportion, which is a request that someone should write an article with that title. When you see that you have created a red link, the responsible thing to do is to correct the link unless you are specifically asking others to write a new article with the red-linked title. Further, ratio and proportion  are not synonyms, and golden proportion is not a common usage, so what you wrote caused unnecessary confusion. Finally, please answer this question, which you overlooked:

And what in the world is "the middle reason of phi"?

Thank you. Finell (Talk) 04:13, 26 May 2008 (UTC)


 * Finell, I removed that "middle reason" thing because I could find no interpretation for it. And I fixed that red link, since he missed your point.  He's put some stuff on my talk page about the "reason" thing, which I still can't interpret nor find a source for.  However, it seems pointless to rub all this in.  Why don't we just work on the article?  I hope you agree that's is better now at least.  The relation of the root five rectangle to phi still seems pretty silly, but they do draw it in books and point out that relationship, which is obvious already in the formula for phi, so I get it's OK to have it in the article.  A good figure would make it more sensible, and there are lots of PD ones we could copy... Dicklyon (talk) 04:37, 26 May 2008 (UTC)

When you see that you have created a red link, the responsible thing to do is to correct the link unless you are specifically asking others to write a new article with the red-linked title. That truly annoyed the hell out of me. You want to rub in. Well, bring it on!:

1. Golden Proportion IS used.

2. Golden proportion is actually more acurate than ratio, since in a golden section you have two ratios being equal. Duh.

3. That's why Pacioli called Divine Proportion. Duh!!!!

4. Besides, EVEN WIKIPEDIA BACKS ME UP:Other names frequently used for or closely related to the golden ratio are golden section (Latin: sectio aurea), golden mean, golden number, and the Greek letter phi .[2][3][4] Other terms encountered include extreme and mean ratio, medial section, divine proportion (Italian: proporzione divina), divine section (Latin: sectio divina), golden proportion, golden cut,[5] and mean of Phidias. Don't you read the articles you're editing?

5. The red link also invites to create a redirect. Duh. Which IS necesary.

You see, I just beat not one but 5 times the crap out of your annoying whining again. I bet you wish you never wrote your last comment. Stop putting yourself in evidence.

The other words I was looking for is Middle (or mean) and Extreme ratio (or section, if you talk about a section). Firts used, btw, by Euclid, which also clarifies that the greek and teh freemasosns did indeed know about these conceps (Book 6, Proposition 30 of the Elements).

Oh and Dick, do your math, it's not silly, (how on earth would that be silly? calling it silly is silly and obnoxious, you have to admit) I'll be adding the reference soon, but the root-5 rectangle, produced by extending the extreme reason twice to a square from both sides (and not by using the diagonal of a root-4), is very used in mayan drawing.--20-dude (talk) 21:38, 26 May 2008 (UTC)


 * Dude, you need to re-read WP:NPA and WP:CIVIL. Please keep your comments focused on the article content, and avoid making disparaging remarks about other editors; consider this a final warning, as I will request a block if you do it again. Dicklyon (talk) 05:10, 27 May 2008 (UTC)


 * ...What's the big deal? I was just being very honest. It IS kind of wrong to have missed all the points I said Finell missed, and still write the stuff he wrote before. I do make mistakes, but I have proved Finell commits more, so we have nothing to do criticizing each other with words as "utter nonsense" or "mess". And when you back him you often corner me, you have to recognize that. After all, let's be realistic, no ofense intended, just being practical: This article is all your and my contribs. Surelly good hearted and well intended, but all Finell has done so far is a couple of citing mistakes and criticism without really being technically aware of what he is saying. Don't take it the wrong way, I mean this as constructive critism. I'm not saying that he shouldn't be part of this, but only that he should make more informed comments, that he should know his theory before speaking. But although you warned him as well, that's only my opinion and he can do whatever he wants with it and that'd be fine.--20-dude (talk) 06:28, 27 May 2008 (UTC)


 * Dear Dude: We can wait for a reference to a reliable source, but in the meanwhile please explain in standard English what you mean by "the extreme reason" and "the middle reason of phi". Also, please lay off the "Duh": You aren't that smart, the rest of us aren't that stupid, and you often turn out to be the one who is mistaken in these exchanges. Thank you. Finell (Talk) 06:14, 27 May 2008 (UTC)

As I told, it is extreme and mean ratio. The term "mean ratio" is the same as "middle ratio". It is from the Elements of Euclid and it is also in the Golden Ratio article, just as I quoted a couple of comments above.

Btw, I still need to know what do you guys commonly call the catheti? I can't even imagine geometry with an equivalent word and it has been driven me crazy lately.--20-dude (talk) 06:36, 27 May 2008 (UTC)


 * Can you say if "mean ratio" or "middle ratio" or "extreme ratio" have numeric values? Is one 1.618 and another 0.618?  What source are you relying on?  And I never used a special term for the two sides of a right triangle that are not the hypotenuse; just sides; just ignorance on my part. Dicklyon (talk) 06:56, 27 May 2008 (UTC)


 * Yes and no, it depends. Golden Section is Mean+Extreme ratios. If the golden section is 1.618, the mean would be 1 and the extreme 0.618. If the golden section is 1, the mean ratio is 0.618m and the extreme ratio 0.382.

