# Talk:Map projection

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Map projection was one of the Geography and places good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article milestones
Date Process Result
December 12, 2005 Good article nominee Listed
September 27, 2008 Good article reassessment Delisted
Current status: Delisted good article

## Planetary texture ?

Shouldn't there be somewhere on this page an indication of which projection to use to make a planetary texture to be used on a sphere ? The first place one searches for such a clue is there... I can't write it down for now, because I haven't found it yet, and moreover I don't know editing rules in Wikipedia, so should I write something that I would surely break many of them ^-^ It seems to be called "square" or "rectangular" on many planet generators, but I don't know the proper geographical term and I thought to find it here. That's why I think it would be useful here. Thanks in advance !

Benoît 'Mutos' ROBIN — Preceding unsigned comment added by 77.193.41.178 (talk) 16:10, 13 November 2011 (UTC)

I think you refer to something often called the “geographic projection” which, in spherical form, is the equirectangular projection. This projection is often used to store geographic raster imagery, but its use is merely a certain form of convenience. Depending on intended use, other projections or data storage methods may be more convenient or better suited. I’m not sure how much sense it makes to emphasize that projection specifically in the article for that purpose. Strebe (talk) 21:48, 13 November 2011 (UTC)

## Images out of place

The images showing examples of projections seem out of place; the images don't relate to the text next to which they are placed. It seems the images placed merely for overall appearance of the article, however this is not very conducive to understanding. —Preceding unsigned comment added by 134.197.40.199 (talk) 19:43, 15 June 2009 (UTC)

## Map projections image files

I am not sure whether I am right on this one, but these images seem identical with ESRI's poster on map projections that comes with their book "Getting to know ArcGIS". Someone should verify the copyright of these images. The USGS website does not mention any copyright information.

## Map projections from Planet math

I don't know if the articles for projections exist, but it might be worth nabbing those that do from Planet math. Mr. Jones 15:05, 8 May 2004 (UTC)

## Formatting criticism

You should put a ":" before the math marker of the Mercator formula, to indent it. Same with the next line starting with phi. – Martin Vermeer

Okay, go ahead cleaning it up :-)

## History of Map Projections

12/29/05

It would be a good idea to add a short section on the history of Map Projections - this is an interesting topic, as it mirrors the evolution of human knowledge over the centuries. Great ingenuity has gone into developing the ideas of map projection to make it more and more useful for navigators and other users.

## Benson Projection

I have invented a superior map. Everyone will agree that it is the best. How do I submit it? 70.177.90.238 20:40, 11 January 2006 (UTC)

You don't. If you want, tell people about it, and perhaps one of them will add information about it to the article. See Wikipedia:Autobiography. ¦ Reisio 21:33, 11 January 2006 (UTC)

## map projection or spherical projection?

IMHO spherical projection is the more standard mathematical term for this. i've done a redirect from spherical projection to this article, but if noone objects, then i would suggest switching the redirect to the other direction - i.e. "spherical projection" would be the main article. Boud 08:41, 27 April 2006 (UTC)

But the main use is cartographical. Mathematicians may have a few projections they use frequently and then generalise. But cartographers use all these and more. --Henrygb 09:05, 27 April 2006 (UTC)
Also note that that the surface to be projected in Cartography is not always a sphere, it might be a spheroid (or ellipsoid). On the other hand, the projection process is not necessarily geometric - From the article: "The term "projection" here refers to any function defined on the earth's surface and with values on the plane, and not necessarily a geometric projection." Alvesgaspar 15:49, 27 April 2006 (UTC)

## European or American map

The article uses maps with America at the centre. I though that the Wikipedia standard was to use maps with Europe/Africa at the centre (because they don't cut Asia in half). If so, does this article deviate from that for a specific reason? And are there names for these maps (I can't find an article on it)? DirkvdM 07:06, 17 August 2006 (UTC)

Most of the maps come from the United States Geological Survey. --Henrygb 09:14, 17 August 2006 (UTC)
Sounds like a good case of needing someone to create a free version specifically for Wikipedia. I have no idea how, before you ask. 82.30.13.134 (talk) 18:34, 14 November 2011 (UTC)

## Triangular map?

A while back I heard of a type of projection that was made up of a bunch of triangles, and that by unfolding it a certain way, it showed the world as a chain of continents surrounded by water, or a chain of oceans surrounded by land. Does anyone have any information on this? Stale Fries 00:13, 3 March 2007 (UTC)

