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Talk:Projective plane

Java app
Have written a java app to find projective planes. Has reached order [16 lines * 17 points] so far.

Degenerate examples
I'm not sure I understand the point being made by the 'degenerate' examples, in detail. Is it just to show what the third axiom rules out?

Charles Matthews 06:54, 26 May 2004 (UTC)

Symmetry group of Fano plane
The 168 symmetries of the Fano plane play a significant role in mathematics. Hence I have added a paragraph linking to a discussion of these symmetries. That discussion is my own. For some background, see other discussions of mine on finite geometry cited at Alan Offer's compilation of online finite geometry notes at Ghent University. Cullinane 13:29, 9 August 2005 (UTC)

affine planes
I added this to the properties : the fact that the order n occurs as order of projective plane is equivalent to existence of an affine plane of the same orde. Why is there no mention at all of affine planes. In fact, i think you can make an affine plane by removing a random line from a projective plane, and two such affine planes are isomorphic if and only if there is an automorphism on the projective plane mapping the first chosen line to the second.

 * You'd better clarify your definition of 'affine plane'. A combinatorial definition would not be the same as affine plane, qua affine space of dimension 2. Charles Matthews 15:04, 1 February 2006 (UTC)

I meant the combinatorial definition (thus without use of any linear space over any field) : three noncollinear points at least, all different two points are on exactly one line, for each point not on a given line there is exactly one parallel line through it. So should i just write "combinatorial affine plane?"

 * No, IMO. An affine plane in the sense of this general article is equally general.  Besides, the fact that deleting any one line from a projective plane gives an affine plane is completely general. The fact that adding a line at infinity to an affine plane gives a projective plane is also completely general. Zaslav (talk) 08:16, 27 March 2011 (UTC)

latin squares
I added a reference to mutually orthogonal latin squares. I find it strange that there was no mention at all. However, one might argue about the whole new section just for that. On the other hand it does explain why Euler proved n=6 impossible with his officers problem.

 * Sorry, Euler had nothing to do with abstract projective planes; they came later.Zaslav 01:50, 7 November 2006 (UTC)

axiomatic affine space/steiner system
I know it has been pointed out that not everyone thinks the same thing of projective planes and axiomatic projective planes, so this might lead to more confusion. However, i created an article Axiomatic projective space and I was wondering where is the best place to refer to it. I think it is important as axiomatic projective planes are what makes axiomatic projective spaces hard to classify.

I also added the converse of the steiner system remark.

Evilbu 17:25, 15 February 2006 (UTC)

I added a reference to Axiomatic projective space in the Finite geometry article. No doubt the reference would also be useful in other articles, but I don't know which ones.

Cullinane 20:06, 15 February 2006 (UTC)

Missing definition of ordinary geometric projective planes???
It appears that the article, when it finishes with combinatorial projective planes, immediately launches into how commutativity of the division ring is unnecessary -- and then "Generalizations" -- without ever defining the geometric projective plane at all! This strikes me as a glaring omission (or does it represent vandalism?). There needs to be an elementary discussion of what the plain vanilla projective plane of a vector space is before beginning to get into the generalizations thereof.Daqu 21:56, 23 October 2006 (UTC)

 * The reader is supposed to use the link to projective space. There is nothing special about the case of the projective plane associated to a three-dimensional vector space. Perhaps links to the pages on real projective plane, complex projective plane should be more prominent. Charles Matthews 22:04, 23 October 2006 (UTC)

 * Indeed it must be more prominent. There is nothing informing the reader of what you just wrote, even if you and I know perfectly well that it is true.  (Also, the very fact that there is a term "projective plane" suggests that the best way to explain it may not necessarily be as a special case of a more general concept.)Daqu 22:09, 23 October 2006 (UTC)

 * I fully agree with Daqu. For example, the Surface article is largely redundant with the Manifold article, just so people can learn the concepts in two dimensions before having to deal with n of them. Additionally, in my experience the linear-algebraic definition is by far the most common (but maybe I'm biased.) What's worse, Projective space is also grossly deficient in the linear-algebraic treatment. If I have time, I'll put in some work on these. Joshua Davis 13:32, 26 October 2006 (UTC)

 * Though I actually agree with the sentiment, this is a POV problem ('must be more prominent' does depend on one's orientation within mathematics). Charles Matthews 13:41, 26 October 2006 (UTC)

 * The projective plane, and not higher projective spaces, are of special importance in combinatorics. It makes natural sense to explicitly discuss the geometric version of this combinatorial object.Daqu 20:20, 14 November 2006 (UTC)

 * I disagree with Charles Matthews (vehemently, actually). It is not a matter of POV, it is a matter of starting at the beginning.  Currently, the introduction only states that there are two definitions of the projective plane (coming from linear algebra and geometry) but doesn't say what they are.  This article would be vastly improved if someone would replace this with a layman's explanation of what the projective plane is, and shift the technical discussion down to start at the first section.  The fact that I came to Wikipedia to learn about projective planes and came away no wiser is not a demonstration of POV success.  Edmund Blackadder (talk) 04:29, 1 September 2010 (UTC)

Missing definition of affine plane
The article makes several references to affine planes but a) without ever defining them and b) without referring to any Wikipedia or external definition of them, either. If you're going to use a technical term, there must a definition either here or elsewhere that the reader can find. . . if you have any desire to be understood.Daqu 22:09, 23 October 2006 (UTC)

Notation
What does "PG(2,F)" really mean? 192.43.227.18 15:00, 4 October 2007 (UTC)

Linear algebra definition
This section needs explanation: Let K be a division ring. How does one construct a projective plane? In the text in the article there is no hint about this. And an example may also be helpful.

TomyDuby (talk) 05:47, 14 February 2009 (UTC)

Topological embeddings
The new subsection "Topological embeddings" needs some work, at least in its terminology. Embedding is the wrong word to use here; the real projective plane cannot be embedded into Euclidean 3-space. And some of the other examples destroy the topology in other ways; e.g. the hemisphere is not homeomorphic to the projective plane, so stereographically projecting it does not yield a projective plane. Mgnbar (talk) 14:24, 28 December 2010 (UTC)
 * Please follow up the references given before you make such uninformed claims. For example the hemisphere as it stands is not homeomorphic to the projective plane, but if pairs of opposing points around the rim are identified as single projective points then it becomes a homeomorph. Weeks (The shape of space, CRC, 2002, p 59) explains it like this; "The projective plane is a surface that is locally like a sphere, but has different global topology. It's made by gluing together the opposite points on the rim of a hemisphere." and gives a nice illustration. You might also care to consider why Klein thought the stereographic projection is also a homeomorph. — Cheers, Steelpillow (Talk) 15:02, 28 December 2010 (UTC)
 * Hi, SteelPillow. Just so we're clear, in my post above I did not say that the section should be thrown out; I was trying to say that the terminology should be clarified. The statements you've made in your post are correct, but they do not refute my argument. In fact, your quote about how "The projective plane is a surface that is locally like a sphere, but has different global topology." supports my argument: The projective plane, the sphere, the half-closed hemisphere, and the plane all have different topologies, and this is why the word embedding is inappropriate. In the cases of Boy's surface and the Roman surface, the projective plane is immersed in 3-space. The fact that the real projective plane cannot be embedded in 3-space is well-known; see the first paragraph of Real projective plane, or Massey: A Basic Course in Algebraic Topology, p. 6, or Bredon, Topology and Geometry, p. 353, for example. Mgnbar (talk) 16:56, 28 December 2010 (UTC)
 * "Just so we're clear" indeed. This could take a while. You misrepresent Week's quote. He says that the projective plane and the sphere are not homeomorphic (they have different global topology). He does not make this claim for the projective plane and the hemisphere as you suggest he does, in fact quite the reverse - he explains how the two topologies are equivalent - his "gluing together" is just layman's language for "identifying". You also quote the Real projective plane article out of context. It remarks that the plane cannot be embedded in 3-space without intersecting itself. I never said that it could. Another mistaken assertion is that the Roman surface is an embedding. It has Whitney umbrellas (or similar features?), therefore it cannot be an embedding. Historically it was widely conjectured that no smooth embedding existed. Boy was set the task of finding a proof - only to discover the counterexample that bears his name. You may confirm all this for yourself from the references I note in the article. If Massey and Bredon truly disagree with Apéry and Brehm then we have an interesting time ahead of us. — Cheers, Steelpillow (Talk) 17:43, 28 December 2010 (UTC)
 * Whoops! My apologies. I got embedding and immersion the wrong way round. I'm always doing that. sigh. — Cheers, Steelpillow (Talk) 18:19, 28 December 2010 (UTC)
 * No problem; we all make mistakes. I like your recent changes, but we do still have some work to do. The Boy surface is an immersion but not an embedding, because it is not injective. I don't know much about the Roman surface, but Roman surface seems to explain in some detail that it's not even an immersion. We should also mention the cross cap, which seems to be an immersion. (By the way, Cross-cap seems to have some errors.) The map from the sphere to the projective plane is very valuable, but it is not an immersion, because it's not injective; it's a quotient map, a covering map, and a submersion. The map from the hemisphere to the projective plane is a quotient map. I vote that we retitle this subsection to something like "Relations to other topological spaces". Regards, Mgnbar (talk) 21:21, 28 December 2010 (UTC)
 * Yes, I now see that you are right that none of these are embeddings. We need a general terms for dropping one manifold inside another space (to allow either injection or surjection). Offhand I cannot think of a suitable one - I believe have seen "projection" used in this context but am not sure if this is a correct choice. Perhaps "examples" is adequate - I'll try it. We need to be clear that these are projective planes in their own right. For example note that Weeks is clear that he is constructing "the projective plane" from his hemisphere, not just an equivalent surface. To a topologist all these forms are the same object, indistinguishable from each other save by external properties. In fact I think it might help if we promote this section a level, call it "topological definition", and provide a bit more explanation. However I am ignorant of the topological properties of the complex projective plane - which is why I put this section under the real projective plane. What do you think? — Cheers, Steelpillow (Talk) 10:50, 29 December 2010 (UTC) (Edited — Cheers, Steelpillow (Talk) 10:52, 29 December 2010 (UTC)]
 * Oops; I made a typo above. The map from the sphere to the real projective plane is an immersion, but not an embedding. Sorry.
 * The functions in question are all different enough that I can't see a common term for all of them beyond the generic "function" or "map". By the way, here's another topological definition: Take a Möbius strip and a disk, both of which have circles as their boundaries, and glue these circles together. The complex projective plane is rather different from the real projective plane --- a complex 2-manifold, and hence an orientable real 4-manifold. It should be described somewhere in this article, but maybe not in this section. Regards, Mgnbar (talk) 13:27, 29 December 2010 (UTC)
 * I think we agree that the current version is now correct. There are many topological constructions, e.g. slice a Klein bottle in half, stitch the sides of a square together in a certain way, etc. I think most of these go beyond the scope of this article (perhaps some of mine have already done so). I agree about the complex projective plane and have started a discussion below. — Cheers, Steelpillow (Talk) 15:08, 29 December 2010 (UTC)

Restructuring suggestions
IMHO this article only makes sense if it focuses on the common features of, and key differences between, the real and complex projective planes.

