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WikiProject Physics (Rated C-class, High-importance)
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WikiProject Mathematics (Rated C-class, High-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
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One of the 500 most frequently viewed mathematics articles.
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Miscellaneous Talk Items[edit]

I couldn't find any examples of Persian Pottery other than an image from the Met; I created a degraded version but I will follow up with an eMail to the curator of that department to obtain copyrgight clearance or an opinion on fair use. Here's what I sent:
I volunteered my efforts on a section of the WikiPedia about symmetry in art (see: <>); for one of the sections (Pottery) I would like to use an image from your Islamic collection. I resized and degraded its quality to better fit the fast-loading requirements of the WikiPedia, and I linked to the Met as a reference. As the WikiPedia is for educational purposes, I thought this would both benefit the Met and the visitors at this online encyclopedia. Please let me know if you have any concerns.

-- Jeff batty boy

I don't think you can say "Symmetry is a characteristic of geometrical shapes, equations and other objects;" and then go on to say "In reality however, ... composed of matter ... Symmetry therefore, is a matter of similarity instead of sameness." Unless with "and other objects", you refer to material bodies. But that wouldn't be correct, because the large material bodies to which the article refers have inherently irregular, asymmetric shapes.

certainly, if you rotate a circle around its center, you get the same circle. Enrique

Axis confusion[edit]

The article states "this is sometimes called vertical symmetry and sometimes called horizontal symmetry". Symmetry is identified by its axis, vertical or horizontal. The current phrasing does nothing to clarify this. Aknicholas (talk) 18:48, 11 December 2011 (UTC)


The Sydney Opera House is an example of symmetry in architecture?? I defy anyone to find a less symmetrical building! --dmmaus 06:36, 29 Jun 2004 (UTC)


-- 00:01, 25 October 2006 (UTC)

"In formal terms, we say that an object is symmetric with respect to a given mathematical operation, if, when applied to the object, this operation does not change the object or its appearance. Two objects are symmetric to each other with respect to a given group of operations if one is obtained from the other by some of the operations"

This paragraph should be altered to make the change.

"In formal terms, we say that an object is symmetric with respect to the set as long as this is the abstract example symmetry. A class unassigned as object to the set then relates abstractly. An element of Aristotle's category applied. In mathematical terms the formal, group then caususally operates. Symmetry is held operation's cause to exist."

So in third relative set I have formulated the correct version ammenable to Aristotle's category where applied transform of category appears the symmetric form.

A cause to operate is the relation applied. Making the abstract subject appear to cause. So the operation is held to symmetrically exist with relation to all element of the appl..

And I need real philosopher help here. I get lost, but it is exquisitly deep as topic.


"[edit] Symmetry in logic A dyadic relation R is symmetric if and only if, whenever it's true that Rab, it's true that Rba. Thus, “is the same age as” is symmetrical, for if Paul is the same age as Mary, then Mary is the same age as Paul.

Symmetric binary logical connectives are "and" (∧, , or &), "or" (∨), "biconditional" (iff) (↔), NAND ("not-and"), XOR ("not-biconditional"), and NOR ("not-or")."

The logic above must be altered in this fashion.

"Any relation as "is the same age as" appears the symmetry of any function of dyadic term."

This is the nontrivial change necessary to your wiki!!! Please consider it seriously.

It solves the True Scotsman fallacy. -- 00:11, 25 October 2006 (UTC)

This whole page is too jumbled[edit]

There should be a disambig on symmetry, this page is a mess of all topics lumped into one. I added to the symmetry (physical attractiveness), which took me some amount of searching to find; and they all need to go on a disambig page. --Sadi Carnot 05:17, 14 February 2007 (UTC)

I second that. The article is almost 50 kB already, it should be broken down into smaller pages organized by likely interest. Also does symmetry (mathematics) need its own article or can it simply redirect to group (mathematics)? --Vaughan Pratt 13:51, 20 August 2007 (UTC)

OR--"creatures peering into mirrors"[edit]

Symmetries can become so familiar that we fail to recognize them. A mirror, for example, performs a conceptually unsettling form of optical surgery in which the left and right sides of any creature peering into it appear switched. Such a drastic change would surely be disturbing to any creature whose left and right sides are distinct, yet the bilateral symmetry of humans is so well developed that they often fail to notice such changes.