I guess that if somebody gives you stick of x size, its MR would be 0.618x and the ER would be 0.382x, but x=golden section. Sometimes, like when you produce an auron of golden rectangle, you start with the mean ratio, which would be the side of the square, produce the golden section by multiplying 1.618 times the side and (here is where it gets messy!!) the extreme mean by multiplying 0.618 times the side!!. So if you start with the golden section and divide it, 0.618 is the mean ratio and 0.382 the extreme, but if you start with the mean ratio (like when producing a golden rectangle), the extreme is 0.618 and 0.382 has nothing to do.

The use of catheti is perhaps just an advantage of spanish. However, although not as used, as far as I can tell, in English, the equivalents are Opposite Cathete (the vertical one)and Adjacent Cathete (the horizontal one)--20-dude (talk) 08:09, 27 May 2008 (UTC)


 * Do you have any sources for this interpretation? I never saw the "and" in mean and extreme ratio interpreted as "plus", but maybe it is somewhere, and maybe the mean an extreme are 1.0 and 0.618, but I have never seen that.  Opposite and adjacent are terms used with respect to an angle, in trigonometry, in a right triangle, to trig function of that angle. Dicklyon (talk) 04:27, 28 May 2008 (UTC)


 * Those terms are old as hell... Actually, kinda... since Diogenes one of the earliest historians references of the golden ratio back in III bC wrote that, Pherecides, uncle and teacher of Pythagora, used the pentacle as a reference to the doorway of Tartarus, which in his time didn't meant hell but void and chaos (actually, for my taste, it only means hell to the less educated authors, who took the idea from the fact that there are supposed to be titans and *some* humans that were put there by zeus). However, the pont is that in Diogenes book, Theano, wife of Pythagora has a treaty, only preserved in his literal quotes, on Golden ratio (even if he lies, which is unlikely, that sets its ofigin somewhere before III bC). The fist preserved treaty talking about golden ratio is the Elements, by Euclides... which is considered the first treaty to also talk about mean and extreme ratio.

I hope that anwers your question.--20-dude (talk) 10:21, 30 May 2008 (UTC)


 * No, it does not at all. I've read what's in Elements, and I don't see your interpretation in it.  Every time "extreme" is used, it's in the context of "extreme and mean"; those words don't get any geometric or numeric meaning, length, or ratio, assigned on their own, do they?  Dicklyon (talk) 15:41, 30 May 2008 (UTC)


 * Dear Dude: Saying "Those terms are old as hell" is not citing a reliable source. What book of Diogenes are you referring to and what passages? What are you referring to as this "treaty" or that "treaty"? What does hell, void, and chaos have to do with the golden ratio or with root-5 rectangles?


 * Euclid's Elements is not a "treaty". Further, Elements did not discuss the golden ratio and "also talk about mean and extreme ratio." Elements defines "extreme and mean ratio" (this expression is never reversed as "mean and extreme ratio") and has several propositions (theorems and constructions, in more modern terminology) that involve extreme and mean ratio—and that is all. The term extreme and mean ratio is based on the extremes and means of a proportion. I have read all of this and the proofs in Elements, the original source; so has Dicklyon, and so have several other contributors to the Golden ratio article and related articles. Have you?


 * Extreme and mean ratio was the standard term until around the late 19th or early 20th century (although divine proportion had limited usage in the Renaissance, and golden cut (the first golden anything) was used by a German writer in the mid-19th century. The next widely used standard term was golden section (is is still the primary term in the Library of Congress subject classifications), followed by the current golden ratio. (No, golden proportion is not more accurate—golden ratio refers to a single number used as a ratio of length, not a proportion, which is an equality of ratios—and golden proportion was never in widespread use. If you think I'm wrong, cite a number of examples that approximates the usage of golden ratio.)


 * Please cite your source for extreme reason and middle reason and for the meanings that you ascribe to them. I have never come across those terms. Neither has Dicklyon. And we have both read a lot on the subject.


 * Dude, if you would just write clearly and carefully, use spell check, use standard terminology that everyone understands (instead of obscure terms that you pick up from sources that you refuse to cite), and cite your sources (specific passages in specific writings that you adequately identify so others can find and verify them), you could begin to make some contributions to Wikipedia that survive. As it is, most of what you write on these topics is either discarded or rewritten beyond recognition. And what is the point of that?