Some key properties that I think deserve their own (sub?)sections include:
 * Projective duality as it applies to the plane.
 * Treatment of the line at infinity, especially its projective lack of distinction with respect to any other line.

I don't know much about the complex one (e.g. how can it be orientable when, as I understand it, the real projective 4-space is not?), so I can't judge how much of the present content applies to both or only to the real one. For example does the bit on duality in the real projective plane apply to both kinds?

For the detailed treatment of each we have separate articles for the Real projective plane and Complex projective plane, but I think that separate (sub?)sections on each are called for here, to provide a home for their key differences.

Can anybody restructure/clarify the relevance of the present content for each type, either below here or just edit the article?

— Cheers, Steelpillow (Talk) 15:08, 29 December 2010 (UTC)

 * I fully agree that the real and complex projective planes deserve their own articles, and that this article should provide just a brief treatment and link to them. However, projective planes can be defined over any field (and even more generally than that), so these are not the only two examples. For example, the three-trait variation of the game Set amounts to finding points in a projective plane over the field of three elements. So I guess I vote that we move most of your new topological stuff to Real projective plane and then clean up Projective plane as you say, to discuss mainly those features common to all projective planes, such as the "key properties" that you mention above. By the way, Projective plane could easily become redundant with Projective space as well. Deciding how many articles there should be, and exactly how material should be divided among them, is not easy. Regards, Mgnbar (talk) 16:55, 29 December 2010 (UTC)

 * Looks like a plan. I would expect that the projective plane has enough meat to warrant an article independent of projective space, we'll see. I'll have to leave most of the work to those more knowledgeable than me. Would it make sense to move wholesale the section on visualising the real projective plane into the article on the real projective plane? — Cheers, Steelpillow (Talk) 12:22, 30 December 2010 (UTC)

 * Really I think that the article should be rewritten from scratch along these lines:
 * first definition: using linear algebra over division ring
 * common properties
 * mention real and complex cases, and link to those articles, but don't go into depth on them
 * projective transformations
 * second definition: combinatorial
 * properties, theorems, etc.
 * planes of small order, etc.
 * I'll start reorganizing and then working on the first definition. I don't have the knowledge or references to handle the second definition. Mgnbar (talk) 16:28, 31 December 2010 (UTC)

 * This makes sense if the properties of projective planes over fields or division rings are used to motivate the abstract (combinatorial) definition.
 * The real and complex planes really do need separate treatments. Most of their uses are not general to projective planes but are specific to planes that are, at the least, manifolds. Zaslav (talk) 08:12, 27 March 2011 (UTC)

Linear-algebraic definition
The lede is much improved, thanks; but I'm struggling with the opening line of the first proper section: "The projective plane is the set of lines through the origin in 3-dimensional space, and a line in the projective plane arises from a plane through the origin in 3-dimensional space. This idea can be made precise as follows." I think the first clause is simply wrong as it stands, but I'm not sure. Certainly it is unclear. --ColinFine (talk) 11:32, 1 January 2011 (UTC)

 * It has the right idea. I guess it might be more accurate to say that the set of lines through a point can be defined as a projective plane: enclose the point by a sphere, and the point-pairs of intersection with those lines make it easy enough to see that the sphere is a projective plane with respect to these point-pairs (antipodal points on the sphere are identified as a single projective point). Likewise a plane through the original point meets the sphere in a projective line (great circle) on the sphere. There is no need to draw the sphere in order to treat the lines and planes through the original point as a projective 2-space. Taking the original point as the origin makes life easier. Not sure how to express this rigorously in terms of linear algebra, so I won't touch the article myself. — Cheers, Steelpillow (Talk) 13:23, 1 January 2011 (UTC)

 * ColinFine: I know that I have yet to add references (I'll try to do so today) but the idea you're discussing is quite standard in mathematics. For example, from Baez: The Octonions: "If K is any field, there is an n-dimensional projective space called KPn where the points are lines through the origin in Kn+1, the lines are planes through the origin in Kn+1, and the relation of ‘lying on’ is inclusion." Is your objection that we're tying the projective plane to a particular construction or representation? We could fix that by adding "In one view...".

 * SteelPillow: I agree that any point could in 3-space be used to define the projective plane. This is analogous to how mathematicians often talk about "the sphere" as being defined by x^2 + y^2 + z^2 = 1, when the details of radius and center don't matter to the math that they're doing. For the projective plane, introducing an alternative "center" wouldn't help anything; you'd get an equivalent definition with more complicated notation, I think. Regards, Mgnbar (talk) 15:23, 1 January 2011 (UTC)
 * Yes, that's why I said taking it as the origin makes life easier. One could equivalently take any spheroid in place of the sphere, probably any quadric surface if one chose an appropriate reference point, but that would get even more complicated. — Cheers, Steelpillow (Talk) 22:15, 1 January 2011 (UTC)
 * Agreed. Regards, Mgnbar (talk) 22:19, 1 January 2011 (UTC)
 * ColinFine: In case my post above came across as dismissive, what I should have said is: The treatment given is correct, but if it's unclear or unhelpful, then please elaborate, so that we can improve it. Mgnbar (talk) 17:39, 1 January 2011 (UTC)

Yes, the usual definition of this type simply takes all lines through the origin. You gain nothing by generality. The proper way to say it, I think, is not to say "the plane" is the set of lines, but that the points of the plane are the lines through the origin. You also have to say what the projective lines are; they are the sets of coplanar lines. I think this change is necessary because some interested readers are not going to understand the definition without its being more concrete. (I have a reader in mind.)

 * The current text is common in math textbooks, because mathematicians are accustomed to conflating an object with its underlying set when necessary. But your new text ("the points of the plane are the lines...") is more precise and not overly wordy, so please put it in.

On the other hand, if you're discussing the concept of projection from an arbitrary point in an affine or projective plane, then you would take the lines through your point. I suggest that the former is best for a definition and the latter for discussing properties of, and constructions in, affine and projective spaces. Zaslav (talk) 08:07, 27 March 2011 (UTC)

 * Yes, the former should be used in the definition, because that is standard in textbooks, and the latter has its place elsewhere.

 * I'm glad that you're making edits to the combinatorial definition, which I edited very little in my recent reorganization. For one thing, you could do a great service by adding some references. Mgnbar (talk) 13:22, 27 March 2011 (UTC)

Definitions
There is a fundamental problem with this page and it has to do with the meaning of a definition. There are some here who view projective planes as whatever is obtained by the standard field plane construction (I am using the term field here in the sense that the French sometimes do, it need not be commutative) which is called here the "Linear Algebra Definition" (should be vector space construction, but that's probably nit-picking). The "combinatorial" (and I wonder where that term came from) definition is then introduced as a generalization (or alternative) of the first. This is wrong on several levels. First of all, the concepts are different, so one could never refer to them as being alternatives. The axiomatic definition encompasses the Linear Algebra construction so it should take precedence. A construction should never be taken as a definition unless you don't know what the object you are constructing really is. In mathematics you will find that there are good definitions and bad definitions, but hopefully the bad ones get weeded out over time. The function of a "good" definition is to provide a way to decide whether or not an object is in the class of things being defined. The problem with using a construction as a definition is that if an object is obtained in a different way you need a theorem to say that the object is isomorphic to something obtained by the construction, rather than simply verifying that the definition is satisfied. While it is true that you see objects referred to as a "generalized" this, or a "generalized" that, when this is properly done, the term "generalized" is part of the name (as in Generalized quadrangle) and has its own specific definition. Advocates of the "Linear Algebra definition" would want to refer to projective planes defined axiomatically as "generalized projective planes". Frankly, this is just not done by anyone. A quick look at any text with Projective Plane(s) in the title or more generally Projective Geometry, will show that only definition is the axiomatic definition. I believe that a reorganization of this page is in order. Wcherowi (talk) 18:31, 26 August 2011 (UTC)

 * You raise some good points, but they do not convince me that the article should be substantially changed. Please consider these counterpoints:
 * When one is trying to learn a difficult concept, it is helpful to see examples before an abstract definition. (I have seen educational studies to support this idea, although I confess that I cannot cite them.) Wikipedia is not a textbook, but it still tries to make concepts accessible. The former definition/construction of projective plane, insofar as it is an example of the latter one, is valuable for this reason.
 * You assert that books entitled Projective Plane (etc.) all use the axiomatic definition. I counter that every topology or algebraic geometry book that I have ever seen uses the linear algebraic definition. So maybe this is a disagreement between sub-disciplines of math. Indeed, from my experience (which I admit is not universal) it seems that projective planes over (A) the real numbers and (B) algebraically closed (commutative) fields account for the vast majority of discussion of projective planes in the modern math literature. So it makes sense to have them explicitly constructed in this article.
 * You also raise a number of semantic points. I agree with you that the latter definition is not really an "alternative" to the former. You also say that the latter definition "encompasses" the former, but is not a "generalization" of it; this makes no sense to me, but maybe it's not important. As far as "linear algebraic definition" vs. "vector space definition" goes, I am indifferent.
 * Would you be satisfied if the first definition/construction, rather than being called "Linear algebraic definition", were simply renamed "Construction over a division ring"? And, by the way, have you seen Projective space? Mgnbar (talk) 19:57, 26 August 2011 (UTC)