I'm moved the text above from the article until its attributed to a source. It too suspiciously like OR. Brentt 22:25, 22 February 2007 (UTC)

I'm the author... and, um... what is "OR?"[edit]

You've got me thoroughly baffled. What is "OR"? I am clearly listed as the author in the history, and I assure you without equivocation that I am -- and not just the text, the entire little thought experiment behind it. Please look more carefully at the full range of entries that I added to that particular article for other examples of my writing style.

As for the unexpected "philosophical" question, my only intent was to try to make a point about how deeply ingrained the perception of bilateral symmetry is. My goal was to create a short thought experiment to help readers recognize how deeply both the physical expression and visual perception of bilateral symmetry are, not... well, whatever it is you mean, I honestly can't quite figure it out.

Terry Bollinger 02:30, 21 March 2007 (UTC)

"OR" is original research, and according to NOR it's not allowed. Unfortunately, you just confirmed that Brentt was correct in his reason for removing that paragraph, and as such, it will probably remain out. However, if you can find an outside source that agrees with you, cite it with the paragraph and feel free to add it back in. -Bbik 02:43, 21 March 2007 (UTC)

True Confessions // Captain Kirk to the rescue?[edit]

Ah, thanks! I'm still not up on some of the lingo.

This is absolutely delightful, however... So, simply constructing a thought experiment to help convey as straightforward and directly visible a concept as bilateral symmetry classifies as "research", as opposed to, say, "trying to convey a concept to a wider audience?" I'm sorry, every time I think about that one, I just start chuckling. Cool!

Having said that and gleefully tossed in the towel of my own inadvertent True Confession, I nonetheless cannot resist: Here, friends, is a truly apt, extremely well documented, thirty-eight years old, very widely known, fully on-line reference that exactly conveys the type of horror that asymmetrical beings might encounter when looking in a mirror. In short... The Reference!:

Star Trek TOS, Episode 3x15: Let That Be Your Last Battlefield

Cheers & chuckles, Terry Bollinger 03:20, 21 March 2007 (UTC)

Such a drastic change would surely be disturbing to any creature whose left and right sides are distinct...
I would imagine it's that specific section that set off the alarm bells, rather than the general attempt at clarifying the concept. It's kind of hard to phrase something about how other creatures think without making it either unencyclopedic or sound like proven fact. And if it's stated as fact, which is what that line leans towards, it needs to be either unarguably obvious (2+2=4 type of obvious), or sourced. And when the topic is other creatures that we can't communicate with well, if at all (In fact, do real creatures like that exist?), it's a pretty clear-cut place to need proof of some sort of study which came to that conclusion. Whether rephrasing and a Star Trek episode would work or not... well, it'd certainly be entertaining!
It's all more than a little silly sometimes, but I'd imagine it prevents a lot of people from adding their two cents about everything, even when they have no clue whatsoever what they're saying, much less how it will be read.
Have fun! -Bbik 04:00, 21 March 2007 (UTC)

I concur, no Asymmetrical Aliens // A plea to retain some math content[edit]

... and just to be clear, lest anyone assume otherwise: I too think my bilateral aliens paragraph should not be in this article, especially in the intro, for pretty much the reasons Bbik just described. The example is just too much of a mind bend, especially when located smack in the intro, and invokes a tone of imaginativeness that to me just doesn't fit this kind of article. I felt twinges when I put it in there to begin with, for just those reasons. This needs to be a true encyclopedic-style article, one that covers a broad range of topics and which consistently uses a tone that lets the reader know she is reading a serious work that contains solid, reliable content. (Attentive readers may have noticed that I have... shall we say, far fewer reservations?... regarding the use of Informal Tone in the discussion sections... 8^)

I do like the way this article is shaping up, and that more folks are starting to pay attention to it. When I first bumped into it, it struck me as a catch-all bin that people had given up on. This kind of refocusing of editing rules on it is a good sign; it shows that folks are re-engaging what seems to me to be a broad, interesting, and deceptively deep topic.

