Talk:Polar coordinate system

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Polar coordinate system is a featured article; it (or a previous version of it) has been identified as one of the best articles produced by the Wikipedia community. If you can update or improve it, please do.

This article appeared on Wikipedia's Main Page as Today's featured article on February 17, 2007.

Article Milestones
Date	Process	Result
September 14, 2006	Good article nominee	Listed
September 16, 2006	Peer review	Reviewed
January 31, 2007	Featured article candidate	Promoted
Current Status: Featured article

This article is within the scope of WikiProject Mathematics.
Mathematics grading:	FA Class	Top Importance	Field: General

This page has been selected for the release version of Wikipedia and rated FA-Class on the assessment scale. . It has been rated Top-Importance on the importance scale.

1 Merge polar graph into polar coordinate system
2 Good articles
3 Elliptical coordinates
4 Another GA Reviews
5 Good Article
6 References
7 Spherical coordinates
8 Partial (trapezoidal) section of sphere/ellipsoid surface
9 Comments
10 Alternative formula for the angular coordinate
11 Section on complex numbers
12 Applications
13 Area swept out
14 Other Shapes
15 NPOV
16 Polar coordinates!
17 2D ?
18 Factual error on the page
19 Further problems in the article

[edit] Merge polar graph into polar coordinate system

I think that these two articles are essentially the same thing, so merging them is the best thing to do. Polar coordinate system is a more complete article, so polar graph should be merged into it. --Mets501^talk 03:19, 19 April 2006 (UTC)

I performed the merge. It seems like no one should have any objections. --Mets501^talk 18:47, 19 April 2006 (UTC)

[edit] Good articles

History, history, its always history! A lack of any discussion on the history of polar coordinates. Who first introduced them, how did the theory develop? Other than that a nice article. --Salix alba (talk) 08:05, 7 September 2006 (UTC)

I added a short history section, though I'm sure it could be expanded. Newyorkbrad 13:52, 8 September 2006 (UTC)

[edit] Elliptical coordinates

You can sort of think of Polar coordinates as being a limiting case of Elliptic coordinates. From the definition of

$x = a \ \cosh \mu \ \cos \nu, y = a \ \sinh \mu \ \sin \nu$

if we let $\mu = \ln(2 r/a)\,$ then $a \cosh(\mu)={a\over 2}(e^{\ln(2 r/a)}+e^{-\ln(2 r/a)})={a\over 2}(2 r/a+a/(2 r))=r+a^2/(4 r)$ . In the limit as a tends to zero, this becomes simply r. The same holds for $a \sinh(\mu)\to r\,$ , and hence the the equations become those of polar coordinates. --Salix alba (talk) 15:44, 9 September 2006 (UTC)

[edit] Another GA Reviews

The lead section is not enough to summarize the article. A context about this article should be given in the lead section, including some advantages and disadvantages using Polar coordinate system. The lead section should explain what the article is about for common readers, that does not have specific knowledge about the article. Guideline is given here: WP:LS.
In Polar Equations section, the statement A polar line/curve is symmetric about the 0°/180° line if replacing θ by −θ in its equation produces in an equivalent equation, symmetric about the 90°/270° line if replacing θ by π−θ produces an equivalent equation, and symmetric about the pole if replacing r by −r produces an equivalent equation. is unclear for a common reader to understand it.
I think the article needs to be expanded further and deeper, rather than just listing Polar Equations for some popular geometrical shapes.

— Indon (reply) — 08:36, 10 September 2006 (UTC)

I've dealt with the first two issues (and Newyorkbrad helped copyedit), but I'm not quite sure what to do about the third. —Mets501 (talk) 14:20, 10 September 2006 (UTC)

Either get to the library and do some research, or ask Salix alba to help out. :) Newyorkbrad 14:26, 10 September 2006 (UTC)

A real library, what's that? :-) Salix alba looks like he knows what he's talking about, though, he should be able to help. —Mets501 (talk) 14:32, 10 September 2006 (UTC)

What me know what I'm talking about, just commiting a bit of original research and shouting history!

