Talk:Polar coordinate system

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This is the talk page for discussing improvements to the Polar coordinate system article.
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To-do list for Polar coordinate system: edit · history · watch · refresh

This to-do list is initially based on feedback from peer review

  • Convert end-of-article refs to inline citations. While I know a lot of this stuff comes from the same half-dozen books and sources, we need to do some stuff inline. All converted; feel free to add more inline citations.
  • Reorganize logically and consistently with other articles. Much better now.
  • Improve information on general theory, including derivative three-dimensional coordinate systems (spherical, cylindrical, etc.) Basics of spherical and cylindrical have been added, including reference to map coordinates. May need better images for these.
  • Condense list of curves and make order more logical.
  • Remove equations which are either unnecessary or esoteric (i.e., those which do not benefit the reader, such as the second equation for a circle). All unnecessary equations eliminated.

Contents

[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. --Mets501talk 03:19, 19 April 2006 (UTC)

I performed the merge. It seems like no one should have any objections. --Mets501talk 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
  1. 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.
  2. 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].
  3. 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.
  4. Sherlock Holmes in Babylon and Other Tales of Mathematical History has a section
    Newton as an originator of polar coordinates
  5. 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

Enlarge

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)
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