 * No one here is hostile toward you. But we are concerned about the accuracy and reliability of Wikipedia, and about upholding the polices and standards that govern Wikipedia and promote collaborative work, accuracy, reliability, and verifiability. You seem to be fighting those standards, and that is a losing fight here, because you will always be outnumbered by the vast majority of Wikipedians who are here because we believe in those standards. Do you see anyone here who is agreeing with you in your arguments? Does that tell you something about how your conduct is viewed by the community? You can change that by changing your conduct here to conform to the community's standards. Or, you may find that you are happier and get along better at other wikis that do not have Wikipedia's relatively rigorous standards, such as the other wikis you say you have experience with. Or, you can continue to butt heads here, but that cannot be very satisfying for you, and is not productive. Finell (Talk) 08:24, 31 May 2008 (UTC)

If you what to know about the hostility I'm talking about, re read what you just wrote. You just claimed I fight wikipedia's standarts (which as long as article writign go, I love and follow since I alone provided most of the verifiability, invited Dicklyon to contribute and go by his recomendations) invited me to leave, claimed my stuff doesn't stay (when it does and far beyond my satisfaction and have becomed two great articles and one category), claimed or insinuated I don't have read stuff (btw, reading the elements it's moot to contribute to the golden ratio article, and I hardly believe you did, infering from the questions you make, but I'll take your word (please do not reply about this)). Don't talk about anybodys actions, only about the content... as I was before your last coment, which I find incredibly ofensive.

Don't EVER reply about our *actions* (it tempts the other to reply as I am, which I hate to), just move on and talk about content. Don't forget, we are only obligated to provide evidence *in the article* about what's *in the article*, just as I have. As far as I can say here, in the talk page, the golden section came out of my butt as per written in the treaty of my behind, book 3, page 0, line beween lines... and if it's true, it's only as a favor that I give away that information. you can only say thanks. do understand my incredibly rethorical and analogical point? I don't have to explain myself to you, only to the readers of the article, to whom I have.

Please, don't reply. I'm sure you meant well, but I don't care for an answer. Especially about my above comment. Move on. If you have a question, focus on content, and in your case, I'll only answer about what I wrote or edit on the article if I mind.--20-dude (talk) 03:27, 1 June 2008 (UTC)

Moving on to stuff that actually matters
1. Where does it say Hambidge coined any term. Stating he did, just because the researcher (not me in this case), can't track older sources is wrong. It can only be said if a. he states so or b. somebody states he did and publish so in a reliable source (and not as "Hambidge's dynamic rectangles" but as "Hambidge coined the term")

2. For the sake of Dicklyon's point, this link doesn't work. It takes me to a page about a non available book. I hope that's a book that features Euclid's book as content and then talks about it, because if not, the entire link is moot to me (I think we do not have to provide sources in a talk page, but if you want to prove a point, you have to go even further than te verifiability of the article).


 * It works for me. Maybe a google account is needed?  Anyway, the ref is Elements of Geometry, By Euclid, John Playfair (1846 New York edition) first page of book VI. Dicklyon (talk) 05:03, 1 June 2008 (UTC)

3. Euclid never assigned a numeric value to phi, the idea is laughable, he didn't have decimal points. I did so to illustrate which part would be extreme or mean given numeric values to the golden section (or starting with the mean ratio and then going on to produce the extreme and the GS). Although not my fault, I'm sorry if you got me wrong. If you did get me wrong, it means you’re probably paying attention to what I'm saying but not to what I'm not, which is always important in a conversation if you want to be ahead of it.


 * Can you provide definitions for "extreme" and for "mean" so I can know what they mean to you?

--20-dude (talk) 03:53, 1 June 2008 (UTC) 4. When did the term harmonic rectangle was taken of and why... I hate when a term is taken of just because of the personal knowledge of the guy that erased it. Did he really thought he somehow know more than Ghyka or what?--20-dude (talk) 04:52, 1 June 2008 (UTC)


 * Not sure, but generally it is acceptable to remove anything that's unsourced. Put it back with a source.  If it was removed impropertly, link the diff so we can see what you're talking about. Dicklyon (talk) 05:03, 1 June 2008 (UTC)


 * For example, in this diff I removed the stuff about "dynamic rectangles" because I couldn't find a source for it. I've since purchased a copy of Ghyka, and also found it in Hambidge 1920, so I've put it back, with citations, and explained it.  Before, not only was it unsourced, but also content free (uninformative as to meaning). Dicklyon (talk) 05:07, 1 June 2008 (UTC)

Yes, I also have a Ghyka from my University library. Hambidge is harder to find. However, nobody cares abou what you don't know (if you get what I mean), you can't go make Hambidge responsible for the coining just because of you (I'm talking generically here) reached researching possibilities. If you don't know who coined it you don't have to make it up. As I said, you have to have a source indicating Hambidge invented the term, other wise why bother, someone did, it'be nice to know, but the article doesn't *have* to feature the fact if it is not clear...

I've put it back, with citations, and explained it. That was a huge mistake on your part, man, don't ever do it again. Too much depends on you for your edits and as I said, Wikipedia doesn't care about your personal knowledge!! (if you get what I mean). I put the sources since the begining... and are the same ones that remain. I have never lied. Much less in such un-ethical way (as it would implied). If I´m telling you the source, keep it that way up until you find out I'm wrong (which you will never do, because I never lie with sources or make up info).

