Wikipedia:Peer review/Polar coordinate system/archive1

Polar coordinate system
This article just made GA, and I'd like a general idea about what needs to be done in order to get this to FA. --Carl (talk 21:13, 14 September 2006 (UTC)


 * Several things could be done to improve this. Although the statements here are mostly analytic/axiomatic, more in-line citations are an absolute must; an article of this size should have plenty of in-line citations. The History section should be first per just about every other article in Wikipedia. The lead needs to be expanded to two paragraphs (or three if there's enough material to work with); you could talk a little about the history there, for example. Other editors that have experience with math articles could probably help you out much more.UberCryxic 02:06, 15 September 2006 (UTC)


 * Hi, the article is good, but it could definitely use more organization and expansion to reach FA status. Presently, the article reads like an unordered list of properties that are not tightly related to each other.  Just as one possibility, you might consider organizing the article into three top-level sections: "Math", "History" and "Applications".


 * Under the "Math" section, I would add something about the singularity at r=0 and the relationship with other two-dimensional and three-dimensional coordinate systems. For example, most of the three-dimensional sets of orthogonal coordinates are derived from either projecting or rotating a two-dimensional orthogonal coordinate system; hence, the rotated ones all include a form of polar coordinates as a subset.  By contrast, the various curves such as the Polar Rose, although beautiful, seem too many and randomly chosen; in principle, every two-dimensional curve has a polar representation.  Instead of showing each of the dozens of well-studied 2D curves in polar coordinates, perhaps just show one exemplary and/or historically important case and then merely list some of the other more famous curves or link to them?


 * Under the "Applications" section, I would place the Keplerian case in the context of the study of mechanics under all central forces and  (historically) the study of planetary motion.  You also mention other applications in the lead, which might deserve coverage in the main article.


 * Under the "History" section, you might want to include a discussion of the history of exploiting angular measurements (e.g., the careful astronomical and architectural measurements of the ancient Egyptians) and the development of trigonometry, which seems pertinent.


 * Hope this helps, and keep up the good work! :) Willow 16:07, 15 September 2006 (UTC)

Echoing one of Willow's ideas, there are three equations for circles in polar form. Are all three necessary? I'd question the middle one. The first is nice as an illustration of how some things are easy in polar form, and the last is general, but I wonder who benefits from the second equation.

The Vector Calculus section would be enhanced by a figure illustrating the unit vectors. It might also be worth stating and illustrating that they vary from point to point, unlike the unit vectors in the x and y directions.

The entire Applications section needs clarification. The opening sentence says "Polar coordinates are a natural setting for expressing Kepler's laws of planetary motion." and the closing sentence says "If e < 1 this equation defines an ellipse, if e = 1 it gives a parabola and if e > 1 it gives a hyperbola." The closing seems unrelated to the opening, but if you intend to draw a connection (e.g. open orbits), it should be made clear. Alternatively, this paragraph about conics could be separated from Kepler's Laws by a new third-level header.

The equation r = l/(1+ecos&theta;) appears twice. The section could be rewritten so that it is only necessary once.

The diagram illustrating this equation does not have a label to show the variable l, although it would be easy to add; e, the eccentricity, could be defined in terms of the parameters in the figure.

Kepler's second law, dA/dt = constant, is not stated in polar form; dA/dt is neither polar nor rectangular nor in any coordinate system. The previous section did discuss dA but the connection is not clear in this section. The variables A and t are missing in the illustration. Anyone who knows Kepler's Second Law knows what this means, but anyone who does not know the law is lost. If you want to redraw the figure with times marked around the edge, that would meet the need of the article, but I'd say it's simpler just to remove Kepler's laws from the article. They have their own article, and add only confusion to the article on polar coordinates.

Other applications could be mentioned, for example, lathes, especially those formerly used to cut masters for pressing vinyl records.

Fg2 06:16, 16 September 2006 (UTC)