Nevermind, it's Dymaxion map. Stale Fries 00:16, 3 March 2007 (UTC)

I think placing the Dymaxion Map under the heading "compromise projections" is missleading as it is the only unique map among those listed and the description for the section in no way describes the Dymaxion Map. I think part of the confusion above stems from the poor classification of this map. 71.214.83.247 (talk) 05:46, 3 January 2008 (UTC)

It makes sense there because it certainly is a compromise projection. An alternative might be to introduce a category "decorative" or "novelty" projections (I think that's the term Snyder uses in his reference manual). The Dymaxion projection would fit there, as well as several of the other "neat looking" projections like the butterfly and heart projections. Paul Koning (talk) 12:03, 3 January 2008 (UTC)

## Cylindrical projections

The statement that cylindrical projections have straight meridians is true only for the conventional (projection axis == earth axis) form, not for the transverse or oblique forms. Paul Koning 17:50, 10 May 2007 (UTC)

## Article focuses on whole-earth projections

... whereas most maps show only a small part of the earth. I realize that this is just "a special case" where you only show part of the map, but given the extremely common nature of this issue there should be some specific discussion of what projections are commonly used for smaller maps (and how to choose the parameters). Personally, I'm trying to figure out which projection to use for my map of a country (Guatemala) but the same issue exists even for the smallest, city-scale maps. --190.56.85.26 17:10, 11 July 2007 (UTC)

It's true that a lot of the decorative and PC projections are meaningful only, or mostly, for whole earth maps. But the mainstream ones are applicable in both cases. For example, you might find Mercator, transverse Mercator, polyconic, and gnomonic projections, to name just a few. I can't see a point in worrying about this for city maps but certainly it's a valid concern for country maps such as the one you mentioned. So the question you'd want to answer: what property matters most? Maps ("charts") for some specific professional application tend to pick a specific projection to meet those requirements – you might find gnomonic or Mercator projections there. (I think marine charts are often in that category.) For others, conformal projections are probably a good starting point. Yes, it might be interesting to talk about this. Snynder could be a good reference, I would think. Paul Koning 18:26, 11 July 2007 (UTC)

Just found [3] which is much more "useful" from my perspective than this article, as it organizes by purpose rather than by mathematical criteria. I would suggest that this article should keep the initial explanations as is, but the actual projections should be reorganized along the lines of this source.

ps. For my purposes, I've chosen LCC - appropriate for a "taller" country and atlas-style "just looking" maps. Now, I just have to figure out how to enter the parameters into GRASS - it asks for "central", "first", and "second" parallels, which default to 23,33,and 45; I try 15,13,and 17 for a map which will extend 13N to 18N and it doesn't accept them... maybe I need to use negative rather than positive numbers for my false northing and false easting...

pps. Sure it makes hardly any difference for city maps - but you still have to choose one. --190.56.85.26 18:48, 11 July 2007 (UTC)

## "Modern notation"

Many articles on projections, such as equirectangular projection, use some kind of "modern notation" in favor of a more understandable x = x(λ, φ), y = y(λ, φ) type of thing that would be easier to understand and is more standard in terms of notation.

This is a notation occasionally used for functions/mappings, but it may not be the best choice here, the shorthand really doesn't make it shorter and only obscures it.

If no one objects I'm intent on fixing all map projection articles that use this convention.

Edit: sorry, forgot to sign. -Ben pcc 22:43, 27 July 2007 (UTC)

I favor this proposal. The so-called "modern notation" is not normal in the professional geographic map projections' literature; nor does it help novices understand what's going on.

Strebe 01:10, 29 July 2007 (UTC)

Done. Whew. -Ben pcc 17:20, 7 August 2007 (UTC)

## Please explain: Polar projection is not a projection; it's an "aspect" of any projection

I was dealing with an edit to mariner's astrolabe (since moved to its talk page) that referenced "polar projection" on an astrolabe. The link provided by the author was to |polar and [[map projection|projection]]; I changed it to polar projection only to discover no such link existed. I looked at this article and saw no polar projection mentioned.

Not being a cartographer, I looked up polar projection and found it described as a map projection and added a section here with an image. It was removed with the comment as in the section headline. Please explain the difference - it's clear that there is some ambiguity in other references that only a cartographer is likely to explain.