Anyway I did a bit of digging in google which turned up

Gregory St. Vincent (Grégoire de Saint-Vincent), with -

The Greeks described a spiral using an angle and a radius vector, but it was St. Vincent and Cavalieri who simultaneously and independently introduced them as a separate coordinate system. In an article The Origin of polar coordinates, J. J. Coolidge refers to the priority dispute between Cavalieri and St. Vincent over their discovery. St. Vincent wrote about this new coordinate system in a letter to Grienberger in 1625 and published the process in 1647. On the other hand Cavalieri's publication appeared in 1635 and the corrected version in 1653.
and Milestones in the History of Thematic Cartography

Development of the use of polar coordinates for the representation of functions. Newton's Method of Fluxions was written about 1671, but not published until 1736. Jacob Bernoulli published a derivation of the idea in 1691. [238,p. 324] attributes the development of polar coordinates to Fontana, with no date.- Isaac Newton (1643-1727), England, and Gregorio Fontana (1735-1803) and Jacob Bernoulli (1654-1705) [238,p. 324]. 1671 is probably too early; 1736--1755 would probably be more appropriate. There are earlier references to Hipparchus (190-120BC) regarding the use of polar coordinates in establishing stellar positions, and Abu Arrayhan Muhammad ibn Ahmad al-Biruni (1021) regarding the use of three rectangular coordinates to establish a point in space.

1843 Use of polar coordinates in a graph(frequency of wind directions)- Léon Lalanne (1811-1892), France [148].
La Habra High School Math History Timeline

Jacob Bernoulli invents polar coordinates, a method of describing the location of points in space using angles and distances.
Sherlock Holmes in Babylon and Other Tales of Mathematical History has a section

Newton as an originator of polar coordinates
Jacob Amsler http://www-history.mcs.st-and.ac.uk/~history/Printonly/Amsler.html

[Amsler] invented the polar planimeter, a device for measuring areas enclosed by plane curves. It was based on polar coordinates whereas earlier instruments were based on cartesian coordinates. In 1856 Amsler published a paper Über das Planimeter in which he gave details of his idea. As Mahoney writes in [1], Amsler's planimeter:- ... adapted easily to the determination of static and inertial moments and to the coefficients of Fourier series: it proved especially useful to shipbuilders and railway engineers.

So it seems there is considerable different accounts of their introduction, and quite a few notable applications. --Salix alba (talk) 16:10, 10 September 2006 (UTC)

Nice research! Do you want to add that to the article (the fact that there are differences in opinion)? —Mets501 (talk) 19:25, 10 September 2006 (UTC)

I think he's leaving it for you to do. :) Although I'm not sure whether it's a matter of differences of opinion, or just that different mathematicians used the concept at different times to do different things. Also regarding expanding the article, you might want to explain in more detail what types of real-world problems are solved more easily using polar coordinates than Cartesian ones. Newyorkbrad 19:33, 10 September 2006 (UTC)

[edit] Good Article

After reading the changes, this article qualifies as Good Article status.

Per WP:WIAGA,

1. Well written

I enjoy reading this article, as there's no complicated mathematical statements. Non specialist readers can benefit for this kind of article to learn about the subject. Structure is quite logical and the lead section has been improved to state the context of this article. I like how editors put mathematical equations. Technical jargons are simply and briefly explained.

2. Factually accurate and verifiability

References are enough and reliable. I cannot really check whether mathematical equations given are accurate, but I hope there is no mathematical typos in the equations. Inline citations are given in the History section.

3. Broad in its coverage.

Broad enough and not too much unnecessary details.

4. Neutral point of view policy.

Passes.

5. Stable

Passes.

6. Images

Very good illustrations. Geometrical shapes are displayed properly to give a good illustration of the polar equations.

Congratulation to the editors' hard work for this article. Further improvements can lead this article to FA status. — Indon (reply) — 09:46, 14 September 2006 (UTC)

Thanks for evaluating it, Indon! —Mets501 (talk) 11:05, 14 September 2006 (UTC)

Polar coordinates is indeed going to feature on the main page someday, although Mr. Mets may not yet appreciate how much work he gets to do on it between now and then. I'll help too, of course. Newyorkbrad 21:05, 14 September 2006 (UTC)

Don't worry, I realise this article isn't near featured status yet :-) —Mets501 (talk) 21:16, 14 September 2006 (UTC)

[edit] References

Format of authors' names in references should be consistent -- either last name first or first name first. Not sure which one you want but we need to pick one or the other. Newyorkbrad 20:01, 16 September 2006 (UTC)

Last, first seems to be the standard (as per the cite templates) so I've changed it all to that. —Mets501 (talk) 20:54, 16 September 2006 (UTC)