 * Thanks for responding so quickly. I think that I should clarify some of the points that I made.
 * Examples are extremely important and this article is in need of more, I am not advocating the removal of any examples. The difficulty that I am trying to point to is calling an example a definition.
 * It is good practice, when writing a textbook or other educational exposition, to proceed an abstract definition with good examples ... provided the reader is familiar with at least some of the examples. If the examples are as novel as the definition, the whole point of doing this is lost.
 * I object to the confounding of abstract and axiomatic. The axiomatic approach is familiar from high school geometry. The axioms for a projective plane are very simple statements and there are only three of them - far less abstract than the concept of an equivalence relation on 3-dimensional vectors defined over a division ring.
 * Recall that the title of the article is Projective Plane, not the "Topological Aspects of Some Projective Planes" or the "Algebraic Geometry view of Projective Planes". I would believe that books with the same title as the page are probably more closely aligned with the intended meaning of the term.
 * There is a reason that you see only the classical construction in Algebraic Geometry books. There are, with very few exceptions, two assumptions made about the geometries that are dealt with, namely, the geometric dimension is at least three and the division ring does not have characteristic two. These assumptions are made so that the theory works out well without exceptions. If either assumption is violated then one has to deal with special behaviours that do not fit into the general framework. Of course, it is sometimes necessary to talk about planes, so when that occurs the planes are restricted to be those of the classical construction and generally over division rings of characteristic zero, so that the general framework does not have to be modified.
 * The reason for the above restriction to dimension three or higher is that it is fairly easy to prove that Desargues' Theorem holds universally there and so the projective space does come from the classical construction, but this is not true in dimension two. In other words, only in geometric dimension two can you get projective geometries which do not come from the classical construction. Such projective planes can not be embedded in projective space and so are not part of that theory. Some will consider these planes to be aborations, but those of us who work in this area celebrate the richness of the variety of these planes. If it wasn't for these examples there wouldn't be much of a reason to have this article, it could just be a section of the projective space article. Wcherowi (talk) 03:32, 27 August 2011 (UTC)

 * Hi again, Wcherowi. I appreciate that you've put some thought into this. Regarding your points here:
 * From my experience in teaching students (which may contradict yours or others'), constructions are always more concrete than non-constructive axiomatic definitions. If you present them with the latter, they ask, "But what is it?" They like triples of numbers, and they love pictures. So I am still of the opinion that having the construction before before the axiomatic definition is useful, or that we should somehow tell the reader to read Real projective plane before this article.
 * The fact that this article is called "Projective plane" does not convince me that books of that title should take precedence, as if it is somehow their turf, or that topological and algebro-geometric properties of projective planes should not be treated. The "intended meaning of the term" in Wikipedia is, to be honest, in constant flux, because it's decided upon by you and me. However, we should be guided by least surprise. Imagine a reader who comes to this page. What is she looking for? Probably RP2 or CP2, really. So we should quickly point out the articles for those two cases. We should also give the construction over an arbitrary division ring, because it generalizes those two cases. We should also give the axiomatic definition, of course.
 * I understand that projective spaces of two dimensions are qualitatively different from those of higher dimension. That is a good reason to have this separate article, as you say. But there are other reasons to have this separate article. People learning a topic find it helpful to learn a low-dimensional version first. Also, low-dimensional examples are disproportionately important; look at how important CP1 is.
 * In case you are not aware (your editing history suggests that you've started editing only recently, but this could be misleading), the mathematics articles on Wikipedia are under constant complaint from readers as being "too abstract" and "written for mathematicians only". For me, this is a key consideration.
 * What changes to the article do you want, exactly? I have proposed renaming the first definition as a mere "construction". Would that satisfy you? What if we moved the construction after the definition? Would that satisfy you? Or do you still feel that a rewriting of the article is warranted? I am not convinced of that. Regards. Mgnbar (talk) 10:26, 27 August 2011 (UTC)

At risk of lowering the tone of this discussion, I am one of those "constant complainers" who seek everyday explanations. The lead introduces the linear algebraic and axiomatic definitions. Good. There follows a section discussing the linear algebraic view. But there then follows a section on the "combinatorial" definition. Are we to take this as another name for the axiomatic? Further, to me the linear algebraic definition arises as a consequence of the geometric observation that a sphere with antipodal points identified is a projective plane (we draw lines joining antipodal pairs). Meanwhile the geometric construction arises as a consequence of the axiomatic treatment (plus some definitions of "point", "line, "plane" and "incidence"). And is not algebra supposedly based on axioms too (or have those been successfully supplanted by set theory, as the latter part of the 20th century set out to do)? It seem to me that these relationships and their explanation should guide the construction of this article. — Cheers, Steelpillow (Talk) 12:12, 27 August 2011 (UTC)

 * Hi, Steelpillow. It's fine with me to rename "combinatorial" to "axiomatic". I disagree that the linear algebraic definition follows from the geometric definition; either one can be made to follow from the other. (The geometric definition of RP2 arises from the algebraic one by picking two points on each line, and then modding out. Very simple.) In modern geometry, it is extremely common to define spaces by "constructions" involving "data". Look at manifold or orbifold or scheme, for example. I say all of this while acknowledging that we should probably change the article to make the axiomatic definition "the definition" and the linear algebraic definition "the crucial class of examples". Mgnbar (talk) 12:31, 27 August 2011 (UTC)
 * Thanks for the prompt reply. I am not saying that the geometric takes absolute primacy over the algebraic, merely that as a simple-minded soul who loves pictures, that's the way I see things. — Cheers, Steelpillow (Talk) 15:03, 27 August 2011 (UTC)

 * Hi again. I don't think we are really very far apart. My pet peeve is what I perceive as an inappropriate use of the term "definition" when "construction" is meant. That aside I don't really see major revision of the page, merely a reorganization (actually along the lines that Mgnbar suggested) that would remove a pov bias (as I see it). So here is what I am proposing -

I hope this gives a better idea of what I had in mind. Wcherowi (talk) 17:59, 27 August 2011 (UTC)
 * 1) Introduction - essentially ok. I would modify the second paragraph a bit and put a stronger emphasis on the link to the Real Projective Plane.
 * 2) Definition - the axiomatic definition, it need not be labelled as axiomatic.
 * 3) Some Examples
 * 4) RP2 - Given as the extended Euclidean plane (i.e., add points to destroy parallels)
 * 5) PG(2,q) - Maybe just a specific one like PG(2,3) with a hint about other finite fields.
 * 6) Moulton plane - An example of an infinite plane which is easy to describe and is non-Desarguesian.
 * 7) Vector Space Construction
 * 8) Classical examples (section 1.1)
 * 9) Topological properties and anything else that needs to be mentioned about the classical examples.
 * 10) Finite Examples - including the Fano plane.
 * 11) Affine Planes
 * 12) Definition and Examples
 * 13) Construction of Projective Planes from Affine Planes (essentially section 2.3 done more generally and a tie in with the very first example. Also includes section 1.2)
 * 14) Generalized Coordinates (PTR's, etc.  essentially section 2.2)
 * 15) Degenerate Planes (section 2.5, but redone to clarify what the seven types are)
 * 16) Collineations (Includes section 1.3 but goes beyond this to include fixed-point configurations)
 * 17) Lenz-Barlotti Classification Scheme of Projective Planes (which is based on the types of degenerate planes)
 * 18) Finite Projective Planes (essentially section 2.4)
 * 19) Projective Planes in Higher Dimensional Projective Spaces (sections 1.4 and 2.6 combined)

 * Now that I have a better idea of what you're suggesting, I like it. Please go ahead. By the way, you might want to read Wikipedia talk:WikiProject Mathematics, where a discussion of the "example before definition" idea seems to be underway. And Steelpillow: I thrive on pictures too. :) Mgnbar (talk) 12:13, 28 August 2011 (UTC)

Major overhaul
I've just finished (or at least – come to a reasonable stopping point of) an overhaul of this page. I've reorganized it and added new material without (I hope) treading too heavily on what was already on the page. Please look it over and give me your reactions, suggestions, etc. Thanks. Bill Cherowitzo (talk) 03:42, 2 October 2011 (UTC)

 * In that nobody speaks, I'd say go ahead! One technical name for a major rewrite that changes structure but not content is a (major) refactor, that might be a good term to use in some of your edit summaries.

 * But one word of caution... the algebraic usage is equally important to the usage in naive projective geometry.

 * Agree that the current article would be improved by discussing the naive approach first, but I think your current draft doesn't strike a balance yet. We might need to consult an algebraist, I did study projective geometry back in the 1980s but that was a while ago! Andrewa (talk) 14:21, 18 October 2011 (UTC)

Having bounced around for the past week or so I am now prepared to go ahead with my major refactor of this page (thanks for the terminology Andrewa). I am being a little timid here, but there is a subtle POV issue in the background and I want to make sure that I get it (NPOV) right. For the past 60-70 years there has been a split in the projective geometry research community. Camp A, most notably algebraic geometers but others as well, believes that projective planes are just the 2-dimensional versions of projective spaces and tends to ignore anything that does not scale up to higher dimensions or puts too much of a burden (in terms of exceptions and alternate treatments) on the algebraic underpinnings. Camp B, I'll call them "foundationists", consider the primary objects of interest to Camp A to be well studied and known topics and are more interested in the projective planes which can not be imbedded in higher dimensional spaces. From the Camp B viewpoint, the field planes (as Camp A sees them) are a very important but special class of examples. As I see the current article, it is written from the Camp A viewpoint with an offhandedly perfunctory nod to Camp B. I believe that this is not the way to write an encyclopeadic article and so I rewrote the article to reflect the more inclusive worldview of Camp B. This did not involve changing a lot of content but it did require some modifications and a lot of reorganization. A comparison of the current article and my refactorization will look like I have totally rewritten the page — but this is really not the case as a closer examination will show. Have I given Camp A equal treatment? - No. Have I given the Camp A point of view? - No. Have I provided enough of an emphasis on the Camp A special case? - that's debateable, and I probably haven't — but what I have done is to open up the structure of the article so that this material can be easily added by any editor. I would urge anyone who is interested in this topic to take a look at User:Wcherowi/Projective planes and let me know if I have stepped over any boundaries that I shouldn't have. Thanks. Bill Cherowitzo (talk) 16:16, 19 October 2011 (UTC)

IP comment on section Projective planes in higher dimensional projective spaces
An IP editor added the following comment to the body of the article. I've moved it here:
 * I suggest to add a sentence at the start of this section, saying that an alternative definition of a finite projective plane of order n with n > 0 is a collection of n^2 + n + 1 lines and n^2 + n + 1 points such that 1. every line contains n + 1 points, 2. every point is on n + 1 lines, 3. any two distinct lines intersect in exactly one point, and 4. any two distinct points lie on exactly one line. (Perhaps this is slightly easier to grasp than saying that "there are four points such that no line is incident with more than two of them.")