Since the description on talk:mariner's astrolabe is lacking detail on what polar projection means specifically, does anyone know what map projection is appropriate to describe? Thanks for your help. Michael Daly 05:40, 18 October 2007 (UTC)

The current talk:mariner's astrolabe links the words "polar projection" to Map_projection#Azimuthal (projections_onto_a_plane) which is right. "Polar" implies a projection related to a point, specifically one of the poles. Azimuthal projections are projections around a point, which may be any point on the globe. "Azimuthal" isn't a specific projection, it's a category – specific examples include stereographic, gnomonic, and many others. So "polar projection" would be a shorthand for "an azimuthal projection centered on the pole". That's still a category, or aspect (where it is centered). If you wanted to describe a specific projection in its polar aspect, you might have "gnomonic projection centered on the pole" (or perhaps more succinctly "polar gnomonic projection"). Paul Koning 18:34, 18 October 2007 (UTC)
Thanks for that. I put that link there as the closest to where I had added "polar projection" to this article. I wasn't sure whether gnomonic would be the correct term in this instance. Michael Daly 19:03, 18 October 2007 (UTC)
I mentioned gnomonic just as an example. Chances are it isn't that one, but I don't have a good guess about which azimuthal projection one might find on an astrolabe. You might be able to figure it out by examination. Or it may be that the "projection" is really just a diagram, centered on the pole but with no well defined scale or geometry. Paul Koning 21:05, 18 October 2007 (UTC)
It would be well-defined. The astrolabe described was used for navigation and other astrolabe types tend to be quite good - they knew their astronomy when they built them. Actually, my initial guess was gnomonic since it's simple and an old projection. However, I only know a few projections, so that assumption is based as much on ignorance as knowledge. I'll leave it until someone, preferably the person who added that info to the article, explains what that astrolabe is all about. Then, with your explanation, I'll have an easier time figuring out a better link to this article. However, I suspect the info will be removed permanently, since it sounds like a "we invented everything" from someone who has done that before in another article. In the meanwhile, I now know the difference between "polar projection" and the general azimuthal projections. Michael Daly 01:19, 19 October 2007 (UTC)

## Projections used elsewhere

The article should also mention that these projections are also used for representations of things lying outside a particular frame of reference. For instance, celestial maps and panoramic photographs. SharkD (talk) 01:12, 15 January 2009 (UTC)

What do you mean by "outside a particular frame of reference"? Strebe (talk) 03:53, 15 January 2009 (UTC)
I have removed that sentence from the text, since the verbiage seems vague, and I cannot find anyone who understands what it intends. Possibly you are saying something important and relevant there. Please describe it here. Strebe (talk) 21:31, 15 January 2009 (UTC)
I think SharkD is trying to say that these projections have several applications, and ideally this article would at least mention several of them, rather than exclusively focusing on only one (admittedly most historically important) application: mapping the surface of Earth.
In particular, there is a conceptual difference between (a) small areas on a map of Earth, which appear similar to the view when looking "inward" at some real piece of Earth from the air, and (b) small areas of a panoramic photograph or a spherical panorama or an IMAX Dome filmstrip or the Cosmic Background Explorer sky map, which appear similar to the view when looking "outward". And then there is (c) X-ray diffraction pattern.
I hesitate to say that the COBE sky map is "looking outward from some point", because it was assembled from "photographs" taken from many different points, all of them carefully looking away from the Sun and away from the Earth.
What is a good way to briefly mention and perhaps link to articles about these other applications? --68.0.124.33 (talk) 21:00, 1 July 2010 (UTC)

## Suggested modifications

This article needs some attention. I suggest modifications as follows:

1 The term aspect should be introduced for orientation of the projection.

Feel free to add. Strebe (talk) 00:29, 6 April 2009 (UTC)

2 The secant projections should not be dismissed so lightly. They are used in almost all projections intended for accurate mapping. (Such as the 60 UTM projections covering most of the globe and the projections used by Great Britain, Australia and many other countries.) In fact the Albers projection shown further up the page is a secant (or modified) projection.

