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helping students master the fundamentals and while they do not intentionally get things wrong, their stripped down and simplified approach can mislead serious students without significantly hurting their intended audience. They are not considered authoritative by the professional community and are often the butt of many jokes among educators. As an example in this article, "a linear coordinate system is a graphical representation of ...", while presenting students with a visual handhold, is technically wrong. This confusion between the coordinate system and its graphical representation will not do too much harm, but they are clearly different things (consider the fact that the coordinate system can exist without having a corresponding drawing). Another example of an incorrect simplification is given by
Schaums' treatment of arrows. Schaums declares that the positive direction on a number line is indicated by an arrow. While this is certainly true sometimes, it is far from universally accepted. Often no arrow is ever drawn and sometimes an arrow just indicates that a line is to be extended in the arrow's direction. These considerations are due to the illustrator's preferences and are not part of any mathematical definition. A final comment about the heading for this section. This is an article about coordinate systems and calling the first example of such a
522:, (1) I agree on "a linear coordinate system is a graphical representation of ...", and it can be rephrased. (2) Schaums is not the only series that advocates usage of arrowhead to indicate positive direction. In fact, books written by different authors within Shaums series may show different treatment of arrowheads. I am not to believe that the way arrowhead is pictured is left to a mere illustrator, this would be akin leaving a big red button to a monkey. This is a very specific part of math notation, and it can be correct or not. Having two arrowheads makes no sense whatsoever. Its proponents say that arrowheads mean that the line goes indefinitely in both directions, but it would do just the same without arrowheads, this is standard geometric convention. Put a terminating point or tick, and then it is a ray or a segment, with terminators. Unterminated, it goes indefinitely. So, arrowheads are not helping. On the other hand, what if one wanted for the numbers to grow to the left? How do you depict this? With one arrowhead it is quite simple, just draw it on the left side. But even if one to agree that drawing none, one or two arrowheads is up to an illustrator, we must either present all three options or choose the one that makes most sense, which is one arrowhead. (3) Naming a chapter
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add them together. We don't scale coordinates either -- how would you scale "Janary 3rd, 2010". Instead, you typically want to take differences, or measure distances or angles between points with specified coordinates. Even in chess, we might want to know how many moves it takes to get a given piece to a given square, but we never add coordinates. Only the difference between coordinates can be added in a way that makes sense. Sometimes people assert that these distinctions are obvious and don't need to be spelled out until you get to more abstract things like a
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why others are not as well suited for coordinates? How does this relate to "analytic" versus "synthetic" geometry? Also, would it be possible to make some categorization scheme that describes the relations between the different types of coordinate system? For example, I noticed that the article mentioned, in the "Other commonly used systems", Plucker
Coordinates before homogeneous coordinates, of which they are subset. I didn't want to make any major changes before seeing what other thought. Thanks for taking the time to read this comment!
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of this convention. These arrowheads belong to the illustration and are not part of any mathematical notation. They are not necessary to indicate the orientation of the number line and can be simply done away with by labeling any other point (with a signed real number) after the origin has been selected. They are part of the art of illustration, not the mathematics. --
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I find your comments on arrowheads to be confused and contradictory. You first claim that other
Schaums authors may use them differently and then claim that this is a standard geometric convention. You claim that having arrows in both directions is meaningless and then claim that there are proponents
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Hello all! I noticed that this article covers various examples of coordinate systems, and in the end mentioned the concept of "intrinsic equations", which made me wonder: Would it be appropriate to explain in this article the reasons why some systems are more suited for describing in coordinate, and
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Yes, the assumptions of "real numbers on manifold" is all together too restrictive. Don't forget about dates, either -- they supply a coordinate system over time, but we don't usually encode those cordinates with real numbers. The other thing about coordinates is that you typically do not want to
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Just to explain why I removed Siting Huo's edit (Coordinate System in GIS): it's too specific, it doesn't belong in a general article on coordinate systems. I tried looking later in the page for a place where it should go, but the whole article is on too much of a general level for that. Perhaps
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have been reverted three times and I would like to explain why in more detail than the edit summaries allow. First of all, the
Schaums outline series that is being used here as a reference is a time honored series of study guides in various subjects. They are strictly formatted for the purpose of
504:, the reader who is unfamiliar with the topic has a chance of connecting to an idea that might be vaguely remembered. This is therefore a much better heading and shows some appreciation for the difficulties that a reader might be having with a mathematics article. --
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is mentioned in the chapter, so I see no harm being done. Also, I suggest merging "number line" and "real line", but this is for another day. Anyway, what could be discussed and edited and fixed, you prefer to simply remove. Uncool.
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I'm not sure what would be the best way to write the idea correctly on the basic description, but what about non-number coordinates? A great example would be Chess
Coordinates, where "E2" defines a position in an R^2 universe.
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You may want to add a section for "how to add coordinates to a wikipedia page" or something, because right now I'm having trouble finding out how to add coordinates, and I'm sure other people are to.
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For example, the
Cartesian coordinate system in 3D can be left or right handed, and have different vectors pointing up. Ex:
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This is the talk page for an article about the mathematical concept. If you want help editing a
Knowledge article, see
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is quite pedantic and presupposes that the reader knows what a coordinate system is already. By calling the section
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In my opinion, the number line is a just a part of the
Cartesian coordinate system.
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I think this is worth mentioning in the article, somewhere.
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