[edit] Spherical coordinates

Adding the section on extension to three dimensions is good. Note that cylindrical coordinates have their own article, but spherical coordinates are discussed under coordinate system. I'm not much of a math editor but there should probably be more consistent cross-referencing between all these articles. In a perfect world, either spherical would be a separate article or cylindrical would not, for parallelism, but making either change would be a little bit too BOLD for me. Newyorkbrad 16:58, 17 September 2006 (UTC)

Yes the various coordinate articles are messy, for starters we have Coordinate system and coordinates (mathematics) which have a large overlap, perhaphs they should be merged. I certainly think that spherical coordinates deserves its own article. Theres also less well know systems like Oblate spheroidal coordinates which don't get a mention, Orthogonal coordinates seems to have a more comprehensive list. A bit of boldness and some cutting, pasting, moving and merging would not go amis. --Salix alba (talk) 17:23, 17 September 2006 (UTC)

I'm being bold and creating a spherical coordinate article. The geographic coordinate system article should probably get a mention as well. I didn't know about it when I originally wrote the spherical coordinate section. --Carl ^{(talk|contribs)} 17:42, 17 September 2006 (UTC)

[edit] Partial (trapezoidal) section of sphere/ellipsoid surface

What is a trapezoidal shaped section of a sphere or ellipsoid's surface called? I think it is something like "quadratic angle" or "quadrilateral section"—? ~Kaimbridge~ 19:37, 12 December 2006 (UTC)

A better place for this would be the Mathematics reference desk. —Mets501 (talk) 21:26, 12 December 2006 (UTC)

Yes - answer is provided there.83.100.254.21 17:58, 13 December 2006 (UTC)

[edit] Comments

This is in response to the request for comment User:Mets501 posted at WPM.

Some comments after a brief scan:

There is no discussion of the problems with the polar coordinate system such as the (coordinate) singularity at the origin or the difficulties associated with the multivaluedness of the θ coordinate.
There should be some mention of the Euclidean metric in these coordinates as well as a discussion of integrating functions in polar coordinates, i.e.

$\int_{r_0}^{r_1}\int_{\theta_0}^{\theta_1}f(r,\theta)\,rd\theta\,dr$
I view as suspect any article using MathWorld as a reference. Some of the references could be improved.
I find the cis(θ) notation to be bizarre and nonstandard. Mention Euler's formula and then just use e^iθ like everyone else.
There is some inconsistency with writing sin θ vs. sin(θ). Not a big deal, just looks weird.

-- Fropuff 00:50, 21 December 2006 (UTC)

Thanks for the comments; I'll place them in a todo section above. It's funny how you say that the cis(theta) notation is "bizarre and nonstandard", it's the only way that I wrote it in school. I will change it however, because if it's awkward to you it most likely is for others as well. —Mets501 (talk) 03:07, 21 December 2006 (UTC)

Note in particular that the "cis" notation receives a serious thrashing in Trigonometric_identities#Pedagogy_and_.22cis.22. I guess it's something of a political issue that we shouldn't get bogged down in, but people might want to look at that article for guidance/ideas on how to handle this. (I saw it in high school, and hated it immediately.) William Ackerman 15:12, 21 December 2006 (UTC)

I don't interpret the text in List of trigonometric identities as "thrashing". I agree with avoiding the use of this cis function here, though. --Lambiam ^Talk 17:11, 21 December 2006 (UTC)

Interesting. Maybe it is standard in some places. Honestly, I've never seen it outside Wikipedia. I do think the article looks much better now with the exponential form. -- Fropuff 03:42, 21 December 2006 (UTC)

We used "cis" notation in school too (late 1970's) so I agree it's been the standard (at least in New York State). Historically, I believe "cis" notation was recommended for publication because it can all sit on one line, as opposed to the alternative. This was important when typesetting was done manually and setting subscripts or exponents could require handwork by the printer with associated costs in time, expense, and risk of error. See any pre-computer-age edition of the Chicago Manual of Style etc. Those considerations, of course, no longer apply today. Newyorkbrad 17:25, 21 December 2006 (UTC)

Never heard of "cis' before. linas 22:43, 21 December 2006 (UTC)

See cis (which is a disambiguation page, look for "in mathematics" near the bottom). Newyorkbrad 23:07, 21 December 2006 (UTC)

Some more GA-article comments: Applications: the applications section should mention the use of polar plots for antenna (radio) radiation patterns (see also side lobe), and for microphone polar paterns (sensitivity plots_. These applications are far more "common" than any of the others mentioned: in particular, they actually have a number of actual polar plots in the articles, whereas the articles on the other applications (robots, compressors, etc) do not. linas 22:43, 21 December 2006 (UTC)