Put it in pespective, I did kinda the same to some of your sources (because I read them and they didn't talk about Egyptian knowledge of golden ratio at all) and you didn't acept my edit, even though I KNOW those sources does not address the issue as a matter of fact!!--20-dude (talk) 05:59, 1 June 2008 (UTC)


 * Personal knowledge is irrelevant. All that matters is that content be verifiable in cited reliable sources.  Stop trying to personalize it.  And I have linked Hambidge 1920 to the full copy on google book search, so you should be able to read it there; I also have a hard copy; let me know if have trouble and I can loan it to you for a while. Dicklyon (talk) 06:04, 1 June 2008 (UTC)


 * Ok, ok. So, does he say he is making up the term or not? The version I read misses some pages, so I'm leaving it up to you. I'm just glad we're on the same page on personal knowledge.--20-dude (talk) 06:34, 1 June 2008 (UTC)


 * He doesn't say. But it sounds made up.  See next section for comments on that. Dicklyon (talk) 06:45, 1 June 2008 (UTC)

Who calls what what
The wording "observes some of the root rectangles are a subset of what is called dynamic rectangles" suggests that some unnamed community already had the concept of "dynamic rectangles" before Hambidge came up with root rectangles. The sources seem to contradict this; it's clear from Ghyka that Hambidge called them dynamic rectangles, so we can say that much, but not more. OK?

As far as I can find, Hambidge barely mentions dynamic rectangles in his 1920 and 1926 books; I can't find support for including root rectangles in them, since he doesn't define them. Ghyka's interpretation says he does, but he doesn't cite the source so we can find a direct Hambidge source. So I just cite Ghyka for the above. Dicklyon (talk) 06:37, 1 June 2008 (UTC)


 * Nope, I choosed the wording "observes some of the root rectangles are a subset of what is called dynamic rectangles" because it can be also infered as "what is called dynamic rectangles [in his book]" I tried to be ambiguos on purpuse.Perhaps if we try: "In the book XX, Hambidge observes some of the root rectangles are a subset of what denominated dynamic rectangles" so that it works whether he made it up or not.


 * Still, "is called dynamic rectangles" is true and can never be false (even if Ghyka made it all up), while "he called dynamic rectangles" is just probbably try and can be false.


 * I think we can rely on Ghyka, who says that Hambidge categorized the rectangles into "static" and "dynamic". We know Hambidge used the phrase, and we have Ghyka's explanation of what he used it for, which suggests an original taxonomy, and does not suggest that anyone else had ever used the terms similarly.  So let's stick as close as we can to what is supportable by Ghyka, unless you find other sources that bear on this.  The only phrase (subject to OCR failure) in Hambidge 1920 is "The Euclidean diagram of the 18th proposition is peculiarly interesting in the light of dynamic symmetry because it suggests what may have been the Greek method of constructing the dynamic rectangles in a square. [paragraph break] The writer's method of constructing a root-5 rectangle in a square is shown in Fig. 32."  He refers to "the whirling square rectangle" the same way; I don't think the definite article in these is intended to suggest that these terms are taken as known; it's just how he writes. Dicklyon (talk) 07:35, 1 June 2008 (UTC)


 * Besides, if he noticed the Greek, Roman, Freemasons (meaning Gothic architects) and Egyptians used to choose among all the dynamic rectangles, it means that back then it was a group of shapes known to those cultures. Even if not with the exact name of "dynamic rectangles". I don't think neidther Matila nor Jay came up with the whole dynamic vs. static terms. And that's why you have not been able to prove it. You underestimate personal ego, when somebody makes up a term he makes a big deal out of it if not he either sources (like such academic authors would) or talk about the terms as if they were common vocabulary as I perceived in the pages I was able to read.


 * I have not attempted to prove anything. But that he referred to them as dynamic rectangles is supportable, while implying the prior existence of that concept is not (unless you present a source). Dicklyon (talk) 07:35, 1 June 2008 (UTC)


 * If you have the possibility, and I'm assuming you live in a more resourceful city, get a copy of Frederik Macody Lund's. the only available copy in my city belonged to the collection of Chanfon Olmos, which was donated to the State University after he died... but it's in French. (an the only person I know that know french is an ex, hehe). As far as I can tell it's an impressive work.--20-dude (talk) 07:08, 1 June 2008 (UTC)


 * Which Lund book do you mean? Ad Quadratum?  A friend in Oslo sent me the English copy (pages shot with his digital camera), but I haven't had time to study it much yet.  Email me if you want a URL where you can download it (about 450 MB).   Dicklyon (talk) 07:35, 1 June 2008 (UTC)


 * Yes, ad quadratum. And wow, you have been doing quite some homework... and wow, that's what I call good contacts!! I'm impressed.

I'll be scanning all of Manuel Amabilis drawings of the regulator lines of the Mayan arcs using Lund's method soon. I'll give you a copy too, as well of one of my thesis once I'm done (don't worry I'm aware that's not WP material), for what's that worth, it features the contemporary view and related work of most academic and profesional authorities in the state and then some Mexican figures. So to avoid future speculation, and keep track of how is it being used (or not) nowdays, at least in the places under my reach and "jurisdiction", hehehe. --20-dude (talk) 23:42, 1 June 2008 (UTC)

A gift:

Definition 3. A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
 * - Euclid in the Elements, book six, Definition 3.