That is not a dismissal you are reading, though I see how you misread it. The wording means it is never advantageous to use a developable surface that is neither secant nor tangent. Perhaps it should be worded differently. Strebe (talk) 00:29, 6 April 2009 (UTC)
Secant projections are important so perhaps this section should be expanded — or a new section created. — Peter Mercator (talk) 21:48, 8 April 2009 (UTC)

3 As pointed out in the discussion pages the section on cylindrical projections is misleading: only normal cylindrical projections project meridians into vertical lines. As shown in the figures the transverse and oblique Mercator projections project meridians into curved lines. Almost all the comments in this section refer to the normal aspect so the illustration of the oblique aspect is completely out of place. Peter Mercator (talk) 12:45, 5 April 2009 (UTC)

I agree with your observations about the Cylindrical section. It's not clear to me that the section needs to be rewritten. It does need to be qualified. And it's certainly true that that the graphic is not helpful. Strebe (talk) 00:29, 6 April 2009 (UTC)
If we simply replace "cylindrical" by "normal cylindrical" then that section may not need editing, other than altering the title. On the other hand I feel that this section is possibly overly long compared with the others. Further, you have to mention the other aspects of the cylindrical projections since they are just as important. — Peter Mercator (talk) 21:48, 8 April 2009 (UTC)

• Comment - I think the Classification section needs attention. Three of the properties are far from being obvious and should be explained:
1. Preserving direction (azimuth)- at least two interpretations of this property can be considered: the conservation of the azimuth of an object as measured at a certain position along the great circle connecting both; and the conservation of the rhumb-line direction (angle with the meridians)between two points.
2. Preserving shape - I've never liked this way of expressing conformality because it calls for an abstraction (conserving shape of an infinitesimal figure). I prefer "conserving angles around a point" or, even better, "making scale constant around a point". Anyway, this needs a careful explanation because it is a common and serious mistake among students (and some professors,hélàs!) to state thatconformal projections preserve shapes.
3. Preserving shortest route - no projectionn exists with this property. The gnomonic does not preserve distance or angles, just makes great circles straigth. -- Alvesgaspar (talk) 13:40, 6 April 2009 (UTC)
I agree strongly that the term "orthomorphic" should be deprecated since it is an approximate property. The two (equivalent) exact statements that I prefer are "conformality at a point" and "isotropy of point scale at a point": I think the first is easier to explain for point scale is much more subtle for non-mathematicians. (I am revising that page at the moment). I am afraid that I find the phrase "around a point" unclear. — Peter Mercator (talk) 21:48, 8 April 2009 (UTC)
• Conformal comes from the latin and means ... "same shape (form)" ;-) -- Alvesgaspar (talk) 22:42, 8 April 2009 (UTC)

Peter Mercator, thanks for the efforts. I think we need to refine the edits.

Any equidistant projection is equidistant from two points, not just one. The difference between Maurer's projection and the rest is that the two-point equidistant allows you to specify the two points independently. In the case of the rest, it's always two antipodal points.

Qualifying cylindric as "normal cylindric" seems less than ideal, since most of the principles discussed apply to any aspect of a cylindric. I think we are failing if we do not describe aspect well enough earlier on to handle the situation gracefully in this section. We need to discuss cylindrics generally, not just in normal aspect. For now I'm going to revert just the header.

I also strongly wish not to leave out the explanation that most projections are not physical projections. Perhaps the wording and organization could be better than it was, but it needs to be there.

Cartesian and polar coordinates need links.

Thanks for the efforts. Strebe (talk) 21:04, 25 November 2009 (UTC)