Mathematicians: Your call, but I do hope you don't completely pull the math section out of this one. This is such a perfect area to show how math really does influence and quantify the everyday. Too many of the math articles already seem inclined to place implicit sign up front that says "Ye who cross this line and are not mathematically trained, abandon all hope!" Perhaps more example-oriented versions of the same topics could remain here, with references to the more precise notations of the symmetry in math article? The helical symmetry section might be somewhat of an example, though since I wrote that it would be better for others to judge, not me.

Cheers, Terry Bollinger 14:48, 21 March 2007 (UTC)

Since you mentioned it... is there even a link to symmetry in mathematics in this article? I see all the links to the main pages for each of the sections, but not a general math one. Though, that in itself is confusing -- If math is a subsection of general symmetry, and it has a main page, then having sub-subsections which also have their own main pages (which are linked from here, rather than math) seems to defeat the purpose of even having a main math page in the first place, whether it's currently linked from here or not. In fact, it seems this "general" article has more about math than the actual math article.
I guess this isn't actually very helpful about what math should or shouldn't stay in, but it certainly seems a bit backwards from a logistical/organizational point of view. Maybe straightening all that out will result in a more obvious answer for what should stay here?
-Bbik 02:00, 22 March 2007 (UTC)

Religious symbols?[edit]

Though I can see symmetry in many of the religious symbols shown, I can't see any in the Hindu, Islamic or Jainist symbols, even if the moon and star would demonstrate symmetry independly of each other... should they be removed from the picture?

I agree and I'd dare to say that most of the other ones bear symmetry just because it gives them not purpose, but just aesthetic balance. For example the (symmetric) shape of the Christian Cross comes probably from the symmetry of the human body, and not because any supposed tendency of people to see purpose in symmetry... Without proper references I think this section makes little sense -- (talk) 07:00, 18 September 2010 (UTC)
I've now changed the image to add the yin yang and swastika, both of which are mention in the text. The islamic one does seem to have reflectional symmetry (the less common Rub el Hizb might make a good alternative).--Salix (talk): 08:59, 18 September 2010 (UTC)

A larger dedication to the concept of translational symmetry[edit]

The symmetries at the top of the page define symmetry as constancy when "we change a way of looking at it, then it is symmetric." However Feynman provides a definition of symmetry in his book six easy pieces (The Feynman Lectures on Physics) in it's chapter on vectors, symmetry in physics. The definition talks about symmetry in translation as well changes in perspective. He quotes Hermann Weyl: "a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation." He goes on to explain this holds true with translation. Should either the beginning definition or the section on physics be changed? I saw that there was a small section about translation, but I think the concept is at least equal to perspective changing. Beast of traal 23:27, 4 June 2007 (UTC)Beast of traal

Recommendation: This should be clarified in the intro (lead) of the article. Also, there is a paucity of cited references in the lead and in other critical sections of this article. This needs to be addressed, so it's also good that you have references, as they will be needed. dr.ef.tymac 14:47, 30 June 2007 (UTC)
Update: I've gone ahead and edited the intro. Inline citations have been added and the meaning of the term was expanded to cover alternate uses. Still missing is expanded treatment of "symmetry as beauty" (something from Plato or Aristotle might be appropriate here), also I did not expand translation using Feynman, although this aspect does have expanded (and hopefully clarified) treatment in the intro. dr.ef.tymac 16:03, 30 June 2007 (UTC)
Per WP policy, the lede requires citations only if the same content does not appear with appended citations later in the article. Indeed, an ideal lede might be considered to be without citations, and simply summarizing and highlighting the key elements of a richly cited body of later text. Note also that there is a special tag for factual statements in a lede that are not common knowledge, where an earlier editor has failed to provide verification for the statement later in the text.[not verified in body] See [1]. More generally, on the writing of a good lede, see: [2]. Le Prof Leprof 7272 (talk) 01:24, 29 May 2014 (UTC)

Sphere image[edit]

I can't figure out what the sphere image is about. The caption says "Sphere symmetry group o." but there is no reference to "Sphere symmetry" in the article, let alone "group o" (All your sphere are belong to us?) And what is with the triangular bit in yellow (I iz in ur sfere, paintin it yello?) Jokes aside, I was going to remove the image as too obscure (Sphere the Obscure?) but I did not want to insult the more mathematically minded here that might know exactly what it is representing. --Justanother 17:03, 3 August 2007 (UTC)