You're welcomed. --20-dude (talk) 07:29, 1 June 2008 (UTC)


 * Right, that's what's on the page I linked above. It's not working for you?  Dicklyon (talk) 07:35, 1 June 2008 (UTC)


 * Hahahaha. No, I told you it's not. But I'm under the impression I told you, you put a better one but I missed it. Anyway, it's good we can pass that page. The other important thing about Euclid, as it is for Plato, is their notion of the nature of the dodecaedre's relation with the "extreme and mean ratio", as they used to call it.--20-dude (talk) 23:23, 1 June 2008 (UTC)

You said:

Yes, I do agree, we cannot imply it is older than him if we don't have sources, but we can't not make it sound as if wikipedia knew as a matter of fact that he is the first either... as it is, because of the use of "he calls". Do you get me?--20-dude (talk) 23:42, 1 June 2008 (UTC)


 * Saying "he calls" isn't a claim that he was the first to call it that. Though it does suggest that possibility, which is part of the intent, since we don't know of any older uses. Dicklyon (talk) 23:47, 1 June 2008 (UTC)

The other reason is that it also sounds pretty much like we are discrediting him as a researcher. Like "he [alone] calls". I'm going to change it to "what has been called", that way we are not saying who or when, but given that in that line we are talking abou Hambidges work, it can be interpteted as "What has been called in Hambidges work".--20-dude (talk) 04:42, 3 June 2008 (UTC)


 * Dude: Dynamic symmetry is Hambidge's theory, and remains Hambidge's theory. Ghyka did not expanded the theory, he just reported what Hambidge invented. This is not like the theory (or theories) of relativity, which has precedents dating back to Galileo and which 100s of physicists and mathematicians continued to develop for decades after Einstein's work (and a few still are). Why would you deny Hambidge credit for all of it, including the terminology he created to describe it? By the way, Hambidge's retrospective analysis of classical architecture and artifacts as fitting into dynamic rectangles is his interpretation, which may be right or wrong. When you take into account vagaries of measurement and the choices involved in precisely where one draws the rectangle in relation to the object, an awful lot of things can be fit into some dynamic rectangle or other. Just like doing the same with golden rectangles, right? Except a golden rectangle has only one aspect ratio, while root rectangles give the "researcher" a lot more to choose from. Again, I am not saying that this makes the analysis or the aesthetic judgment wrong, only that it can never stand on as firm a foundation as, say, the atomic weight of helium. Finell (Talk) 02:06, 4 June 2008 (UTC)

I've always though"he calls" as weasel words, put I was not able of understanding why, but this is the reason [weasel words are the] general principle of introducing some proposition without attributing it to any concrete source, which is kinda whtat the aforementioned words do. Even though it is not technically a weasel sentence, it comes off in the same spirit, so let's not get married to those words. There are infinite ways to express the same without implying Hambidge invented anything, why to pick that particlular one that suck so hard. --20-dude (talk) 04:59, 3 June 2008 (UTC)


 * Weasel words is when you don't say who; like "many call..." or "experts call..." would be weasel words. Here he has a clear referent, and it's sourced (or if it's not, let's put the citation).  Nobody is saying he invented it, but it leaves that possibility open, since we don't know anything else about the concept; all we know about "dynamic rectangles" in relation to "root rectangles" is that Hambidge called the rectangle with root proportions root rectangles, and he included them in what he called dynamic rectangles.  If you have another way to express that, then up with it. Dicklyon (talk) 06:54, 3 June 2008 (UTC)


 * Yes, I did said that they're not weasel words, they only have certain air. Where does the term comes from anyway? is it from wikipedia? I think they should change it, I felt very uncomfortable, because even though I'm talking about the content, the usage of the word "weasel" looks adderessed to the person that placed them.


 * See Weasel word.


 * On another matter, I really need a good source explicitly ditching or criticizing phi in the pyramids. I think you once showed me a link to a sort of academic page with an article from a guy that didn't think was present in anything at all. I have been neglecting a lot that kind of necessary criticism (that creates impartiality) in my thesis... can you remember? Thanks beforehand--20-dude (talk) 10:23, 3 June 2008 (UTC)


 * I think the Martin Gardner book cited at pyramidology was good on that. The article you recall is probably the Keith Devlin cite at "list of". Dicklyon (talk) 15:29, 3 June 2008 (UTC)


 * Actually, Livio, or this book may be better. Dicklyon (talk) 02:08, 4 June 2008 (UTC)

Reacting to 20-dude's latest assertion that "is called" is better sourced, I checked the cited source again, and found that in his table of contents, Ghyka refers to "The dynamic rectangles of Hambidge". Seems clear that he is attributing the concept and terminology to Hambidge. I also looked for other sources, and did not notice what I'd called any consistently agreed usage or definition; some say that root rectangles is another term for dynamic rectangles, effectively leaving out the "golden" variants. It would be interesting is someone wanted to do some actual research to try to trace the usages and meanings of these terms, and see if there's an actual definition or two that we could use. Dicklyon (talk) 15:50, 8 June 2008 (UTC)

