Talk:Cartesian coordinate system

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first you go[edit]

first you go on the y axis then x axis or roll out of bed and stand up. go to the place then go up the alevator —Preceding unsigned comment added by (talk) 20:07, 13 April 2009 (UTC)

The note that this needs more references is probably unwarranted. Do you want people referencing their textbooks from junior high? — Preceding unsigned comment added by (talk) 09:12, 20 March 2014 (UTC)

The 3rd dimension[edit]

Headline text[edit]

I think this page doesn't talk about the third dimension (i.e. 'z') nearly enough. Just because co-ordinates are cartesian, doesn't mean they are 2-dimensional. 3-dimensional co-ordinates are usually expressed as cartesian co-ordinates as well, and it seems that this has been included into this article merely as an afterthought.

You are correct in that the 3d aspect of CCS is an afterthought. I spent a _long_ time trying to add information that wasn't so "common". In short, I ran out of time. The problem is when you add more information on this you are moving away from originator of the idea; too, you would probably have to discuss the properties in a 3d system that are different in a 2d system. For instance, slope in a 3d system makes little sense.

I thought it would be an easy article, but actually I need to upload some pictures, that's the only really clear way to explain it (and that ASCII picture is atrocious). I add more later; thanks for the input. Feel free to add :)

Let me know if this is more fully fleshed-out.

Thank you for your valuable input. Adamcscott

Should mention be made of the name of the z-coordinate? I believe it is "applicate" in english.


Someone made these images. If you want to use them you may have to re-upload them with the extension changed to .jpg. (The wiki software doesn't seem to recognise uppercase .JPG as something that should be an inline image.) --Zundark, 2002 Jan 11

1)If you want the images to display in the article itself, you should upload them to

and then use the URL of the page in the meta where the image is displayed. 2). Before you mark off, say x units on the x axis, you have to "choose" a "unit" length. RoseParks----

Z-axis not until 19th century?[edit]

Sometime in the early 19th century the third dimension of measurement was added, using the z axis.

Was it really that late? Euler didn't think of it? Gauss was already 45 when the 19th started. AxelBoldt 03:09 Jan 23, 2003 (UTC)

I removed this statement. It can go back if someone finds a reference for it. Withour reference it doesn't have any credibility. --345Kai 07:49, 23 April 2006 (UTC)

This might be trivial. But the red point is NOT at (-5, -5, 10) but at (-5, 0, 10), or (-5, -5, 12.x).

I fixed that, now it is. I hope I've drawn it somewhat intuitive. (In the process I unfortunately created a second image of the same name but with the extension "jpg" (lowercase). Does someone have the rights to erase that?). DrZ 15:59, 20 Feb 2004 (UTC)


I suggest using "two-dimensional" instead of "two dimensional".


Well, I took initiative, I was bold, and the page is now being merged with Point plotting (don't bother goin there, I redirected it here). HereToHelp 21:15, 20 August 2005 (UTC)

who invented the number line?[edit]

I would be really interested in knowing the origins of the idea of the number line. This is also very relevant to the article.

Image:Coor planes Color.png[edit]

Added this image to replace the old one. The old one had two major problems:

  1. It was a jpg
  2. It was not well lined up, some supposedly parallel lines were not

The new one might be better as a pure black and white, and you may want to add dotted guide lines like the old one, but I do think it's a step in the right direction. --Falcorian (talk) 05:11, 13 February 2006 (UTC)

Thanks, it's much better than the last one. The colors are ok, I think (…maybe the green could be a bit darker?). Perhaps you could provide a vectorized(SVG) version, or was it created as a bitmap? –Gustavb 17:39, 13 February 2006 (UTC)
I can definately change the color. It was created as a bitmap, and I've never worked with SVG... But the medium seems to offer so much that I think I must try it. --Falcorian (talk) 23:54, 13 February 2006 (UTC)
Yes, it's really worth the effort to give a try. Inkscape is probably the best (open) SVG editor… –Gustavb 07:56, 14 February 2006 (UTC)

Orientation and "handedness"[edit]

If the forefinger of the right hand is pointed forward, the middle finger bent inward at a right angle to it, and the thumb placed a right angle to both, the three fingers indicate the relative directions of the z-, x-, and y-axes respectively in a right-handed system.