I don't think deletion of the image would be a good idea. If you would like confirmation on its relevance, please consult Wikipedia:Reference desk/Mathematics and ask for help from anyone familiar with Group theory. dr.ef.tymac 18:32, 3 August 2007 (UTC)
So what exactly is it saying about symmetry? --Justanother 19:12, 3 August 2007 (UTC)
I agree with User:Justanother, the reference is indeed obscure to anyone who isn't already intimately familiar with the concept. To answer the "what exactly" question, the group being illustrated is a finite subgroup of the continuous group of all rotations of the sphere (under composition of rotations). An object exhibits spatial symmetry of this kind whenever it can be rigidly transformed or reflected so as to produce the "same" object. The illustrated sphere subgroup is finite and discrete, the whole sphere group is infinite and continuous. By the same reasoning a square is symmetric: the set of its 90-degree rotations forms a group, and can be thought of as a subgroup of the group of rotations of a regular octagon (also finite and discrete) and of the (infinite and continuous) group of rotations of the circle. Note that discrete need not imply finite: the line of integers forms a group under translation by an integer; this group is infinite and discrete. Unlike the sphere group and (most of) its subgroups the circle group and all of its subgroups are abelian groups. --Vaughan Pratt 14:11, 20 August 2007 (UTC)

Vitruvian Man image[edit]

The caption under image stated the year 1492. I changed this to (ca. 1487) to make it consistent with the main article for Vitruvian Man. I'm assuming this is more accurate? —Preceding unsigned comment added by (talk) 12:59, 21 May 2008 (UTC)

Symmetry vs. Assymetry[edit]

The best I like about what's gone wrong with this article claiming that Symmetry is ...aesthetically-pleasing proportionality and balance and representation of symmetry in the human body and, by extension, the natural universe by Leonardo da Vinci's Vitruvian Man, yet the da Vinci's figure has purposely posed asymmetrically if anybody want's to take a second and closer look. The article needs a serious review, at least the parts dealing with aesthetics.--Termer (talk) 22:13, 9 December 2008 (UTC)

Why symmetry is an important measure of beauty and physical attractiveness[edit]

Ever wonder about this? Why are symmetrical faces seen as beautiful? I've been contributing in Wikipedia on these articles. I knew the importance of symmetry with beauty, but I had not understood why symmetrical faces are seen as being more attractive. But I think I've figured it out and I pose a tentative hypothesis here. I'm pretty sure this guess is right -- and I'm wondering -- do you agree? If you agree, has it been written about somewhere else before? Or is it new knowledge? I'm wondering about these things. Btw this article is great with all the math; good job people.-Tomwsulcer (talk) 21:10, 18 July 2011 (UTC)

scale symmetry[edit]

"Scale symmetry refers to the idea that if an object is expanded or reduced in size, the new object has the same properties as the original"

does this mean they look exactly the same (akin to reflectional and rotational symmetry in a circle-they are indistiushable from the identity.), or does it mean that that some property/ies remains the same, but other aspects are different?

if the latter, there can be objects which are identical e.g. a square, with another square half the size inside, and a square half the size of that inside it, and so on ad infinitum, as well as squares double the size outside the square ad infinitum. this is identical if scaled by 2^n, or 1/2^n, with point of origin the center of these squares. so why isn't that version of the symmetry included?

i can think of countless more examples, including a few in elliptic space that use only one, finite shape. (talk) 21:24, 20 November 2011 (UTC)

Featured picture candidate[edit]

500px|thumb|The ceiling of the 400 year old Sheikh-Lotf-Allah mosque in Isfahan, Iran This picture has been nominated as a featured picture, please voice your opinion if this picture meets Featured picture criteria for the category "Featured pictures/Places/Interiors". Discuss on the page at here. All editors are welcome to vote. Penyulap 04:40, 4 April 2012 (UTC)

Expand article to include Inversion Symmetry[edit]