[edit] Alternative formula for the angular coordinate

Currently this article only has a formula to calculate the angular coordinate in the interval [0, 2π). However, in many cases, e.g. complex numbers, the angular coordinate usually is calculated in the interval (-π, π]. Therefore I suggest to add a formula for this case, so other articles like "complex number" can reference to this article. As a compensation the section on complex numbers could be merged into the article on complex numbers. --IP 01:35, 2 January 2007 (UTC)

[edit] Section on complex numbers

I suggest to remove the section on complex numbers, because all this is treated in the article complex number. Perhaps a note could be made that polar coordinates are used e.g. in complex numbers. Instead, it would be useful to extend the section on calculating the angular coordinate with a formula that provides the angle in the interval (-п, п] as it is used in complex numbers. --IP 12:55, 2 January 2007 (UTC)

I think the section is good. It happens to be one of the major uses of the polar coordinate system in mathematics, so it should belong in the polar coordinate system article. It can also have the same information as complex number with no problems. —Mets501 (talk) 21:49, 2 January 2007 (UTC)

Yea, it would be a glaring ommision to talk about the polar coordinate system without talking about Complex Numbers. It's be like the article on Newton having no mention of the theory of gravity. Brentt 01:35, 17 February 2007 (UTC)

[edit] Applications

Following discussion on Wikipedia:Featured article candidates/Polar coordinate system I'm working on a draft of the applications section here. Its very sketchy at the moment, feel free to kick it into shape. --Salix alba (talk) 20:02, 17 January 2007 (UTC)

I'll edit it a bit now. I'm a little confused by:

Measurment

When the distance and angle are measured

Communication

Polar coordinates can be used for communicating positions

Storage

Is that part of a draft or something? —Mets501 (talk) 22:21, 17 January 2007 (UTC)

Yes I'm not quite happy with it yet. Their seem to be a few main uses: measurement, storage, communication, modeling, calculation, probably others I haven't identified yet. There seems to be quite an overlap between the first three and I'm not sure of how best to word it. Apologies for bad spelling and grammar, I was on a computer which didn't have a spellchecker installed. --Salix alba (talk) 22:36, 17 January 2007 (UTC)

No problem; I've cleaned it up quite a bit, and think it's basically ready to go in the article. —Mets501 (talk) 23:09, 17 January 2007 (UTC)

No time to really edit this now. But it should be noted that the robot thing is a bit misleading. The robot will have to do non-trivial trigonometry no matter what: once it starts moving, the new coordinates of an object that does not lie on the ray that the bot moves on will have to be recalculated. Pascal.Tesson 23:17, 17 January 2007 (UTC)

Yes I'm concerned about the robots, referenece is one paper of some guys personal way of doing things, not representatitive of robotics in general. Possibly quite POV and borderline OR.

As for calculation, the example I had in mind was finding the integral of $e^{-x^2}$ , which was a well remembered A-level exercise. This is not intergratable my normal means, but you can consider the 2D version $e^{-x^2-y^2}=e^{-x^2}e^{-y^2}=e^{-r^2}$ switching back and forward to polar coords makes the problem tractable, see Gaussian integral for the proof. It seems to me that there are probably quite a few similar formula where using polar coords really help. --Salix alba (talk) 00:09, 18 January 2007 (UTC)

I've redone the robot section and merged this into the article. —Mets501 (talk) 02:48, 19 January 2007 (UTC)

[edit] Area swept out

I removed the following fragment from the article:

"Let $\mathbf{A}$ be the area swept out by a line joining the focus to a point on the curve. In the limit $d\mathbf{A}$ is half the area of the parallelogram formed by $\mathbf{r}$ and $d\mathbf{r}$ ,

$dA = \begin{matrix}\frac{1}{2}\end{matrix} |\mathbf{r} \times d\mathbf{r}|,$

and the total area will be the integral of $d\mathbf{A}$ with respect to time."