I edited this to correctly reflect which axis is which, but the image is wrong. The z-axis is the "new" axis and so goes "into" the page when added to a 2D coordinate system. In a left-handed system the z-axis is positive away from viewer, "into" the page, and in a right-handed system it is positive towards the viewer, "out of" the page. Since I don't have a clue how to edit those images, can someone else do it? Also, the image shows a rotation that seems meaningless. Positive rotation about an axis is always anticlockwise when looking at the origin from that positive axis. Apologies if I have misinterpreted the image. kthx, Al

rewrote this section. Is hopefully fixed now, but could use a lot of improvement, still. --345Kai 07:49, 23 April 2006 (UTC)

in physics[edit]

It is important to note that a dimension is simply a measure of something, and that, for each class of features to be measured, another dimension can be added. Attachment to visualizing the dimensions precludes understanding the many different dimensions that can be measured (time, mass, color, cost, etc.). It is the powerful insight of Descartes that allows us to manipulate multi-dimensional objects algebraically, dispensing with physical tools.

The above paragraph didn't make sense in the section it was in, so I put it in its own section, which needs to be further fleshed out. --345Kai 07:49, 23 April 2006 (UTC)

It is not clear to me what the author wanted to say with this that also belongs into an article about Cartesian coordinates. Based on 345Kai's comment from over a year ago, I suggest removing the paragraph "In Physics" from the article and also remove the related paragraph from this discussion. --[] 8 May 2007

Axonometric projection[edit]

Can the cartesian coordinate system be considered a space for displaying points in a axonometric projection? --Abdull 21:02, 28 May 2006 (UTC)

Cartesian Plane[edit]

I think cartesian plane should redirect to an independant article or a section should be added to this article specifically about the cartesian plane as there is no formal reference to it yet all articles on the cartesian plane redirect to here. 11:31, 5 August 2006 (UTC)

Vector Representation[edit]

I added a short section describing the representation of a point in Cartesian coordinates by a position vector. Alden Jurling 06:29, 20 May 2007 (UTC)

y axis[edit]

isn't the positive y-axis up? K25125 22:32, 26 May 2007 (UTC)

I have always used that convention: X - left to right. Y upwards. Z front to back. (I have also seen Z back to front).

Markhobley (talk) 22:05, 15 April 2011 (UTC)

Is this about the sentence: For three-dimensional systems, mathematicians usually draw the z axis as vertical and pointing up, so that the x and y axes lie on an horizontal plane.? I would have said y upward was at least as common, but the claim is only made for mathematicians, not engineers or physicists. Nevertheless it may be worth marking this as {{dubious}}. --catslash (talk) 00:31, 16 April 2011 (UTC)
It usually depends on the subject of interest. I'd guess computers use Y as up because that's inline with what the monitor already displays. Other topics, as mentioned, have a top-down plan (like a map) with X and Y flat on the paper, and Z representing height. Cypherzero0 (talk) 22:55, 28 September 2011 (UTC)

Correct name of axes[edit]

in the article you can read "the x-axis or abscissa and the y-axis or ordinate"

This is wrong, those axes are USUALLY named that but that is not the reference name of the axes, the correct names are abscissas´ axis and ordinates' axis and you can name them whatever you want please specify this. 23:55, 16 August 2007 (UTC)

History of x, y and z designation[edit]

Any one know who chose the letters x, y and z? --catslash 10:53, 11 September 2007 (UTC)


As x-axis coordinate is called abscissa, and y-axis one ordinate, what's the English name of the z-axis coordinate? In Portuguese and Spanish and maybe the other Romance languages is "cota" (abscissa, ordenada, cota, from Latin), but I don't know the English name. Cotation? Height? (talk) 00:47, 12 January 2008 (UTC)

Right-handed vs left-handed coordinate systems[edit]

"Different disciplines use different variations of the coordinate systems. For example, mathematicians typically use a right-handed coordinate system with the y-axis pointing up, while engineers typically use a left-handed coordinate system with the z-axis pointing up. This has the potential to lead to confusion when engineers and mathematicians work on the same project."

