# Talk:Spherical polar coordinates

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 Definition:  Angular coordinates on a sphere: longitude angle φ, colatitude angle θ [d] [e]

I reverted changes by Anthony Argyriou because I don't know why he made them. Had I known I would have strived for a compromise. --Paul Wormer 06:45, 16 January 2008 (CST)

I protest. My reasons for the changes were made in the edit summary, and you did not ask me for further detail if you did not understand the issues I had. The reason I changed the article is that you have introduced your own personal point of view into the article, in a way which detracts from the quality of the article. You say "Unfortunately, some American mathematical textbooks..." - the unforuntateness of this is clearly a statement of opinion, and unsupported opinion at that. (The article presents the reason for this supposedly "unfortunate" state of affairs.) The paragraph following the quote is pure editorializing, and isn't very clear, either. My edit also clarified what was meant by "Ref.", and added a wikilink to spherical harmonics, which would presumably be a useful article to link to from this one. But rather than ask, you reverted without question. Anthony Argyriou 00:48, 17 January 2008 (CST)
Dear Anthony, you are turning things upside down. You should have started the discussion by explaining what was bothering you in my text and then we could have come to a text acceptable to both of us. Instead you started by deleting two of my paragraphs with the cryptic (for me) comment "editorializing". I don't understand what you mean by that, apparently it is something negative?
As I understand you now, the word "unfortunately" is the problem? But do you realize the consequences of this rash decision of some textbook authors? Until about 1970 nobody needed to explain θ or φ. Now you must always say in scientific articles something like θ is the angle of the vector r with the z-axis. I also happen to know how Maple got to use the "wrong" convention. In the beginning of the 1980s a computer science grad student was hired to program some additions to Maple relating to spherical polars. The guy had some vague notion about it, and since he didn't want to bother the professors behind Maple, he got a random textbook from the library and without knowing about the huge (believe me) literature using these coordinates and without realizing the extent of his decision he went to work. If you furthermore see the very silly reason why θ and φ were swapped, I think "unfortunate" is a very meek qualification. Anyway, also Eric Weisstein recognizes the fact that the literature on spherical functions covering 200 years cannot be rewritten, so now one must accept a (completely unnecessary) break in definition, if one grows out of the textbook and makes the transition to the real-world literature on spherical functions.
This doesn't mean that I'm not open to improvements/alterations of my text. You, and any other Citizen, may make any suggestions (with reasons) and I will adapt it along the suggested lines. --Paul Wormer 03:16, 17 January 2008 (CST)
PS. I checked the dictionary and found the word editorialize. I didn't know it, now I do: Giving opinions rather than facts. This raises an interesting question: is an editor entitled to an opinion and if so may (s)he express it in a CZ article?--Paul Wormer 03:47, 17 January 2008 (CST)
The short answer to your question ("is an editor entitled to an opinion and if so may (s)he express it in a CZ article?") is no. See the CZ:Neutrality Policy. It is perfectly acceptable to describe the problem, that some textbooks and programs have reversed the order of the coordinates, and to note that much confusion is caused thereby, and to note that historically, only one convention was used. It's also valid to point out that in one subfield, one coordinate system is used by everyone, even by people who ordinarily use the other one. However, if you are going to say that the pedagogical reason for changing the convention is weak (or strong), you should have a reference for that contention. (For that matter, even mentioning that pedagogy is the reason that some people adopted a different convention requires a reference, but you provided that in Weisstein's quote.)
Please also consider your statement: You, and any other Citizen, may make any suggestions (with reasons) and I will adapt it along the suggested lines. in light of CZ:The Author Role#How does collaboration work? and CZ:Be Bold. Anthony Argyriou 20:41, 17 January 2008 (CST)
I removed the word "unconvincing" and replaced it by the reason why the θ-φ swap was made. I quote here Weisstein, but I've known this reason for many years (since my days as applied math professor in Waterloo). However, I cannot refer to this, because I got this knowledge in private discussions with some of my former colleagues in the math department, who were teaching the stuff (and didn't like the fact that they were forced by their textbook to use the "new" convention).
Another thing: I expressed myself poorly by implying that I reserved the right to make changes. Of course, anybody can make changes and deletions in my texts. But this is not WP, I expect the courtesy of explanation why the deletions/changes were made. That is what I tried to express.
And the final thing: this discussion so far was basically about a few words, how about all the mathematical equations and their presentation, no comments there?--Paul Wormer 02:55, 18 January 2008 (CST)
Weisstein is a sufficient reference for the assertion that the change was made for pedagigcal reasons - someone presumably expert said it in writing, that's good enough. The math, to the extent I can follow it without referring back to my old textbooks, appears fine. I haven't gone over it with a fine-tooth comb to make sure there are no sign errors or other typographical mistakes. It might be useful to add a section on how spherical polar coordinates compare to geographic latitude and longitude and astronomical right ascension and declination. Anthony Argyriou 11:03, 18 January 2008 (CST)
And I apologize for being quite so harsh - your English is in general pretty good, and I forget that you are not a native speaker, and may not be entirely familiar with the various idiomatic expressions used to define the culture Larry's trying to build here. Anthony Argyriou 11:13, 18 January 2008 (CST)

## Determinant expression for curl

The reason for my edit is that the determinant expression for the curl in spherical coordinates is actually rather subtle. It only works if you compute the determinant by developing it to the first row, but not if you develop it to the first column. On the other hand, it is a useful shorthand and also used in text books. I'm not sure what the best solution is. These are the alternatives I thought of:

• mention both the long expression and the determinant expression, with a comment on the subtlety. Disadvantage: the long expression is, well, long.
• mention only the determinant expression, with a comment on the subtlety. Disadvantage: might not be clear.
• rewrite the determinant as a triple scalar product. Disadvantage: not everybody knows triple scalar products, and the determinant expression is also widely used, I believe.