Move article to "Dynamic rectangle"?
Given the recent expansion of scope by addition of root-phi rectangles, maybe we should move the whole thing and refocus it on that slightly broader scope. Or merge the whole thing into Jay Hambidge would be another alternative. Ideas? Dicklyon (talk) 00:10, 4 June 2008 (UTC)


 * I don't know. Dynamic rectangles do seem to be the main focus of this article, and that was so even before root-φ was added. Meanwhile, the article on Hambidge's main dynamic symmetry book was recently merged into Jay Hambidge. That is unfortunate, because the article on the book could have been expanded (although I am not volunteering), while his biography article (which is not limited to dynamic symmetry) could also be expanded. So I would prefer not to stick this into Jay Hambidge too. Should there be an article entitled Dynamic symmetry (it is a redirect now), since Hambidge's theory spans 2 books (at least), which would also borrow from the dynamic symmetry section Jay Hambidge; it would still be a stub, because a decent treatment of the theory would have more that all the present material combined. Finell (Talk) 01:32, 4 June 2008 (UTC)


 * So maybe merge the rectangles into dynamic symmetry when we're more ready? What about for now?  Keep root, or move to dynamic? Dude, what's your thoughts on this? Dicklyon (talk) 02:10, 4 June 2008 (UTC)

Dynamic rectangle inconsistency
The article says that root rectangles are part of the broader group of dynamic rectangles. It also says that dynamic rectangles have irrational (in the mathematical sense) proportions. But a lot of root rectangles have rational proportions. Hambidge himself illustrates a root-4 rectangle, which is rational. So is root-1, a square. Something is not quite right here. Finell (Talk) 02:13, 4 June 2008 (UTC)


 * Yeah, you might have noticed that inconsistency in my own edits. When I found the definition with irrational, I said "some" of the root rectangles are dynamic.  Later I found Hambidge, or Ghyka, in some note saying that these could be used as either static or dynamic.  It's not exactly a taxonomy.  Personally, I take it all to be bullshit; I'm doing my best to represent the claptrap that these guys made up, since it appears to be notable from all the references to it, but it sure doesn't make any sense.  Just more pyramidology, really. Dicklyon (talk) 03:57, 4 June 2008 (UTC)


 * I am slightly, but only slightly, more tolerant. I am willing to accept that artists and designers do know something about aesthetics, including proportion. When they attempt to understand and to quantify their learned or instinctual sense of aesthetic proportion, I consider that to be more desirable than simply treating it as purely subjective. Conversely, most artists (I know many of them) accept that scientists really do have some understanding how things work, which might otherwise seem like magic to them. By the way, every artist I have spoken with learned about what they usually call the golden mean in their formal training, and considers it to be one design principle among many others that informs their compositions. Finell (Talk) 16:00, 4 June 2008 (UTC)


 * Well, I'm not really intolerant, just expressing my assessment of the value of pseudo-scientific encodings of aesthetics. The math is fun, but there's little or no evidence of any ACTUAL relationship to aesthetics.  It's just like numerology and pyramidology. Dicklyon (talk) 18:46, 4 June 2008 (UTC)

This is a very smart observation! (the part about the inconsistency in Hambidge and Ghyka's theory) However, ho did you expect to know more about aesthetics than artists??!!! The statement is a contradiction. Then again, you're forgeting that the men behing phi are Pythagora, Euclid and Fibonacci, pilars of European mathematics, can it really get more scientific than that? And underestimating artist is poor judgement, after all, math and art are related skills.

And yes, there are several types of proportion, Golden, Harmonic, Fractal, Musical (the ones used by Andrea Palatio), and perhaps others I ignor. (I'm coining the term Fibonaccean in my thesis). For instance, information that includes stuff I can't cite: The trion (2/3 root-3) is related to the trinagle (the longer side is the conjugate of the proportion of the height of a trinagle), 1:1 or root-1 is the square (tetragon), phi to the pentagon, the decagon and every polygon multiple of 5 and root-3 is related to an hexagon. Root-5 has that weird connection with phi. I ignore if there is a realtion with the heptagon (root-2??), octagon and further non multiple of 5 poligons, but I guess so.

However, time spend on our personal perception is time wasted, nobody cares (or should care). The real contribution here is Finell's discovery. I do remember Ghyka's statement abouth root-1 and 2, but I never realized that is might be somewhat contradictory.

Perhaps the key character here is Mark Barr, has any of you read his work (I'm not supposed to get there before studing Kepler and Zeising, but I guess I can twist my schedule a little)

By the way the spiral property of root-phi and root-2 (and phi and the fiboancci sequience) is not a property of the rest of the root rectangles.--20-dude (talk) 09:14, 8 June 2008 (UTC)

To add another perspective: Dynamic Rectangles, also called Root Rectangles, are the series of rectangles which grow from the diagonal of a square. -Michael S. Schneider. Constructing The Universe Activity Books. Volume 4: Dynamic Rectangles Between that an Hambidge's statement we can get it right. Dynamic rectangles are all built with diagonals (not *any* irrational number), root rectangles are are the subset that are built with vertex to vertex dyagonals. The only problem is how to write it in a logical way for the article (the way I stated it is right, but I'm clearly twisting my sources' words to explain my point).--20-dude (talk) 10:21, 8 June 2008 (UTC)