I am an engineer and I have never used a left-handed coordinate system. A left-handed system is a tool of the Devil. Would you please cite a few sources to justify your point. --xerm (talk) 18:11, 15 February 2008 (UTC)

I also have never experienced this notion that engineers "typically" use a left-handed coordinate system. However, in the special case of computer programming, a left-handed system is often used when drawing 2-D graphics on the screen, reflecting the preference for left-to-right and top-to-bottom movement around the screen: the origin is often the top left, with x positive to the right, and y positive going down.

In general it is probably better to rephrase this to talk about the problem domain in which a system is used, rather than what certain people do, since people do different things in different situations (i.e. engineers and mathematicians would both use the coordinate system needed by the software when they are drawing 2-D screen graphics). Agenteightysix (talk) 22:58, 23 February 2008 (UTC)

I've never come across a left-handed coordinate system in the field of engineering. In the absence of a citation I'm going to remove this statement. Incidentally, I'd say it's not uncommon to have x and y axes pointing to the right and upward respectively (as in 2D), with the z-axis 'coming out of the page' - but this is still right-handed. --catslash (talk) 21:12, 13 March 2008 (UTC)

Orientation of the right hand in the illustration[edit]

For maximum clarity, the hand should be palm up with the index finger pointing away from the viewer, and the perspective should be looking at the hand from a three-quarter above view. In this way, the X axis will increase positively to the right, the Y axis positively going away from the viewer, and the Z axis positively going up. As it stands, the illustration is very confusing when trying to relate it to the conventional directions a 3d system is displayed in. (I'm speaking of the Y horizontal increasing away from the viewer, Z vertical convention as opposed to the Y vertical, Z towards the viewer convention. The current illustration depicts neither.) --HarmonicSphere (talk) 15:15, 23 October 2012 (UTC)

I agree that the illustration of the right-handed axes represented by the fingers ought to conform with the figure above it. But I disagree that the position of the hand ought to change, rather the axes in the figure ought to change to conform to the hand shown in the illustration. This is because it is much easier to put one's fingers and hand in the position shown in the illustration. Being able to easily put one's hand into a representative position assists with comprehension of the handedness concepts. Otherwise, one becomes distracted by attempting anatomical contortions and the potential derogatory implications that a vertical z-axis position may convey. Dawnvawn (talk) 20:19, 24 November 2015 (UTC)

2d Right Hand Rule ambiguous[edit]

The text currently in concern is: "Placing a somewhat closed right hand on the plane with the thumb pointing up, the fingers point from the x-axis to the y-axis, in a positively oriented coordinate system". This text is ambiguous, because a "somewhat closed" hand is not defined, and I am not able to reproduce the positive x,y orientation using this. It's also unclear what axis the thumb is aligned to. A picture might be helpful, but this article has enough pictures already. IsmAvatar (talk) 00:05, 28 February 2008 (UTC)

Actually I would go a step farther -- "handedness" is a concept that is only properly applied to a 3D system, not a 2D system. The concept of right- or left-handedness doesn't apply to a 2D system at all without the context of a third axis. For either of the two possible 2D orientations (x right / y up or x right / y down), both a left- and right-handed 3D system could be created by adding a third axis "into" or "out of" the plane. —Preceding unsigned comment added by (talk) 22:04, 28 August 2008 (UTC)

I have read in more than one linear algebra text that left- and right-handedness do not apply to two-dimensional systems. At best, the article assumes that the handedness of a 2D system depends on the orientation of the "thumb" being up, and at worst, the concept of handedness is meaningless in 2D. By assuming the thumb is pointing upward in determining an orientation for a 2D system, a third axis is being added implicitly to the logic.