I went for the first alternative, but I could also live with the others. I also wrote down the long expression in a way which makes it obvious that it's the same as the determinant. Perhaps it's better to simplify it (e.g., you can move the factor r out of the parentheses in the first term). -- Jitse Niesen 12:53, 18 January 2008 (CST)

Dank je wel Jitse, it is a perfect addition. I must confess that I did not think of it that this kind of determinants could be developed other than along the first row. Also because of the presence of the differential operators one more or less intuitively does the evaluation in one (the right) way only. But you are right, and writing this I had a déja vu, didn't we have a similar discussion about orbital angular momentum operators? It shows me that my memory is deteriorating; when I was younger I needed such a discussion only once :-( .--Paul Wormer 03:18, 19 January 2008 (CST)
I don't quite remember (I'm also getting older) but I believe that our previous discussion was about something else. By the way, you're right that it's "develop along the first row" and not "develop to the first row" as I wrote, so your English is not that bad. -- Jitse Niesen 11:49, 19 January 2008 (CST)

## Geographical coordinates

Anthony added a subsection on which I have the following comments/questions. When these are answered it seems to me that geographical coordinates (or a similar title) could very well be an independent article (and a nice one at that).

1. As part-time mathematician I don't like words in formula's. In the very least they should be set roman, but better is symbols, for instance λ for longitude. My first question is: do geographers have standard symbols for altitude, longitude and latitude? If so let's use them.
2. The standards are a point of concern. I learned in school (many, many years ago) that the zero meridian went through the observatory in Greenwich. Now with centimeter accuracy of GPS one would expect something like: the zero meridian goes through the lightning rod of the west wing of the Greenwich observatory. My second question is: what is the zero of longitude?
3. In Holland we use an altitude standard called above the new Amsterdam scale. This suggests to me that altitude standards are national. My third question is, is this true? Related to this is: have the center and the radius of the Earth standardized values? This is necessary if Anthony's definition of altitude is the international one.
4. Fourth question: how is the equator defined? With respect to the Sun on June 21, or the stars?

PS. I'll post a link to this in the geography forum. --Paul Wormer 06:23, 13 February 2008 (CST)

Some responses:
1. If there are standard abbreviations, common to more than just United States use, I'd be happy to see them used in the formulae. But I don't know what they are; I've mostly seen abbreviations: lat., long., alt.
2. I believe there's a mark somewhere at the Greenwich observatory to denote the Prime Meridian.
3. In the United States, there are a multitude of elevation/altitude standards. The NOAA and USGS use "mean sea level", while another agency uses "mean lower low water". There's WGS84 and WGS27. Etc. Meanwhile, the figure of "mean sea level" is not an actual sphere, in pretty much any accurate system.
4. I believe that the equator is defined physically.
However, the answers to 2, 3, and 4 are irrelevant for this article. The point of the section here is to show that geographical coordinates are a special case of spherical polar coordinates, and can, at a first approximation, latitude/longitude/altitude can be related to proper spherical coordinates, even if there is some significant departure when one starts to examine the details. The details can be left for the articles on latitude, longitude, Prime Meridian, equator, pole (earth), etc. Anthony Argyriou 11:42, 13 February 2008 (CST)
I believe the idea behind Anthony's edit is a good one. The article used to fob off the relation between spherical coordinates and latitude/longitude in one or two sentences, because it seems trivial. However, I think it is not that trivial for people that have never heard about spherical coordinates. Hence, I think a paragraph about latitude/longitude is helpful. I would place it either at the top of the definition section or just above it. I also wouldn't talk about x, y and z-axis but put everything in terms of equator, prime meridian, north/south pole.
Altitude is problematic, because the Earth deviates from a sphere by more than 10 km (I believe). This should be mentioned. Anyway, I'd stress the connection between lat/long and phi/theta; I don't expect people to have trouble with the r in spherical coordinates.
I wouldn't write down the formulas. They're very simple and also explained in words in the paragraph above it, so they don't add much to the article. Formulas also imply a precision that's just not present.
I'm getting a bit interested in geology lately (especially how the magnetic field is generated in the core). I believe that the definition of the equator is derived from the poles. The poles are defined by the rotation axis of the Earth. Unfortunately, the axis wanders around a bit (not precession, which takes place on a time scale of thousands of years, but the Chandler wobble which is not caused by the Sun or Moon, with a time scale of months). I don't know how they correct for this. -- Jitse Niesen 13:19, 15 February 2008 (CST)
I disagree regarding the equations. For some people, it's easy to read the text and figure out the right way to convert from one system to the other, but for others, having the equations is much more useful.
I'm thinking about adding, to that section, something about astronomical coordinates, also, with a little bit about proper motion as a vector. Anthony Argyriou 15:32, 15 February 2008 (CST)
Anthony, I propose that you either split off geographical (and possibly astronomical) coordinates to a new article (plus links from here to the new article and vice versa) that you carry responsibility for, or you make a compromise. The compromise is: (i) omit altitude (ii) introduce the notation λ for latitude and φ for longitude as is done at this NASA site. Further it would be useful to mention the notation E, W, N, S, for the respective signs +, −, +, − of longitude and latitude. --Paul Wormer 01:43, 16 February 2008 (CST)