--JBL (talk) 02:36, 20 July 2012 (UTC)

 * I assume that it is the finite projective plane section that is being discussed. There are some problems with this suggestion. First of all, it is not an alternate definition, it is a theorem which follows from the definition of a projective plane and the assumption of finiteness. The proof of this theorem involves counting, and the result is essentially what is given in the first sentences of the section. Secondly, the suggestion would include the case of n = 1, which gives a triangle. It is almost universally accepted that a triangle is not to be considered a projective plane, but rather a degenerate form of a projective plane. Admittedly, this is a convention, but to do otherwise would require the constant exception of this case in most general statements of theorems concerning projective planes. The IP editor seems to be confused about the meaning of "there are four points ..." in the definition of a projective plane. This condition is specified to eliminate the seven degenerate cases, one of which is the triangle. In those treatments of projective planes which only deal with finite projective planes from a block design point of view, one may see the suggestion given as a definition (even with the casual disregard of the n = 1 case), but this is not acceptable in the geometry community. Bill Cherowitzo (talk) 18:28, 20 July 2012 (UTC)

 * IP means Internet Protocol, and terms like "IP editor" are nonsense because that obviously doesn't have anything to do with the Internet Protocol. YOU CAN'T DO THAT - which I mean is to create new acronyms and initialisms without explaining what they mean. All such things must be explained upon their first appearance. Furthermore, in Air Force terminology, IP means "initial point", which is a certain place in a bombing run. Don't go around using undefined acronnym, etc., especially when they conflight with well-known ones like IP = Internet Protocol. And then you want to do that on the Internet? Completely ghastly.98.67.106.148 (talk) 15:32, 22 September 2013 (UTC)

 * And you left out Intellectual Property and International Police and about a zillion other possible interpretations in your tirade. In the Wikipedia community, an anonymous user who has not created an account (such as yourself) is identified by their IP address as explained at WP:IP. Such editors are casually referred to as anonymous IP editors, or just IP editors. On talk pages, such as this one, editors talk to other editors about how to improve the associated articles. Jargon such as this is a natural development in such an environment and not the ghastly abomination you seem to think it is. There are also several other conventions that are in use in this community such as: using all caps is called shouting and is frowned upon. One learns about such conventions generally by observation over time. Bill Cherowitzo (talk) 16:28, 22 September 2013 (UTC)

I doubt that the "Definition" suffices to avoid all degenerate planes.
The textbook ''Lars Kadison und Matthias T. Kromann: Projective Geometry and Modern Algebra. Birkhäuser, Boston/Basel/Berlin 1996, ISBN 3-7643-3900-4'' has together with the 1st and 2nd instead of the 3rd axiom "There are four points such that no line is incident with more than two of them." in the article now 2 axioms:
 * P3: There exist three noncollinear points and
 * P4: Every line contains at least 3 points.

In my point of view an Y-graph (or Mercedes-Stern without outer circle) (4 points, 3 lines, exactly 2 points on each line, all three lines intersecting in one single point) should fulfill all the present 3 axioms in the article and is rather degenerate. Or abstractly speaking: How the hell should the dual of the third axiom in the article be proven from 1.-3., without making this dual form 3.D an axiom?--KlioKlein (talk) 15:12, 8 August 2013 (UTC)

I saw now that my example Y does not fulfill 2. and is wrong. But an inline-citation for the axioms would be nice! :-) (Or did I overlook something?) A little soubt remains... --KlioKlein (talk) 15:26, 8 August 2013 (UTC)

 * The nondegeneracy axiom stated in the article is equivalent (in the presence of the first two axioms) to the P3 and P4 axioms of Kadison and Kromann. This is a standard homework exercise in a projective geometry course. The overwhelming majority of the references will give the axioms as presented (or equivalents - the usual phrasing of axiom 3 is : There exist four points no three of which are collinear), although there are a couple of notable exceptions (Beutelspacher & Rosenbaum, and Coxeter come to mind immediately). Having 4 axioms instead of 3 is an older tradition and some authors still find it useful for their expositions. I have noticed that Kadison and Kromann tend to use older terminology which is consistent with an algebraic geometry point of view. I could provide the citations and mention this issue if you think it will improve the page (someone else wrote that section and I didn't think that this was important enough to modify it). Bill Cherowitzo (talk) 20:49, 8 August 2013 (UTC)

Poor English sprinkled through
Poor English sprinkled through: "...lines keep the points with negative x-coordinates..." Lines are inanimate objects, and they are incapable of possessing or doing anything at all. Furthermore, there were statements about "the points" (in a plane) which means any points whatsoever - all of them - instead of a specified subset of points. You really must write clearly and specifically, and not vaguely and indeterminently - and especially in mathematics. Also, there was the problem of writers making up words that do not exist in the dictionary or common usage. Even if those are "jargon words" in the field, that is BAD, because that is jargon that should be avoided at all costs. This article should be written in Plain English that the general reader can read and understand, even if he cannot understand the mathematics. I will just make one up as a specific example: pseudohypergeometrization. Don't do that. I am not stating that his one was really there, mind you, but I am creating an EXAMPLE.98.67.106.148 (talk) 15:42, 22 September 2013 (UTC)
 * About English: Some of your complaints have been fixed. Other examples are idiomatic to mathematics writing, and hence may not be fixed.
 * About jargon: Mathematics, like any highly technical field, has its own jargon, which does not appear in non-mathematical dictionaries. Part of the function of Wikipedia is to explain and exemplify jargon for readers, so that they can understand other texts that use such jargon.
 * About difficulty: This is a common complaint about mathematics articles on Wikipedia. (See FAQ at the top of the project talk page here.) This Projective plane article is not a bad offender, in comparison to many other articles. It attempts to give visual intuition, historical context, applications, etc. The later parts of the article are more obscure, but only highly motivated readers will attempt those anyway. Fundamentally, this is an article about a moderately advanced mathematical topic, that few non-mathematical laymen ever encounter. So the difficulty seems about right to me. Yes, there is always room for small improvements, but no dramatic change in tone, organization, content, etc. is warranted. Mgnbar (talk) 16:04, 22 September 2013 (UTC)

Vector space sentence correct?
In the vector space construction, we're defining planes through the origin in K^3 as (kx + ly) for k,l in K. Then this sentence:

"This plane contains various lines through the origin which are obtained by fixing either k or l."

Since we're talking K^3, wouldn't fixing k or l just make lines parallel to y or x (resp.), that don't pass through the origin? It seems like it's the ratio of k and l that needs to be fixed to get lines through the origin.

173.25.54.191 (talk) 02:27, 9 April 2014 (UTC)

 * Good catch. I didn't pay much attention to this section and just assumed it was correct, but you are right. As stated you get lines which do not pass through the origin. I'll fix it. Bill Cherowitzo (talk) 03:29, 9 April 2014 (UTC)

title: Talk:Projective plane


text: Talk:Pennywise (album)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Pennywise (album)


text:
Chitimacha

The Chitimacha (or  ) are an Indigenous people of the Southeastern Woodlands in Louisiana. They are a federally recognized tribe, the Chitimacha Tribe of Louisiana.

The Chitimacha have an Indian reservation in St. Mary Parish near Charenton on Bayou Teche. Their reservation is a small part of their precontact territory. They are the only Louisiana tribe who still control some of their original land, where they have long occupied areas of the Atchafalaya Basin, "one of the richest inland estuaries on the continent." In 2011 they numbered about 1100 people.

Historically, the Chitimacha spoke the Chitimacha language, a language isolate. The last two fluent speakers died in the 1930s, but the tribe has been working to revitalize the language since the 1990s. They use notes and recordings made by linguist Morris Swadesh around 1930. They have also started immersion classes for children and adults. In 2008 they partnered with Rosetta Stone in a two-year effort to develop software to support learning the language. Each tribal household was given a copy to support use of the language at home. The Chitimacha have used revenues from gambling to promote education and cultural preservation, founding a tribal museum and historic preservation office, and restoration of their language.

The Chitimacha are one of four federally recognized tribes in the state.

Name
According to the Chitimacha, their name comes from the term Pantch Pinankanc, meaning "men altogether red," also meaning "warrior." The name Chawasha, a subtribe of the Chitimacha, is a Choctaw term for "Raccoon Place." Washa is also Choctaw and means "Hunting Pace." Yaganechito means "Big Country."

Subtribes
The Chitimacha were divided into four sub-tribes: the Chawasha, Chitimacha, Washa, and Yagenachito. These were divided by their geography.

Historical lifeways
The Chitimacha established their villages in the many swamps, bayous, and rivers of the Atchafalaya Basin, "one of the richest inland estuaries on the continent." They knew this area intimately. The site conditions provided them with a natural defense against enemy attack and made these villages almost impregnable. As a result, they did not fortify them. The villages were rather large, with an average of about 500 inhabitants. Dwellings were constructed from available resources. Typically the people built walls from a framework of poles and plastered them with mud or palmetto leaves. The roofs were thatched.

The Chitimacha raised a variety of crops, and agricultural produce provided the mainstay of their diet. The women tended cultivation and the crops. They were skilled horticulturalists, raising numerous, distinct varieties of corn, beans, and squash. Corn was the main crop, supplemented by beans, squash and melons. The women also gathered wild foods and nuts. The men hunted for such game as deer, turkey and alligator. They also caught fish. The people stored grain crops in an elevated winter granary to supplement hunting and fishing.

Living by the waters, the Chitimacha made dugout canoes for transport. These vessels were constructed by carving out cypress logs. The largest could hold as many as 50 people. To gain the stones they needed for fashioning arrowheads and tools, the people traded crops for stone with tribes to the north. They also developed such weapons as the blow gun and cane dart. They adapted fish bones to use as arrowheads.

The Chitimacha were distinctive in their custom of flattening the foreheads of their male babies. They would bind them as infants to shape their skulls. Adult men would typically wear their hair long and loose. They were skilled practitioners of the art of tattooing, often covering their face, body, arms and legs with tattooed designs. Because of the hot and humid climate, the men generally wore only a breechcloth, and the women a short skirt.