As far as I can remember, this is only used when deriving Kepler's second law. While undoubtedly an important application, I don't think it is important enough to be mentioned here, especially as a slightly different form is used in the article on Kepler's law. Additionally, I think the fragment as it is, is hard to understand because it lacks precision. -- Jitse Niesen (talk) 12:42, 30 January 2007 (UTC)

No problem. —Mets501 (talk) 16:55, 31 January 2007 (UTC)

[edit] Other Shapes

The page shows a spiral and a rose, but I think pictures of Lemniscates, Limaçons, & Cardioids should also be added. Would do it myself, but I'm not too swell at Wiki-ing.YeoungBraxx 17:23, 16 February 2007

This article is probably long enough, but you can find information on those other shapes at the articles about them—see lemniscate, limacon, cardioid. Newyorkbrad 16:19, 17 February 2007 (UTC)

[edit] NPOV

0 degrees should be on the left hand side of the y axis. I know us leftists are in the minority, but minority views should be mentioned. The article is clearly positive-right-centric. Brentt 06:08, 17 February 2007 (UTC)

No. 0 degrees (or 0 radians, whatever, they're the same angle at zero...) goes to the right hand side because when you draw a polar function you pipe r and θ into the parametric x=r cos θ, y=r sin θ, and that kind of just wants to put zero on the right hand side (and you can't argue with it, it's the nature of the Universe, not a man-made convention!) Perhaps when god designed the triangle (and therefore sin and cos), it was discriminating against lefties... :P Not likely. Not a NPOV issue (as far as I know, anyway. In my opinion, etc). Stuart Morrow 21:05, 20 February 2007 (UTC)

While I agree with Stuart that we should follow the standard convention, the choice of which axis goes first and indeed which direction is considered to be positive is a convention. There are eight equally valid arangments for the axis. I don't know who chose the particular system we use which is a good question. cartesian coordinates does not seem to have the answer for this, nor does the Number line. --Salix alba (talk) 22:06, 20 February 2007 (UTC)

Guys, it was a joke. But Stuart, your wrong about it not being a convention. The universe has no preference for left or right in physical laws or math. All left right or left hand representations are by convention (yes, even the right-hand rule. Math and physics would look exactly the same if it was the "left-hand rule"). See Feynman's Symmetry in Physical Law lecture, it talks about this. Parametric plots would work just as well if the 0 was on the left. As a matter of fact, if you look at a parametric plot in the mirror its not like it won't make any sense. All the same information would be there and would mean exactly the same thing. Brentt 17:47, 26 February 2007 (UTC)

[edit] Polar coordinates!

They are awesome! Yeah! 132.161.164.75 06:46, 17 February 2007 (UTC)

Congrats to everyone that has contributed to this article! I have one suggestion: it would be helpful if the unit circle graph included radians as well as degrees. User:swimguy112

[edit] 2D ?

Are there no 3D polar coordinate systems (article says its 2D only)? Seems easy enough to add another parameter (I'll call it the 'up-down angle' in my own unscientific way) and you have a 3D system. Surely someone invented that too? MadMaxDog 13:33, 17 February 2007 (UTC)

Did you find the section called "Three dimensions"? It seems to be in there. -- Jitse Niesen (talk) 13:38, 17 February 2007 (UTC)

Madmaxdog, see Spherical coordinate system for the 3d analog of the polar coordinate system. Raul654 14:21, 17 February 2007 (UTC)

See also Cylindrical coordinate system which is a direct translation of polar coordinates into 3d. Raul654 14:21, 17 February 2007 (UTC)

What about polar coordinates in higher dimensions than 3? Jeltz talk 16:35, 17 February 2007 (UTC)

Applications

"Polar coordinates are two-dimensional and thus they can be used..."

My fault for not seeing that one (the "Three dimensions") - I was only skimming and landed in the above subsection, which contradicts it, then... MadMaxDog 23:41, 17 February 2007 (UTC)

[edit] Factual error on the page

While translating the article into Esperanto for Esperanto-Wiki we found a crude factual error in the English version. The statement

If k is irrational, the curve forms a disc since every point in the coordinate plane with r < a will satisfy the equation for some value of θ.

seems to be wrong. Here's the spontaneous disprove of this statement: Let's take the equation r=a*cos(k*t) (a - radius of the disk) let's take z<a and greater than 0 let's explore the circle with radius z. We look for points of this curve on this circle, they should be derived from the equation z=a*cos(k*t) The set of possible solutions of this equations is a denumerable set. The set of all points of a circle with radius s is continuous and thus greater than the denumerable set. Therefore there must be some points on the circle (and these points constitute the majority) which are not crossed by the curve. The solution of the equation z/a=cos(k*t) is the following: t=(2*pi*integer+acos(z/a))/k t=(2*pi*integer-acos(z/a))/k The whole set of solutions is denumerable. Thus the set of points on this curve is not more than denumerable. The set of a circle is continuous hence bigger than any denumerable set. Alaudo 17:57, 30 March 2007 (UTC)