I noticed that the inversion symmetry (point reflection) is briefly mentioned but not discussed at all. There should be at least a small section describing it, maybe with a link to the point reflection article. DeMk9D76 (talk) 17:03, 8 May 2012 (UTC)

Yes check.svg DoneSymmetry#Point reflection and other involutive isometries. Please, use "+" link to add a new topic next time. Incnis Mrsi (talk) 18:26, 8 May 2012 (UTC)

Antipodal symmetry[edit]

We need an article on antipodal symmetry. -- The Anome (talk) 18:32, 7 October 2013 (UTC)

Is that the same as central point symmetry? Inversion_symmetry#Inversion_with_respect_to_the_origin Tom Ruen (talk) 20:53, 7 October 2013 (UTC)
From sources [3] and [4], it looks like antipodal symmetry is the same thing as inversion symmetry through the origin. I've added a sentence to that effect in this article. I've also boldly created a redirect from antipodal symmetry to Tom's target. That redirect could be expanded into a separate article if it was found different enough from inversion symmetry through the origin, but they seem like synonyms to me. --Mark viking (talk) 21:48, 7 October 2013 (UTC)

Mathematical model for symmetry[edit]

Stopped here to add a couple of lines to the chemistry subsection, then skimmed the article as a whole. The article begins well, and is on a generally solid trajectory. This subsection (see headline) is, however, currently, by far, inappropriate to the rest of the article, in terms of length, level of detail, and lack of verifiability. Compare this subsection to the arguably comparable subsections below it for chemistry and biology (5-6 lines each). Those sections are readily understandable to a lay audience, and are linked to their full wikipedia treatments via a "main article" link and interspersed wikilinks. This subsection has neither of these characteristics. It may indeed, as a "mathematical model for symmetry", be either cribbed academic content of someone's ideas on the subject, or, alternatively, it may be an editor's original research. In the former case, it violates WP verifiability policies; in the latter it violates WP original research edicts. In short, this section has to be trimmed down, mightily, to be suitable for this general article. Le Prof Leprof 7272 (talk) 01:11, 29 May 2014 (UTC)

Glad to hear that someone who knows more math than I do has the same queasy feeling about that section. Let's cut it now as WP:OR and very possibly worse. Chiswick Chap (talk) 08:34, 29 May 2014 (UTC)

Proposed rewrite[edit]

After comments about the state of the article by other users, I reviewed the article more closely, and created the following draft to be closer to Wikipedia Summary Style: User:Brirush/sandbox

Major changes include:

  • Replacing the geometry section with a summary, and splitting the original material into a new article. I have not created the new article yet without consensus, but the material in place would be a fine mathematics article.
  • Consolidating the geometry and mathematics summaries.
  • Making the physics section a summary more inline with the other summaries. With Wikipedia Summary style, the specific details like monads and symmetry groups can be relegated to the specific article. Some of the deleted material could be worked into symmetry (physics).

I'd like to hear your feedback. I feel that this would greatly improve the article, but I won't move forward if this is generally opposed. Brirush (talk) 13:43, 9 November 2014 (UTC)

The idea certainly has its advantages, but we need to consider it carefully. I'd agree that the sandbox article covers symmetry as generally understood; it is plainly a non-mathematical article and as such needs better citation. However, it remains a bit of a jump from there to say that symmetry-in-geometry is a subsidiary concept, not least because geometry feels like the place that the concept came from. I'll be happy to go along with the consensus opinion, whether that's to split or to keep. Chiswick Chap (talk) 13:56, 9 November 2014 (UTC)
The mathematics and geometry part look good to me. The logic section seems to have gone. It might be worth mentioning symmetrical relations and logical operators. --Salix alba (talk): 21:25, 9 November 2014 (UTC)
I've reintroduced the logic material. Let me know if you have any other suggestions.

I've also posted at Wikipedia talk:WikiProject Mathematics directing people to this discussion; there is a set of comments there, as well.Brirush (talk) 21:43, 9 November 2014 (UTC)

I have now completed the split-off.Brirush (talk) 01:08, 11 November 2014 (UTC)

That's very bold of you, considering discussion has hardly begun, let alone consensus reached. Chiswick Chap (talk) 07:06, 11 November 2014 (UTC)