Like many Native American peoples, the Chitimacha had a matrilineal kinship system, in which property and descent passed through the female lines. The hereditary male chiefs, who governed until early in the 20th century, came from the maternal lines and were approved by female elders. Children were considered to belong to their mother's family and clan and took their status from her. Like other Native American tribes, the Chitimacha at times absorbed and acculturated other peoples. In addition, as Chitimacha women had relationships with European traders in the decades of more interaction, their mixed-race children were considered to belong to the mother's family and were acculturated as Chitimacha.

The Chitimacha were divided into a strict class system of nobles and commoners. They had such a distinction that the two classes spoke different dialects. Intermarriage between the classes was forbidden.

Precontact
The Chitimacha Indians and their ancestors inhabited the Mississippi River Delta area of south central Louisiana for thousands of years before European encounter. Their oral history states that their territory was marked by four prominent trees. Archaeological evidences suggest that the Chitimacha and their ancestors have lived in Louisiana for perhaps 6,000 years. Prior to that, they may have migrated into the area from west of the Mississippi River.

Colonial period to 20th century
At the time of Columbus’ arrival in America, historians estimate the combined strength of the four Chitimacha groups was about 20,000. Although the Chitimacha had virtually no direct contact with Europeans for two more centuries, they suffered Eurasian infectious diseases contracted from other Natives who had traded with them, such as measles, smallpox, and typhoid fever. Like other Native Americans, the Chitimacha had no immunity to these new diseases and suffered high fatalities in epidemics.

By 1700, when the French began to colonize the Mississippi River Valley, the number of Chitimacha had been dramatically reduced. Estimates for that time: the Chawasha had about 700 people, the Washa about 1,400; the Chitimacha some 4,000; and the Yagenichito about 3,000. (Kniffen et al. said 4,000 people in total in 1700; they may have known only about those classified as only Chitimacha.)

The sub-tribes of the Chitimacha confederation occupied a total of about 15 villages at the time of encounter with French explorers and colonists in the early 18th century. The French described the villages as self-governing groups. The Grand Chief represented the central governing authority of all the sub-tribes, but they operated in a highly decentralized manner. Between the years 1706 and 1718, the Chitimacha engaged in a long, bitter war with the French. With their superior firepower, the French nearly destroyed the eastern Chitimacha. Those who survived were resettled by the French authorities, away from the Gulf of Mexico and farther north along the Mississippi River, to the area where they live today. Disease caused more deaths than did warfare and ultimately resulted in dramatic social disruption and defeat of the people. The use of alcohol also took its toll, as they were highly vulnerable to it. By 1784, the combined numbers of the tribes had fallen to 180. In the early 1800s, a small group was absorbed by the Houma of Louisiana.

In the late 18th century, the British deported the Acadians (French colonists in Acadia) from eastern Canada after defeating France in the Seven Years' War and taking over their territories in North America east of the Mississippi River. Some Acadian refugees were resettled in Louisiana along the Mississippi River; their descendants became known as Cajuns. They also put pressure on the Chitimacha population because they took over their land.

Eventually some Chitimacha married Acadians and gradually became acculturated to their community, including converting to Catholicism. Others absorbed Europeans into Chitimacha society. Mixed-race children born to Chitimacha women were considered to belong to their mother's families and generally were raised within the Indigenous culture.

The Chitimacha in the mid-19th century sued the United States for confirmation of title to their tribal land. The federal government issued a decree establishing an area of 1,062 acres in St. Mary Parish as Chitimacha land.

20th century
The 1900 federal census recorded six Chitimacha families with a total of 55 people, three of whom were classified as full-bloods. In 1910 there were 69 Chitimacha recorded; 19 of their children were students at the Carlisle Indian School in Pennsylvania, where they boarded full time along with other Native American students from a wide variety of tribes. The Indian boarding schools were considered a means to assimilate the children into mainstream United States culture. They disrupted transmission of native languages by forcing the children to use English at school and taking them away from their families for lengthy periods of time.

The tribe was under economic pressure in the early 20th century, and sometimes members were forced to sell land because they could not afford taxes. Sarah Avery McIlhenney, a local benefactor whose family owned and operated the factory to manufacture Tabasco, responded to a call for aid by Chitimacha women. She purchased their last 260 acres of land at a sheriff's sale in 1915; then transferred it to the tribe. They ceded the land to the federal government (Department of Interior) to be held in trust as a reservation for the tribe. McIlhenny also encouraged Federal recognition of the Chitimacha as a tribe, which the Department of Interior granted in 1917. The Chitimacha were the first Native American tribe in Louisiana to gain federal recognition. Most Native Americans of the Southeast had been forcibly removed to Indian Territory or Texas west of the Mississippi River during the 1830s. The tribe received some annuities and financial benefits as a result of formal recognition. But the population continued its decline and by 1930, the Chitimacha had a recorded total of 51 people. Between 1903 and 1919, tribal members of mixed African and Native American ancestry were disenrolled from the Chitimacha tribe of Louisiana, and their descendants have since then been denied tribal membership.

Since that early 20th-century low, the population has increased as the people have recovered. Men began to gain better employment by working in the Louisiana oil fields as drillers and foremen. In the early 21st century, the tribe reported it has more than 900 enrolled members. The 2000 census reported a resident population of 409 persons living on the Chitimacha Indian Reservation. Of these, 285 identified as solely of Native American ancestry.

The reservation is located at 29.88389°N, -91.53111°W in the northern part of the community of Charenton, in St. Mary Parish on Bayou Teche. This is in the Atchafalaya Basin, a rich estuary. The Chitimacha are the only Indigenous people in the state who still control some of their traditional lands. As with many Native American tribes, the Chitimacha took over their children's education and have established the Chitimacha Tribal School on the reservation; it is sponsored by the Bureau of Indian Affairs.

The Tribal Council is involved in ongoing negotiations with the United States to obtain compensation for the land expropriations of the past. With revenues derived from its gaming casino, the Chitimacha have purchased additional land to be held in trust for its reservation, and now control 1000 acres. It has established a casino, school, fish processing plant, and tribal museum on its reservation.

21st century
Native Waters: A Chitimacha Recollection (2011) is a documentary directed and produced by Laudun for Louisiana Public Broadcasting. It won a 2012 Telly Award.

Language
The Chitimacha language became extinct after the last two native speakers, Benjamin Paul and Delphine Ducloux, died in the 1930s. But young linguist Morris Swadesh had worked with Paul and Ducloux from 1930 to record their language and stories. He made extensive notes in an effort to save the language and its traditional accounts. Most contemporary Chitimacha speak Cajun French and English.

With revenues from gaming, the tribe has established cultural revitalization activities: a tribal historic preservation office, language immersion classes, a tribal museum, and a project to promote river cane regrowth on tribal lands to support weaving traditional baskets. In the early 1990s, the tribe was contacted by the American Philosophical Society Library, which said it held Swadesh's papers and had found extensive notes on the Chitimacha language, including a draft grammar manual and dictionary. A small team was recruited to try to learn the language quickly and begin to prepare materials to transmit it, such as a storybook. Language immersion classes were started in the school for children.

In 2008 the tribe partnered with Rosetta Stone to develop software to document the language and provide teaching materials. Each tribal household was given a copy of the software, to support families learning the language and encouraging children to speak it at home. The collaborative project is also producing a complete dictionary and learner's reference grammar for the language.

Government
The Chitimacha re-established their government under the Indian Reorganization Act of 1934, considered President Franklin D. Roosevelt's Native American New Deal. The tribe successfully resisted efforts in the 1950s to terminate them as a tribe under federal policy of the time, a move which would have ended their relationship with the federal government.

In 1971 they adopted a new written constitution. They have an elected representative government, with two-year terms for the five members of the Tribal Council. Three are elected from single-member districts and two members are elected at-large.

Citizenship
Like all federally recognized tribes, the Chitimacha, through passage of their constitution, have established their own rules for tribal membership. According to the constitution, they require that members have a certain blood quantum and be able to document direct descent from a member listed on one of two official rolls:
 * Annuity Pay Roll of 1926, recorded by the Bureau of Indian Affairs, or
 * Revised census roll of June 1959, of record at the Choctaw Indian Agency, Philadelphia, Mississippi.

In addition, a prospective member must be able to document having at least one-sixteenth (1/16) degree Chitimacha Indian ancestry (equivalent to one great-great-grandparent). Children of one-sixteenth (1/16) degree or more Chitimacha Indian blood born to any enrolled member since 1971 (when the tribe adopted their Constitution) are entitled to membership.

Basketry
Among their arts, Chitimacha women weave highly refined baskets from rivercane. They typically use three colors: yellow, red, and black. They have woven baskets for sale throughout the centuries to today, as an important part of their economy. One basket maker who excelled at the double-weave technique, Ada Thomas, was honored as a National Heritage Fellow by the National Endowment for the Arts in 1983.

Notable Chitimacha people

 * Christine Navarro Paul (1874–1946), basket maker
 * Ada Thomas (1924–1992), basket maker

title: Chitimacha


text:
Judge Reinhold

Edward Ernest "Judge" Reinhold Jr. (born May 21, 1957) is an American actor who is best known for his work in Hollywood films during the 1980s. He has starred in several popular films such as Stripes (1981), Fast Times at Ridgemont High (1982), and Ruthless People (1986). He has co-starred in all of the films in the Beverly Hills Cop series (1984, 1987, 1994, and 2024) and The Santa Clause (1994, 2002 and 2006) franchises.

Early life
Reinhold was born in Wilmington, Delaware, the son of Regina Celeste ( Fleming; 1923–2023) and Edward Ernest Reinhold (1907–1977), a trial lawyer. He was raised in Fredericksburg, Virginia and attended James Monroe High School until his family moved to Martin County, Florida prior to his junior year in high school. He attended Mary Washington College and Palm Beach Community College (known as "Palm Beach Junior College" at the time). His maternal grandfather was from County Meath, Ireland.

Early roles
Reinhold had a lead role in the movie Running Scared (1980) and a supporting part in the comedy Stripes (1981), which was a big hit. He was one of many names in the flop comedy Pandemonium (1982).