What is the coordinate for the 4th Dimension? Colinstu (talk) 23:26, 2 January 2009 (UTC)

This whole article seems to imply that cartesian space only applies to 2 or 3 dimensions, when in fact you could have an n dimensional cartesian space. (talk) 02:09, 15 March 2014 (UTC)

There is no such concept as a Cartesian space. These are Euclidean space and real coordinate space that represent valid concepts. Incnis Mrsi (talk) 13:23, 15 March 2014 (UTC)
Considering that there is the section named Cartesian space, you can hardly blame the OP. The article does need fixing. —Quondum 16:18, 15 March 2014 (UTC)

Reference to part II of the 'Discourse on Method'[edit]

In the 'History' segment of the article, it mentions that a citation is needed. Well there is a copy of the discourse on Project Gutenberg. The relevant quote is right there in the third-to-last paragraph. I just don't know how to make citations. —Preceding unsigned comment added by Zmalk (talkcontribs) 10:07, 26 February 2009 (UTC)

Cube Reference[edit]

Does it really need to be there? It really derails the article towards the realm of ridiculousness. —Preceding unsigned comment added by Ridonculous (talkcontribs) 22:32, 3 April 2009 (UTC)


The article as now written makes no mention of functions. The Cartesian coordinate system is most useful in its depiction of functions. Functions deserve some mention as they are the basis of much of Calculus and analysis, e.g. complex and functional analysis. Appropo (talk) 03:48, 20 April 2009 (UTC)

same unit of length[edit]

The first paragraph of the article has the following:

... which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

"measured in the same unit of length" refers to the unit of the axis / pair of numerical coordinates, which is wrong. As unit of the axes need not be same.

Rajmathi mehta (talk) 07:13, 7 May 2009 (UTC)

  • Most formulas dealing with Cartesian coordinates, such as the Pythagorean formula for distance, assume equal units. One can generalize the definition in various ways, such as non-orthogonal axes and unequal units, or to non-geometric spaces, such as pairs (position,time). Or even to curved axes (as in polar, spherical, etc.) These possibilities are already mentioned in the appropriate section of the article. Using the generalized definitions from the start would be "non-pedagogical" and make many sections more verbose and confusing. All the best, --Jorge Stolfi (talk) 18:39, 26 May 2009 (UTC)


Ordinate redirects to this page - but ordinate is not even mentioned in the text. —Preceding unsigned comment added by Borek (talkcontribs) 15:28, 26 May 2009 (UTC)

Ordinate is mentioned under Notations and conventions --catslash (talk) 16:53, 26 May 2009 (UTC)
I agree with Borek, both Abcissa and Ordinate link here, they are links provided in a large number of pages but both are poorly defined. Not seeing Abcissa in the article _At All_ I did a find in Firefox and it only found the work in the search feild of the side-bar and and the redirect line.PB666 yap 19:52, 26 May 2009 (UTC)

Red, Green, Blue standard for X, Y, Z[edit]

Hi, we should probably add the standardized RGB coloring to the XYZ lines (X is red, y is green, z is blue) - I'll do it as soon as I have some refs. I have some for neuroimaging, but it would be nice to get more general ones. -kslays (talkcontribs) 17:08, 30 June 2010 (UTC)

Cartesian Coordinates in Computer Graphics[edit]

Shouldn't somebody help explain the following phrase…:

"However, in computer graphics and image processing one often uses a coordinate system with the y axis pointing down (as displayed on the computer's screen). This convention developed in the 1960s (or earlier) from the way that images were originally stored in display buffers."

…by giving more detail on how display buffers generally worked from the upper left-hand corner of a computer's screen to the bottom right-hand corner?

BCG999 (talk) 21:40, 30 November 2012 (UTC)

Fig. 8 – The right-handed?[edit]

The comment with Fig. 8 that it is right-handed is not visually clear. It is an Optical_illusion, so you can see both handedness. The x-axis can be viewed as going in as well as out of the screen. John W. Nicholson (talk) 00:26, 26 January 2013 (UTC)

Formula for rotation is wrong?.. (resolved)[edit]

I am new here and I worry to be wrong, so I ask someone else to also check the math.