And Dicklyon, I'm challenging your comment because I'll personally benefit from your justification. But I believe the only bullshiter here is... well... youuu-know the answer (please, I beg, prove me wrong with a spectacular smack-down answer!). I'll elaborate. You say pseudo-scientist, but I have only quoted academic sources and the fathers of math... can it really get more scientific than that? Then again, none of your sources reject the theories of Stonehenge, da Vinci or the piramids. They provide alternative thories that show as may flaws and are not necesarely incompatible. Actually, I've been letting you get away with original research there, because you're linking theories that the authors do not link. Which are your your sources for the "negative" (which don't get me wrong, I think we should have) statements??--20-dude (talk) 09:37, 8 June 2008 (UTC)


 * I have no problems with the math; that's the good stuff. It's the non-specific and impossible-to-evaluate (or even pin down) stuff about aesthetics that is largely BS.  I'll grant you that you and these authors know more about aesthetics than I do, but when you try to make it mathematical, that's where it becomes BS.  Pythagoras, Euclid, and Fibonacci, didn't do there; they stuck to the meaningful stuff. Dicklyon (talk) 15:10, 8 June 2008 (UTC)


 * Dear Dicklyon: Some human aesthetic choices already have a well established foundation in science and math. Harmony in music (which was well understood in classical Greece and was considered a sub-discipline within mathematics) and color theory (which is always taught in formal art instruction) are two examples. Some aesthetic choices involved in the selection of mates are well explained by the theory of natural selection (the choice of features that imply traits that will promote the survival of offspring). The normal aesthetic preference of symmetry over asymmetry was explained several years ago by a study of female birds' choices of mates: the females chose mates with symmetrical bodies. The explanation offered was that asymmetry in males resulted from losing a fight (and a body part in the process—better to mate with the winner) or a genetic defect. I expect that other aesthetic choices that are not purely personal (and, eventually, those too) will yield to mathematical and scientific analysis and explanation. (It is also my opinion that the case for free will is greatly overstated, but that is getting way too far afield to discuss here.)


 * Historically, science has often advanced by the proposal of theories and classification schemes that had no known physical basis, but for which physical bases were later discovered. The periodic table and chemistry based on valences, the classification of organisms, early genetic theory, the theory of natural selection, and Kepler's laws of planetary motion are a few examples. Therefore, in my opinion, it is worthwhile for scholars to propose hypotheses of the bases of aesthetic choices, and it is worthwhile to test these hypotheses scientifically. Some of methodologies for that testing only became avaiable in recent years. Finell (Talk) 19:41, 8 June 2008 (UTC)


 * Finell, all good points. I certainly accept and work with things like musical harmony, which have relatively simple physical, physiological, and psychophysical correlates and explanations.  The stuff about fitting a whole bunch of rectangles to Greek vases and ancient monuments is, in my opinion, just numerology.  Sometimes it's not obvious what category to put something in, so I often hold off judgement.  In this case, however, I've studied it long enough to have formed a solid opinion; doesn't mean I can't change it if new info warrants it. Dicklyon (talk) 00:42, 9 June 2008 (UTC)


 * Dear Dude: Unfortunately, Mark Barr is a dead end. He never published a book. It does not appear that he ever published a math paper (a couple of Wikimathematicians here have looked in indexes of math papers that cover Barr's era). Cook's book says that Barr taught Cook the math behind the golden ratio and, most famously, suggested to Cook the use of phi (for Phidias) as its symbol. Ghyka's mention of Barr is via Cook (i.e., secondary).


 * I do not believe that there is any "inconsistency in Hambidge and Ghyka's theory" because, according to my recollection of Ghyka's book (I read it a few years ago), Ghyka does not have or claim a theory. Ghyka was a dilettante of Romanian royal birth who studied and wrote on a wide variety of subjects that interested him. As best I recall, everything in this book by Ghyka is derivative of Cook, Hambidge, and many others. So if Ghyka says something that in fact is inconsistent with Hambidge, it is just Ghyka's mistake.


 * Dynamic symmetry is exclusively a theory (although not in the scientific sense) that Hambidge put forward; ditto dynamic rectangles, which are exclusively Hambidge's classification as part of his dynamic symmetry theory. Neither dynamic symmetry nor dynamic rectangle is defined in the few dictionaries that I consulted, which included the OED. So neither of these concepts by Hambidge is sufficiently notable to warrant an article in Wikipedia. Finell (Talk) 18:57, 8 June 2008 (UTC)


 * Sorry if I misled you, I'm not asking you if there was an inconsistensy, because I know that, to whatever level it has, there is one. As Dicklyon put it:I found Hambidge, or Ghyka, in some note saying that these could be used as either static or dynamic, which is in Ghyka's book. You should read it "again", hahah, "if so", you readed it too long ago, "recolletions" are moot to the article (and also incredibly inconsistent with what you askes at the top of this talk page, in which you were completely unfamiliar with all the terminology, but don't worry nobody is expecting anybody to be human libraries, we are researchers of researchers).
 * The inconsistensies are there because root-1 and 4 are not dynamic according to Ghika's own definition (if I had a source, I'd rather define the dynamism not with irrationality but with the use of diagonals from diverse points). I'm also not asking you anything about Dynamic symetry, our your opinion of their permanence on wikipedia. I'm sorry to remind you, but you (as the rest of us) lack that sort of authority.