Reinhold's first major film role was as high school senior Brad Hamilton in Fast Times at Ridgemont High (1982), along with then-unknown actors Sean Penn, Phoebe Cates, Forest Whitaker, Jennifer Jason Leigh, and Nicolas Cage. "I thought my career would really take off after that role," Reinhold said later. "Instead, Sean's career took off."

Reinhold had small roles in The Lords of Discipline (1983) and Gremlins (1984), and he appeared in an uncredited role in Pat Benatar's music video for "Shadows of the Night".

Beverly Hills Cop and stardom
Reinhold's career began to gain momentum when he played Detective Billy Rosewood, the junior police detective sent to trail Eddie Murphy's character, in Beverly Hills Cop (1984).

The film's success led to Reinhold being given starring roles in Roadhouse 66 (1985), Head Office (1985) and Off Beat, but none of those were particularly successful. However, Ruthless People (1986), where he had a supporting role, was a big hit. That year, he said in an interview, "In my movies I portray this 'Everyman' persona, someone everybody can empathize with. People can identify with a guy like me."

Reinhold tried to get financing for a film based on Carl Hiaasen's best-selling novel Tourist Season, but it was never made. Instead, he appeared in Beverly Hills Cop II (1987), which was another large success.

Reinhold was given the lead in Vice Versa (1988), but it flopped. "That was really the end of my highfalutin Hollywood career," Reinhold said later. "That's when the phone stopped ringing." He also developed a reputation for being difficult on set. "I was spoiled, and I was arrogant," said Reinhold of this period later. "I was very demanding, had an overblown image of who I was and got a reputation for being difficult. And rightfully so."

Return to supporting roles
He had supporting roles in Rosalie Goes Shopping (1989) and Daddy's Dyin': Who's Got the Will? (1990) and the lead in Enid Is Sleeping (1991) and Zandalee (1991).

Reinhold starred in the Canadian hard rock band Harem Scarem's 1992 music video "Honestly" as the male love interest. In 1994, Reinhold appeared in Beverly Hills Cop III and The Santa Clause. He reprised the latter role of Dr. Neal Miller in The Santa Clause 2 (2002) and The Santa Clause 3: The Escape Clause (2006).

Later career
Reinhold was nominated for an Emmy for a role on Seinfeld in which he played the "close talker" who develops an obsession with Jerry's parents. He can also be seen in Steven Spielberg's epic miniseries Into the West and replaced Charles Grodin in two direct-to-video movies in the Beethoven film series.

Reinhold appeared in the 2008 political satire Swing Vote.

In September 2022, it was confirmed Reinhold reprised his role as Detective Billy Rosewood in Beverly Hills Cop: Axel F.

Personal life
Reinhold was nicknamed "Judge" because, when he was a baby, he looked stern and judge-like.

He and his second wife, Amy Reinhold, have a daughter named Haley Rose who was born in February 2013. They live together in Little Rock, Arkansas.

Reinhold was arrested at Dallas Love Field airport on December 8, 2016, for disorderly conduct after objecting to a patdown from security shortly after he was released from the hospital following an adverse reaction to a medication. He spent ten hours in jail and accepted a deferred adjudication agreement under which charges would be dismissed in 90 days.

In popular culture
Reinhold has occasionally been referred to in film and television, largely in reference to his nickname, Judge. The earliest example was Clerks: The Animated Series, where Reinhold voiced a judge called Judge Reinhold. In the Becker episode "Trials and Defibrillations", the presiding judge is called Judge (Miriam) Reinhold.

In Arrested Development, Reinhold, playing himself, appears as the judge of a fictional court show, a parody of such series as The People's Court, Judge Judy and Judge Mathis. In the film Fanboys, Billy Dee Williams appears as a courtroom judge named "Judge Reinhold".

Reinhold stars as the ex-boyfriend, terrorized by a jilted lover, in Jo-El Sonnier's 1988 music video for "Tear Stained Letter".

title: Judge Reinhold


text:
Stockholm, New Jersey

Stockholm is an unincorporated community located in the southeastern part of Hardyston Township in Sussex County, in the U.S. state of New Jersey. Its ZIP Code is 07460. Like many neighboring towns, Stockholm is home to a number of lakes including Deer Trail Lakes, Lake Stockholm, Lake Gerard, Beaver Lake, Lake Tamarack and Summit Lake.

Stockholm was known in colonial times as "Snufftown", which got its name from the action for traveling to the top of the mountain to go buy liquor. Those residing in other towns would proceed to Snufftown to go drinking. The New Jersey Midland Railway named a station in the area "Stockholm", which replaced "Snufftown". Despite the name, there is no evidence of a connection to Sweden or to settlement by Swedes in the area.

As of the 2010 United States Census, the population for ZIP Code Tabulation Area 07460 was 3,457.

Climate
This climatic region is typified by large seasonal temperature differences, with warm to hot (and often humid) summers and cold (sometimes severely cold) winters. According to the Köppen Climate Classification system, Stockholm has a humid continental climate, abbreviated "Dfb" on climate maps. This climate makes it suitable for naturism and the Rock Lodge Club naturist resort is near Lake Stockholm.

Emergency service
The Stockholm Fire Department, also known as the Hardyston Fire Department Company 1, was founded in 1955. It is located at 7 Colson Terrace.

Notable people
People who were born in, residents of, or otherwise closely associated with Hardyston Township include:
 * A. L. A. Himmelwright (1865-1936), a civil engineer, author, adventurer and marksman who was the general manager of The Roebling Construction Company.
 * Christopher Sieber (born 1969), actor best known for his roles as Kevin Burke in Two of a Kind starring Mary-Kate Olsen and Ashley Olsen, and Lord Farquaad in Shrek the Musical.

title: Stockholm, New Jersey


text:
Talk:1916 Summer Olympics

Comment
Why does this need a Wikipedia article?? Are there many people who think there really were Olympics in 1916?? 66.245.119.206 00:04, 26 May 2004 (UTC)

 * H.L. Mencken had something to say on that point - not about the Olympics, but about it being impossible to underestimate the intelligence of...ah well, people, I don't want to be US-centric here ;-) even when it's directed at my own country. Ellsworth 22:54, 20 Jun 2004 (UTC)

 * For the sake of completeness, if nothing else. It could even go further in-deph, illustrating how much work was done, and the details behind the cancellation. Nprefontaine 23:41, 14 Oct 2005 (UTC)

 * There was planning and preparation. It was not a null event. -68.90.158.6 (talk) 03:28, 5 March 2010 (UTC)

Incomprehensible phrase
...because the IOC designed to Berlin over Budapest...

Huh? --zenohockey 06:09, 3 January 2006 (UTC)

Image
Is there any type of main image anyone can get for this to make this look similar to the other pages of the Olympic Games?

Was there ever any image/logo for the 1916 games?

A program cover, official logo, etc.?

Berlin 1916 dates
According to this web site: Marcolympics, site dedicated to all Olympics programs (www.marcolympics.com) the Games of the VI Olympiad was scheduled to start in Febraury 1st to August 20, 1916: From 1 to 6th Febraury would be celebrated winter sports competitions.--Nekko09 (talk) 23:29, 21 February 2010 (UTC)

Move discussion in progress
There is a move discussion in progress on Talk:1896 Summer Olympics which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 18:47, 24 April 2022 (UTC)

Move discussion in progress
There is a move discussion in progress on Talk:1896 Summer Olympics which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 15:46, 9 February 2023 (UTC)

 * These discussions do not seem to have resulted in a consensus. Rontrigger (talk) 04:25, 10 June 2023 (UTC)

"Before the war started"
I suggest that if it is ultimately decided not to move this page, that the section "Before the war started" be removed. It seems to have been written at about a high-school level to begin with, and I heavily edited it before finally giving up. Rontrigger (talk) 04:27, 10 June 2023 (UTC)

title: Talk:1916 Summer Olympics


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Full Circle (The Doors album)

Full Circle is the eighth studio album by the American rock band the Doors, released in August 1972. It is the second album after Jim Morrison's death, and their last until the 1978 album An American Prayer. The album includes "The Mosquito", the last Doors single to chart.

Recording and composition
The band's first album without Jim Morrison, 1971's Other Voices, had reached No. 31 on the Billboard chart, showing the group could survive Morrison's death. The band – now a trio consisting of keyboardist Ray Manzarek, guitarist Robby Krieger, and drummer John Densmore – chose to record Other Voices at their rehearsal space known as the Workshop, the same two-story building at 8512 Santa Monica Boulevard they had recorded the successful L.A. Woman, but for Full Circle they opted to move to Hollywood's A&M Studio. While Other Voices was, to a degree, an extension of the L.A. Woman sessions (some of the tracks had been worked up before Morrison had left for Paris), Full Circle was a standalone work that saw the band delve deeper into jazz and work with some top-shelf session musicians. Bruce Botnick, who had engineered all the Doors albums up to that point and co-produced both L.A. Woman and Other Voices, declined to participate in the sessions. In 2015 he admitted to Uncut's Tom Pinnock that he could not remember whether he was asked to return or not, but maintains he would have turned down the offer, reflecting, "The guys wanted to have a chance to work with some other musicians. As they went into Full Circle they took that extension even further."

The Doors hired Henry Lewy to replace Botnick, who in turn brought in Charles Lloyd and a host of session players. Lloyd contributed tenor sax and flute to the songs and also played behind the band at Central Park and at the Hollywood Bowl. As with Other Voices, Manzarek and Krieger assumed vocal duties, which were augmented with backing vocalists. Although both post-Morrison albums are viewed as non-essential to many Doors fans and critics, Full Circle produced a global hit for the band: "The Mosquito". As recounted in Uncut's 2015 profile of both LPs, the song has become one of the band's most enduring tracks across the globe, with the song's author Krieger recalling:

"I was on vacation down in Mexico, and these three local musicians came down out of the hills. That would sing mariachi stuff, and they had this one song about a mosquito and that inspired me. That was actually our biggest selling single after Jim died because it was in Spanish and it did very well around the world.  Not only in Latin countries, but in Europe.  In fact there were a lot of covers, and some of them are pretty good."

Full Circle showed the band was still evolving musically, with the Latin fusion of "The Piano Bird" and the complex funk of "Verdilac," but tensions were mounting between Manzarek, who wanted to explore jazz, and Densmore and Krieger, who wanted to persevere with rock. "Ray just kinda said, 'Look, I'm outta here, I'm getting tired of this, it's not working,'" Krieger recalled to Uncut in 2015. "So we gave up. John and I were trying to make it work.  Would we have carried on?  Yeah, for sure."