I am pretty sure that formula for counterclockwise rotation given in section 5.2.2 is wrong. Instead, it should be

--Liartar (talk) 17:57, 15 March 2013 (UTC)

The formula in the article is correct and easily verified. Why did you think that it is in error? Bill Cherowitzo (talk) 02:54, 16 March 2013 (UTC)
I tried to verify it. Here is my drawing: It seems to me, that should be equal to . I've derived formula for y' in a similar way. --Liartar (talk) 11:09, 16 March 2013 (UTC)
Personally, I would like to see the reference where the formulas came from. It seems to me that there is something missing. Namely, use of the Pythagorean theorem. To me, it should be the same as polar coordinate system with (x,y) converted to (r,alpha) and (x',y') is (r, alpha+theta) (talk) 01:55, 17 March 2013 (UTC)
I beg to pardon me: I've made a conceptual mistake here, I thought that "rotation" section refers to rotation of coordinate system, while it actually refers to rotation of an object inside stabe coordinate system. Here is where sign change comes from: rotation of an object is equivalent to rotation of coordinate system in opposite direction. Shall I remove this section of discussion, because it has been resolved? --Liartar (talk) 14:36, 17 March 2013 (UTC)

Applications section[edit]

Which doubts do exist about importance of graph of a function as an application of Cartesian plane? Incnis Mrsi (talk) 16:19, 20 July 2013 (UTC)

When consulting an "Applications section" I am pretty sure that the overwhelming majority of Wikipedia users (including mathematically inclined readers like myself) would implicitly be expecting to see - at least somewhat - practical applications: for example cartography or architecture in the case of the Cartesian coordinate system. Certainly there are also endless appearances of the notion of Cartesian product in abstract mathematics - note the ubiquity of Cartesian Closed Categories throughout mathematics. The graph of a function is absolutely one of those appearances and indeed a quite fundamental one. However, personally I don't feel the applications section is a good place for this. Obviously the original contributor and the esteemed contributor who reversed my deletion disagree and if they still feel strongly that the graph of a function belongs in the application section then so be it! Pmokeefe (talk) 11:05, 21 July 2013 (UTC)
That expectation seems to me to be satisfied. I lean (along with Incnis) on the side of graphs being a clear-cut everyday application, albeit in depicting mathematical functions. The section as a whole could do with a copyedit though: it rambles and should be subdivided by application with subheadings. — Quondum 11:36, 21 July 2013 (UTC)
That, of course, is a very good point, there's a great - and quite practical - application in visualizing functions and relations which the paragraph in question does in fact go on to mention. Unfortunately, that paragraph begins with the formal definition of the graph of a function, which I strongly suspect will immediately lose the vast majority of the mathematically unsophisticated Wikipedia users who were reading the applications section hoping to find out what Cartesian coordinates are actually good for. I definitely made a mistake by deleting the paragraph and should have instead rewritten it to reflect those concerns:( It's on my to-do list, but it would be even better if someone truly talented in that sort of exposition got there first. Pmokeefe (talk) 12:21, 21 July 2013 (UTC)
There is a subtle point involved here, and since it centres on a blurriness of terms as uses in a mathematical context, I am a little skittish to get involved yet (I find mathematicians frustratingly obtuse at times, if I may be forgiven this utterance, for at times failing to see when it is necessary/helpful to distinguish different meanings of a term, especially in the WP context). Here we are dealing with a the distinction between the formal definition of a graph as a subset of the Cartesian product of sets and its use as a depiction (what one might call a plot, chart or graphical representation) of a function or graph. The depiction crucially adds a mapping from the Cartesian product of sets (of which the graph is a subset) onto a manifold, usually physical space. Incnis may well mean either, but as an illustrative example I think only the sense of a graphical representation should be used here, and this does require a wording change for clarity. I do not deny the utility of the formal (first) sense, but that relates to the Cartesian product (which is a set of n-tuples) rather than Cartesian coordinates (which parameterize a Euclidean space). — Quondum 14:23, 21 July 2013 (UTC)


The applications part of this page is written is a very odd manner. — Preceding unsigned comment added by Lwotton (talkcontribs) 10:54, 13 March 2014 (UTC)

Rectangular coordinates[edit]

This name redirects here and should be mentioned at the start of the article.--عبد المؤمن (talk) 21:31, 26 October 2014 (UTC)