I removed the claim. Whenever you find something like that, you might as well delete it from the article at the same time you bring it up on the talk page. Although that claim is not right (otherwise it would be a very simple example of a space filling curve!), the graph ought to be dense in the disc, which will look like it is the entire disc when you try to graph it on a calculator. This could be the source of the mistake. CMummert · talk 18:40, 30 March 2007 (UTC)

The graph is really "dense everywhere" (as we write in in Esperanto-version), still there are some points which it does not cross. I did not dare to delete this very dubious statement just because the article was selected as "an excellent article" and was tagged as "reviewed". Alaudo 19:47, 30 March 2007 (UTC)

Featured article review checks many things but does not include a line-by-line fact check. In this case, the error was hidden in the phrasing - if it had said "the graph includes the entire unit disc" then someone would certainly have noticed it. CMummert · talk 00:36, 31 March 2007 (UTC)

As a matter of fact, I did pause at the sentence when it was up for review but I considered it to be an acceptable formulation to convey "dense everywhere", which to me seems too technical for this article. In hindsight, it is better to remove the claim, as CMummert did, because the point it makes is not germane to the topic. -- Jitse Niesen (talk) 05:03, 31 March 2007 (UTC)

For me, as a non-native speaker, the wording used in the article was in no way meaning "dense everywhere", but rather as "completing the whole space". For those, who do not know the difference it does not matter, for those, who does, it can be crucial! Please, notice, that this equation strictly speaking does not result the subspace which is "dense everywhere" (we already corrected it in our Esperanto-version), but rather simply "dense". There are further problems in this article which I report in several minutes (I need some time to formulate that in English), if not, than tomorrow afternoon. Alaudo 22:54, 1 April 2007 (UTC)

[edit] Further problems in the article

(I am writing on behalf of several contributors and use "me" only for convenience).

Problem 1. The article correctly states

To get a unique representation of a point, it is usual to limit r to non-negative numbers r ≥ 0 and θ to the interval [0, 360°) or (−180°, 180°] (or, in radian measure, [0, 2π) or (−π, π]).[9]

but if we look at the polar rose equation r(t)=a*cos(k*t+t0) we can notice, that in some cases the sign of the radius can turn negative. For the polar rose it means, that some "petals" disappear, because by some t there are NO "petals" in this direction. Basically, if we look at the illustration in the article, we expect only one petal in the quote between 12 and 3AM, namely that pointing approximately to 2AM. That's true for other quoters as well. So, it is evident for me, that the author either used the modulus for the angle between pi/4 and pi/2 (that's not stated!), or they took the negative value, thus placing the "petal" which had to be put on 1 AM to 7AM (and visa versa, hence getting the full rose). Both would be quite voluntary and must be duly described. Alaudo 23:05, 1 April 2007 (UTC)

This is not a conflict. We clearly state: to get a unique representation of a point; this has nothing to do with curves. It is understood when the domain or range is not stated that it is over the entire domain of theta or entire domain of the radius. We often don't want a unique representation of points, either, for curves, such as lemniscates. The same thing can be observed in the Cartesian coordinate system with the equation for a circle:

x 2 + y 2 = r 2

. —METS501 (talk) 00:03, 2 April 2007 (UTC)

I am not talking about a conflict. I am just trying to emphasize that maybe one should describe these points more explicitly. I do understand the idea and the assumptions which are taken for granted, but some other readers could stumble. Alaudo 07:36, 2 April 2007 (UTC)

Problem 2. The article states:

Note that these equations never define a rose with 2, 6, 10, 14, etc. petals.

That's in my opinion not true. Carefully dealing with the definition domain one can define these roses. Alaudo 23:09, 1 April 2007 (UTC)

Again, we assume that these equations are over the entire domain. I'll edit the article to reflect that. —METS501 (talk) 00:03, 2 April 2007 (UTC)

That should be explicitly mentioned. Alaudo 07:36, 2 April 2007 (UTC)

You might like to cast your eye over Rose (mathematics) which may have similar problems, feel free to fix as appropriate. --Salix alba (talk) 07:54, 2 April 2007 (UTC)

If the assumption that the entire domain be used is explicitly articulated, then I suppose the issue is solved. Nevertheless, it it worth pointing out here (probably not in the article, though) that the 2, 6, 10, etc. petalled roses obtained by restricting the domain do not exhibit nice symmetry, and therefore might be ruled out. VectorPosse 23:28, 2 April 2007 (UTC)

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