In 1972, the Doors released "Get Up and Dance" as a single; the B-side was the non-album track "Treetrunk", one of only three non-album studio tracks released by the band. According to Robby Krieger, the track was left off the album because "it sounded too commercial." The song was finally given official re-release as part of the Japan edition of the Doors Singles Box in 2013.

Release and reception
Full Circle was released on August 15, 1972 and peaked at No. 68 on the Billboard chart. In a retrospective assessment, AllMusic stated "While there are a handful of undeniably remarkable cuts scattered throughout, Full Circle is increasingly sporadic and less focused than its predecessor" but asserts that the album's centerpiece is "the nearly four-minute jam tacked on at the end. Manzarek's impassioned electric organ, Densmore's tricky timekeeping, and Krieger's transcendent string work are all worth mentioning as the intensity of their interplay hearkens back to former glories." In 2011 Uncut surmised of the LP, "Now the problems start. A strained-sounding attempt to boogie like a bar band, with lame lyrics about "good rocking"... its eagerness to get our hands clapping makes it sound desperate."

Record World called the single "Get Up and Dance" a "steady rocker which is just different enough to stand up to repeated listenings."

Later releases
For years the Doors have largely disregarded the two post-Morrison albums, with no official American CD releases. Full Circle was released on CD October 23, 2006 by the Timeless Holland label, along with the previous (post-Morrison) Doors album Other Voices. It is relatively easy to find unofficial CD copies of Full Circle and Other Voices on the Internet, but most of these vinyl-to-CD transfers do not contain the single-only "Treetrunk", except for the Howling Wolf Records 2010 release of the two albums on one CD. This release also featured the edited single versions of "The Mosquito" and "The Piano Bird." "Treetrunk" was finally given official re-release as part of the Japan edition of the Doors Singles Box in 2013. The Doors' management has stated they are not in possession of the master tapes to the two post-Morrison albums, but remastered tracks from both of them can nevertheless be found on later official releases. The first track from Full Circle the Doors have reissued was "The Mosquito", released in 2000 as "No Me Moleste Mosquito" on the double-disc version of The Best of The Doors.

On September 27, 2011, the Doors finally gave Full Circle, along with Other Voices, its first official reissue through digital download. It was confirmed that the original master tapes were used for these reissues.

On May 29, 2015, it was announced that Other Voices and Full Circle would be re-released together on a 2-CD set and individually on 180-gram vinyl by Rhino Records on September 4 of that year. The CD set features "Treetrunk"—the B-side of the "Get Up and Dance" single—as its only bonus track.

Personnel
The Doors
 * Ray Manzarek – lead vocals, keyboards
 * Robby Krieger – lead vocals, guitar, harmonica
 * John Densmore – drums

Additional personnel
 * Chico Batera – percussion on "The Piano Bird" and "The Peking King and the New York Queen"
 * Leland Sklar – bass on "Hardwood Floor", "The Mosquito" and "It Slipped My Mind"
 * Jack Conrad – bass on "4 Billion Souls", "Good Rockin", "The Piano Bird" and "The Peking King and the New York Queen"; Rhythm Guitar on "The Piano Bird"
 * Charles Larkey – bass on "Verdilac" and "The Piano Bird"
 * Chris Ethridge – bass on "Get Up and Dance"
 * Venetta Fields – vocals
 * Clydie King – vocals
 * Melissa MacKay – vocals
 * Bobbye Hall – percussion on "Verdilac", "The Piano Bird" and "The Peking King and the New York Queen"
 * Charles Lloyd – tenor saxophone on "Verdilac", flute on "The Piano Bird"

Technical staff and artwork
 * The Doors – producer
 * Henry Lewy – engineer
 * Pacific Eye & Ear – cover concept
 * Joe Garnett – cover illustration

title: Full Circle (The Doors album)


text:
Talk:Full Circle (The Doors album)

Singles
Hey, should the non-album track "Tree Trunk" be mentioned in conjunction with the article? After all, it's one of only three non-album tracks The Doors released. The others, of course, being "Who Scared You?" and "Don't Go No Further". Hey, what track was it a B-side to, anyways? --Tirolion 12:18, 4 February 2007 (UTC)

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title: Talk:Full Circle (The Doors album)


text:
Beverly Hills Cop

Beverly Hills Cop is a 1984 American buddy cop action comedy film directed by Martin Brest, with a screenplay by Daniel Petrie Jr., and story by Danilo Bach and Daniel Petrie Jr. It stars Eddie Murphy as Axel Foley, a street-smart Detroit detective who visits Beverly Hills, California, to solve the murder of his best friend. Judge Reinhold, John Ashton, Ronny Cox, Lisa Eilbacher, Steven Berkoff, Paul Reiser, and Jonathan Banks appear in supporting roles.

This first film in the Beverly Hills Cop franchise shot Murphy to international stardom, won the People's Choice Award for "Favorite Motion Picture", and was nominated for both the Golden Globe Award for Best Motion Picture – Musical or Comedy and Academy Award for Best Original Screenplay in 1985. An immediate blockbuster, it received positive reviews and earned $234 million at the North American domestic box office, making it the highest-grossing film released in the U.S. in 1984.

Adjusted for inflation, it is the highest-grossing R-rated film in the U.S. since 1977, with a total box office gross of $730,714,743 in 2024 dollars.

Plot
Axel Foley is a plainclothes Detroit police detective whose latest unauthorized sting operation goes sour when two uniformed officers intervene, resulting in a high-speed chase through the city that causes widespread damage. Axel's superior, Inspector Douglas Todd, reprimands him for his reckless behavior and threatens to fire him unless he changes his ways.

Axel arrives at his apartment to find it has been broken into by his childhood friend, Michael "Mikey" Tandino. Mikey had done prison time for a car theft the pair had committed in their youth, but has since landed a job as a security guard in Beverly Hills thanks to mutual friend Jenny Summers.

Mikey shows Axel some German bearer bonds and Axel wonders how he got them, but chooses not to question him about it. After going out to a bar, they return to Axel's apartment, where two men, Zack and Casey, knock Axel unconscious, confront Mikey about the stolen bonds, and murder him.

Axel asks to be assigned to investigate Mikey's murder, but Inspector Todd won't allow it due to his close ties to Mikey. Under the guise of taking vacation time, Axel travels to Beverly Hills to solve the crime himself. He finds Jenny working in an art gallery and learns about Mikey's ties to Victor Maitland, the gallery's owner. Posing as a flower deliveryman, Axel goes to Maitland's office to question him about Mikey, but is thrown out of a window by Maitland's bodyguards and arrested for trespassing.

At the local police station, Beverly Hills Police Department Lieutenant Andrew Bogomil assigns Sergeant John Taggart and Detective Billy Rosewood to follow Axel. They have a humiliating and comical encounter with him when he temporarily disables their car. As a result, Rosewood and Taggart do not get along with Axel at first, but the three begin to develop a mutual respect after they foil a robbery at a striptease bar.

Continuing his investigation, Axel sneaks into one of Maitland's warehouses, where he finds crates full of coffee grounds. He suspects they have been used to pack drugs, since he knows they are often used to cover the scent of drugs from police dogs. Axel also discovers that many of Maitland's crates have not gone through customs.

After being arrested again, this time after a scuffle with Zack at Maitland's country club, Axel attempts to alert Bogomil that Maitland must be a smuggler, but Beverly Hills Police Chief Hubbard, who has learned of Axel's ill-advised investigative actions, orders that he be escorted out of town. Axel convinces Billy to pick up Jenny instead and take her with them to the warehouse, where a shipment is due to arrive that day.

Axel and Jenny break into the warehouse and discover several bags of cocaine inside a crate. Before he can get this new-found evidence to Billy, Maitland arrives with his associates Zack and Casey. Maitland takes Jenny and leaves Axel, ordering that he be killed. Zack then tells Axel that he was the one who killed Mikey. After some hesitation, Billy enters the warehouse and rescues Axel after a brief gunfight during which he kills Casey.

Taggart tracks Axel and Billy to Maitland's estate, where he joins the two in rescuing Jenny and bringing Maitland to justice. Together, the trio wipe out a number of Maitland's men, including Zack. With Bogomil's help, Axel then fatally shoots Maitland and rescues Jenny.

Bogomil fabricates a story to Hubbard that manages to cover for all the participants without discrediting the police department. Axel, realizing that his exploits while "on vacation" will likely get him fired, asks Bogomil to smooth matters over with Inspector Todd. When Axel mentions the possibility of setting up shop as a private investigator in Beverly Hills, Bogomil nervously agrees to wipe the slate clean for him.

Later, Taggart and Billy meet Axel as he is checking out of his hotel and pay his bill. He invites them to join him for a farewell drink, and they accept the offer.

Cast

 * Eddie Murphy as Detective Axel Foley
 * Judge Reinhold as Detective William "Billy" Rosewood
 * John Ashton as Sergeant John Taggart
 * Lisa Eilbacher as Jeanette "Jenny" Summers
 * Steven Berkoff as Victor Maitland
 * Ronny Cox as Lieutenant Andrew Bogomil
 * James Russo as Michael "Mikey" Tandino
 * Stephen Elliott as Chief Hubbard
 * Paul Reiser as Jeffrey Friedman
 * Bronson Pinchot as Serge
 * Jonathan Banks as Zack
 * Michael Champion as Casey
 * Frank Pesce as Cigarette Buyer
 * Gilbert R. Hill as Inspector Douglas Todd
 * Damon Wayans as Banana Man
 * Martin Brest as Beverly Palms Hotel Checkout Clerk

Development and writing
In 1977, Paramount executive Don Simpson came up with a movie idea about a cop from East L.A. who transferred to Beverly Hills. Screenwriter Danilo Bach was called in to write the screenplay. Bach pitched his idea to Simpson and Paramount in 1981 under the name Beverly Drive, about a cop from Pittsburgh named Elly Axel. However, his script was a straight action film and Bach was forced to make changes to the script, but after a few attempts the project went stale. With the success of Flashdance (1983), Simpson saw the Beverly Hills film as his next big project.