 * Your research about Barr was very useful, though. Congratulations. However, you missed a point, if Barr did not write, it only means the next target is Cook--20-dude (talk) 00:25, 9 June 2008 (UTC)


 * Dear Dude: To whom do you refer as "the only bullshiter [sic: bullshitter] here"? Finell (Talk) 18:57, 8 June 2008 (UTC)


 * Please, don't address me as "dear", is very uncomfortable. You're making me think you're trying to pick a fight with your last comment. It's not relevant, it's self explanatory, and it's much less relevant to you.

Dicklyon: The point is. You keep repeating BS, but don't make me think you're BSing me, we're are these sources stating tha the academic sources linking phi to art are BS???. The esplicit ones, not the ones that requires the WP readers to infer your points. Where are these academic mith busters you talk about so much?? I can't find them, and I really could use thir words (both here where they are really needed and in my work)--20-dude (talk) 00:31, 9 June 2008 (UTC)


 * I'm not sure what sources you are referring to as academic. And my opinion about what is BS really has no relevance to anything; sorry I brought it up. Dicklyon (talk) 00:42, 9 June 2008 (UTC)

Yes you are, you talk about it all the time, you taught me how to recognize them. Relatively fine imprints, college professors, backed by Universities, quoted in trascendental works etc. What are your sources saying the Pyraminds, Stonehenge and the rest of the da Vinci work has nothing to do with Golden proportion?? I need to know.


 * Have you read Livio? It's probably the most complete contemporary analysis of the use and abuse of golden ratio.  But there are many more.  Of course, one can't "prove" much about these old things; one can, however, point out the lack of rigor and logic behind attempts to show such a connection. Dicklyon (talk) 13:46, 9 June 2008 (UTC)

Also: Is doesn't not necesarely implies a community. It can be is, as in is called in Hambidges book, lifetime work, teachings, etc. Or it can be is and in the community of the only relevant researchers like Ghyka, Hambidge, Elam, Amabilis, Chanfon... that that's only because those are the only ones I have researched in a fine maner, because there are many other and at least docens of internet pages using that terminology (the internet part alone at least renders it as pop cult phenomena). So it's not becuse of a community, and if so, your point is also crushed by the existense of an academic community. --20-dude (talk) 00:48, 9 June 2008 (UTC)

According to Ghyka, it's the 'dyanamic rectangles of Hambidge'; That makes it right to say what "he calls". But your following statement, nobody else called them that when he including root rectangles in the them, confuses me. I think I don't understand it at all, but if you're saying what I think, I have no doubt it is a very common term anong scholars and even the internet amateurs bunch. I'm also sure the concept is almost acient, because such category of rectangles is a frequent theme on Gothic churches and greek architecture (that's why hambidge talk about them in the first place, as you can see in ghyka's book), but the part I have never had the tools to deny is that there is no use of the word "dynamic" before hambidge. With Ghika's statement, it also becomes accurate to say what "he" calls.--20-dude (talk) 11:58, 9 June 2008 (UTC)


 * I should have been more clear; I meant as far as we know nobody else used the term before him, nor contemporaneously, other than his followers. Dicklyon (talk) 13:39, 9 June 2008 (UTC)

Cook relation to Hambidge, Zeising, and golden ratio
Dude, I found you a good book source on this: Proportion: science, philosophy, architecture, by Richard Padovan. Very quotable re Hambidge and architecture. Dicklyon (talk) 04:19, 9 June 2008 (UTC)

Here's another good one that connects a bunch of stuff that you're into. Dicklyon (talk) 04:31, 9 June 2008 (UTC)

Impressive links. I have never stepped into that material before.

You once gave me a link to some scholar article of a guy who was ditching several key golden ratio "sightings"... Do you remember it? I'm also looking for that sort of stuff.--20-dude (talk) 11:46, 9 June 2008 (UTC)


 * Don't recall which one that would be; maybe the one quoted on your "list of" page? Or the Livio book?  Dicklyon (talk) 13:42, 9 June 2008 (UTC)


 * Where does livio stand? I have the impression he is not such a fan of "sightings"?--20-dude (talk) 19:55, 9 June 2008 (UTC)


 * Exactly. Isn't that what you wanted? Dicklyon (talk) 01:29, 10 June 2008 (UTC)


 * Yes that's what I want. Livio is quite eu-φ-ric. Fortunately, as your impressive link shows, eight years after he proposes the use of phi, Cook didn't end ub being too much of a Hambidge and dedicated an entire book to ditch the concept if its presence in Architecture. I'm surprised he went against Hambitge, since Zeising and Fetchner have much more soft spots (although Fetchner's wouldn't be obvious untli the late XX century).--20-dude (talk) 06:28, 10 June 2008 (UTC)