Daniel Petrie Jr. was brought in to rewrite the script and Paramount loved Petrie's humorous approach to the project, with the lead character now called Axel Elly, from Detroit. Producer Jerry Bruckheimer claimed that the role of Axel Foley was first offered to Mickey Rourke, who signed a $400,000 holding contract to do the film. When revisions and other preparations took longer than expected, Rourke left the project to do another film. Martin Scorsese was offered to direct the film but turned it down as he felt that the film's concept was too similar to Coogan's Bluff. David Cronenberg was also offered to direct the film but also turned it down.

Sylvester Stallone was originally considered for the part of Foley. Stallone gave the script a dramatic rewrite, removing all the story's humor and turning the film back into a standard action movie. In one of the previous drafts written for Stallone, the character of Billy Rosewood was called "Siddons" and was killed off half-way through the script during one of the action scenes. Stallone had renamed the lead character to Axel Cobretti, with the character of Michael Tandino being his brother and Jenny Summers playing his love interest.

Stallone has said that his script for Beverly Hills Cop would have "looked like the opening scene from Saving Private Ryan on the beaches of Normandy. Believe it or not, the finale was me in a stolen Lamborghini playing chicken with an oncoming freight train being driven by the ultra-slimy bad guy." Producer Don Simpson let it be known they didn't want to move forward with Stallone's revisions; since Stallone wasn't willing to negotiate the rewrite, Simpson asked writer Charles "Chip" Proser if he could return the script to previous iteration, while leaving most of Stallone's character revisions intact. However Proser found the task (and turnaround time) preposterous."'They offered me the rewrite when it was nothing more than Sylvester Stallone and an exotic gun—which was pretty ridiculous', remembered screenwriter Chip Proser, who would later write [an uncredited rewrite of] Simpson and Bruckheimer's Top Gun."According to co-producer Don Simpson, Stallone’s new script spent too much time on the star 'soaping down his muscles.' Stallone ultimately dropped out two weeks before filming was to start, ostensibly to concentrate on his next picture, the 1984 film Rhinestone. Stallone later used the bulk of these ideas as the basis for the 1986 film Cobra.

Don Simpson would later tell friends a story—impossible to corroborate—about how he finally got Stallone off the project and got the project back on track: He and Stallone had a mutual interest in "youth treatments" and Simpson knew of a Swiss doctor who was experimenting with injections of a sheep hormone that increased tumescence. Simpson managed to get Stallone's name "put at the top of the list," Simpson boasted to a friend, for an appointment with the very exclusive doctor. Stallone flew to Switzerland, and Simpson promptly continued working on Beverly Hills Cop without him.

Two days later, the film's producers, Simpson and Bruckheimer, convinced Eddie Murphy to replace Stallone in the film, prompting more rewrites. Besides Stallone and Rourke, other actors who were considered for the role of Axel Foley included Richard Pryor, Al Pacino, and James Caan. Harrison Ford was offered the role of Axel Foley but turned it down. The final shooting draft of the script, which was extensively revised with Murphy's input, was not completed until the day production began.

Filming
The film was budgeted at $14 million, including $4 million for Murphy, and was completed for around $13 million. Production began in May 1984 and continued into the summer, taking place mostly in and around Los Angeles. The opening sequence was filmed over several days in Michigan, in Detroit and nearby Wayne. Many scenes set in Beverly Hills were shot in Pasadena, as the city of Beverly Hills prohibited filming after 10:30 p.m.

Soundtrack
The soundtrack was released on MCA Records and won the Grammy Award for Best Score Soundtrack for Visual Media (1986). It featured three top 10 singles on the Billboard Hot 100, the instrumental title tune, "Axel F", composed and performed by Harold Faltermeyer, the Glenn Frey song "The Heat Is On", and "Neutron Dance," performed by the Pointer Sisters. The soundtrack also had two Patti LaBelle hits, "New Attitude," which hit the top twenty on the US, and the Grammy Award-winning "Stir It Up."

Box office
Beverly Hills Cop was released on December 5, 1984, in 1,532 theaters. It debuted in first place at the US box office, making $15,214,805 in its first five days of release. It expanded on December 21 into 2,006 theatres. The film stayed at number one for 13 consecutive weeks and returned to number one in its 15th weekend making 14 non-consecutive weeks at number one tying Tootsie for the film with the most weeks at number one.

The film earned $234,760,478 in the United States, being the highest-grossing film released in 1984. Adjusted for inflation, it is the third highest-grossing R-rated film of all-time behind The Exorcist and The Godfather. For nearly two decades, Beverly Hills Cop held the record for having the highest domestic gross for an R-rated film until 2003, when it was taken by The Matrix Reloaded.

Adjusted for inflation, it is the highest-grossing R-rated film of all time at the U.S. box office, with a total box office gross of $730,714,743 in 2024. Box Office Mojo estimates that the film sold over 67 million tickets in the US.

Critical response
On review aggregation website Rotten Tomatoes the film has an approval rating of 83% from 53 critics with an average rating of 7.3/10. The site's consensus reads, "The buddy cop movie continues its evolution unabated with this Eddie Murphy vehicle that's fast, furious, and funny." Janet Maslin of The New York Times wrote "Beverly Hills Cop finds Eddie Murphy doing what he does best: playing the shrewdest, hippest, fastest-talking underdog in a rich man's world. Eddie Murphy knows exactly what he's doing, and he wins at every turn."

Richard Schickel of Time magazine wrote that "Eddie Murphy exuded the kind of cheeky, cocky charm that has been missing from the screen since Cagney was a pup, snarling his way out of the ghetto." Axel Foley became Murphy's signature role and was ranked No. 78 on Empire magazine's list of The 100 Greatest Movie Characters of All Time. Entertainment Weekly magazine ranked Beverly Hills Cop as the third best comedy film of the last 25 years. According to Christopher Hitchens, the British novelist and poet Kingsley Amis considered the film "a flawless masterpiece."

John Simon of National Review called Beverly Hills Cop "a truly contemptible film."

In 2003, the film was picked by The New York Times as one of The 1000 Best Movies Ever Made.

Accolades

 * This film is No. 22 on Bravo's list of the 100 funniest films.

American Film Institute Lists
 * AFI's 100 Years... 100 Movies – Nominated
 * AFI's 100 Years... 100 Laughs – #63
 * AFI's 100 Years... 100 Heroes and Villains:
 * Detective Axel Foley – Nominated Hero

Sequels
The film spawned a film series with three sequels, Beverly Hills Cop II, Beverly Hills Cop III and Beverly Hills Cop: Axel F, all starring Eddie Murphy. Judge Reinhold reprised his role for the sequels. John Ashton returned for the second and fourth film, but not third. The second film met with mixed reviews but was a box office success, while the third film was unsuccessful, both critically and commercially.

In 2013, a television series was reported to be in the works for CBS. The pilot was written by Shawn Ryan and directed by Barry Sonnenfeld. Brandon T. Jackson was cast as Axel Foley's son. The series was not picked up, but Ryan reported that it tested well enough for Paramount to put a fourth film into production.

On November 14, 2019, Deadline Hollywood announced that Paramount Pictures made a one-time license deal with an option for a sequel to Netflix to create the fourth film. In April 2022, Mark Molloy was announced as the film's director, while Will Beall penned the script. The official teaser trailer for the fourth film was released on December 14, 2023. The film was released in July 2024.

title: Beverly Hills Cop


text:
Frederick Ouseley

Sir Frederick Arthur Gore Ouseley, 2nd Baronet (12 August 1825 – 6 April 1889) was an English composer, organist, musicologist and priest.

Biography
Frederick Ouseley was born in London, the son of Sir Gore Ouseley, and manifested an extraordinary precocity in music, composing an opera (L'Isola disabitata) at the age of eight years. In 1844 he succeeded to the baronetcy. He had matriculated at Christ Church, Oxford in 1843, where he graduated BA in 1846 and MA in 1849. He was ordained in the latter year, and, as curate of St. Paul's Church, Knightsbridge, served the parish of St. Barnabas, Pimlico until 1851.

Throughout his life, Ouseley experienced a social conflict between his aristocratic heritage and his interest in the performance of Anglican church music, an activity which was seen as beneath someone of his stature. In 1850 he took the degree of Mus.B. at the University of Oxford, and four years afterwards that of Mus.D., his exercise being the oratorio The Martyrdom of St Polycarp. He was Heather Professor of Music at Oxford from 1855 to 1889. In 1856, Ouseley both founded and endowed with his own funds St Michael's College on the outskirts of Tenbury Wells, a choir school intended to serve as a model for Anglican church music. Ouseley was very clear that the standard of music in the English church was lacking and through his Foundation at Tenbury, he would help to change that. As well as being the College founder, he became the school's first Warden.

Death
Ouseley died in Hereford, where he had been precentor at Hereford Cathedral since 1855.

Works
Ouseley's works included a second oratorio, Hagar (Hereford, 1873), a great number of services and anthems, psalm chants, cantatas, chamber music, organ pieces and songs. Among his instructional treaties on harmony, counterpoint, fugue, and composition are Harmony (1868) and Counterpoint (1869) and Musical Form (1875). He also added a series of chapters on English music to the English translation of Emil Naumann's History of Music, the subject having been practically ignored in the German treatise.

Choral
[unfinished]
 * Anthems:
 * All the kings of the earth
 * And there was a pure river of Water of life
 * And there was a war in heaven
 * Ascribe ye greatness
 * Awake, thou that sleepest
 * Behold, how good and joyful
 * Behold now, praise the Lord
 * Be merciful unto me
 * Blessed be the Lord God of Israel
 * Blessed be Thou
 * Blessed is he whose unrighteousness
 * Blessed is the man
 * Christ is risen from the dead
 * Except the Lord build the house
 * From the rising of the sun
 * Give thanks, O Israel
 * Great is the Lord
 * Happy is the man
 * Haste Thee, O God
 * How goodly are the tents
 * Is it nothing to you
 * It came even to pass
 * Jerusalem on high
 * O Saviour of the world
 * Oratorios
 * St Polycarp (1854)
 * Hagar (Hereford Festival, 1873)
 * Services
 * Evening Service in B flat
 * Evening Service in E flat
 * Miscellaneous
 * Gloria in D
 * Te Deum in D
 * Te Deum in F
 * Hymn tunes
 * Contemplation (When all thy mercies, O my God)
 * Hereford (When wounded sore the stricken heart)
 * Bewdley (Children of the heavenly King)
 * St. Gabriel.

title: Frederick Ouseley