Daniel. Sorry about yesterday's rush of blood; too much, too hurried. (BTW I presume you are the Strebe acknowledged in the preface of 'Flattening'. Am I correct?) Most points you make are fine and there are three options for each: A, I try again; B, I revert to your original; C, you re-edit first. (And another BTW. I presume you are the principal author of this document. Correct? )
1. Equidistant. Suggest B or C. Mentioning Maurer is confusing. It's just that the interpretation of 'from two . . locations' is difficult when one or both of the locations is a singularity of the transformation and is not represented by a point on the projection. This may be hard to grasp for the non-specialised reader, whereas 'lines radiating from a single point' (as in azimuthal) is clear with the normal usage of the word point. If you opt for C please leave citation for 'Flattening' somewhere on the page.
2. Normal or not. Option C? In the first sentence of 'Cylindrical' you must agree that the qualifier 'normal' is essential to make the sentence correct. The trouble is that the 'mutatis mutandis' statement is then out of place in that sentence with further discussion of aspect. (The original text is still in the file but commented out). Not sure about how to proceed on this section.
3. Not perspective. Option B, C or A. I think we agree on this and I thought my mod conveyed the same thrust. But perhaps your ordering is better. In fact I think this point should be made more strongly. Possibly a bit of bold text in the right place? I removed the last sentence here so that in the paragraph the contrast of perspective and formulae is enhanced.
4. I removed the link to a mathematical discussion of point since its common usage is adequate here. Such links make the non-mathematical reader feel they are missing something profound. But happy with option B for that. On the other hand we need the links for Cartesian and polar. Option A or C.
5. In 'Construction' I removed the comment on 'scale' since clarification requires a discussion of distinction between intrinsic projection scale and overall scaling by some constant to the final printed map. So we get into topics like representative fraction, generating globe, unit sphere. I have tried to put some of this into scale (map) but I'm not particularly happy with the state of that article. Option A, C or just leave it out?
Looking forward to your comments or actions. Peter Mercator (talk) 12:20, 26 November 2009 (UTC)
Peter Mercator, thanks for the clarifications. You have blown my cover; I am that Strebe! I am not, however, the original author of this article and have not put nearly as much work into it as it needs or as I would like. Mostly I have just tried to stave off the entropy. I am very pleased to have seen your efforts in these articles dealing with map projections. This one, at the very least, needs much work.
The reason for the (perhaps strained) original verbiage in the Construction of a map projection section was to try to get people to understand that the following sections were only conceptual and should not be taken literally. I am not sure I even like the classical approach of explaining developable surfaces, since they have so little to do with real map projection construction. It seems inevitable, though. So, yes, let us figure out an effective way to convey this. Perhaps, for example, those sections should be subordinated to Construction of a map projection. I'm not sure why they aren't already.
I heartily agree that linking to "point" is, well, pointless. I will think about how to handle the equidistant case. I agree the cylindric discussion was careless in the face of aspect change, and I will think about how to deal better with that as well.
Also, by the way, along the lines of improving the graphics: I can easily generate such graphics according to whatever standardized schema we agree is best, in whatever quantity and quality, in whatever aspect, both for this article and more specialized ones.
Strebe (talk) 21:36, 26 November 2009 (UTC)
Please see detailed comments on my talk page. Peter Mercator (talk) 17:28, 27 November 2009 (UTC)

The gnomonic projection has the property that "The points along a straight line between any two points on the map corresponds to the points along the shortest route between the corresponding points on the globe". That's a bit long-winded, so some people try to convey that idea with the brief phrase "Preserving shortest route". Alas, some people misinterpret "Preserving shortest route" as "preserving the length of the shortest route", or perhaps "preserving the direction of the shortest route", and conclude that "Preserving shortest route - no projectionn exists with this property." Is there some other phrase we could use to give a correct understanding to our readers, or are we forced to use the long-winded description? --68.0.124.33 (talk) 04:45, 16 July 2010 (UTC)

## Projection used in Google Earth and similar

Google Earth and similar applications are very popular these days. What is the name of the projection that we get by "photographing" the Earth from a certain distance, just like GE does? It is the most natural projection, but only half of the Earth can be seen this way. Qorilla (talk) 20:53, 23 August 2009 (UTC)

It is the perspective projection. Strebe (talk) 19:12, 24 August 2009 (UTC)

## Two corrections

The section on classification of projections contains two errors in the statement "pseudoconic (meridians are arcs of circles), pseudocylindrical (meridians are straight lines)". The bracketed 'explanations' are incorrect, as evidenced by the Bonne and the Sinusoidal projections respectively. Replacing 'meridians' by 'parallels' gives correct statements but these are not definitions.Since the remaining projections in this list are unqualified in any way I suggest that the bracketed comments are simply removed until this article is revised thoroughly. I have removed these statements for the time being. Peter Mercator (talk) 21:28, 1 November 2009 (UTC)

## Can thin out the list of examples.

All of the map projections are going into List of map projections. I suggest that the list of examples in each projection type is thinned to a few key examples, linking to the complete list. I will do it myself in a few days if no one objects. Noodle snacks (talk) 01:29, 8 November 2009 (UTC)

That seems like a good edit. Strebe (talk) 01:49, 8 November 2009 (UTC)
Happy to see the list of projections. Is the long term aim for this to be a fairly compehensive list of 200 or so projections? Will every projection be added at least twice, eg Mercator under cylinder and conformal? What plans for this (map projection)page? Just a query . . . .Peter Mercator (talk) 22:56, 11 November 2009 (UTC)

## Illustrations of projections

I am a little concerned about the images illustrating the projections in this page and also 'List of projections'. I feel that that any illustration should show the overall shape of the projection and also show a clearly defined graticule (with significant lines such as standard parallels or central meridians emphasised if possible). The land/sea boundary should be clear and colours such that the graticule should be clearly visible over both. There is no need for content on the landmasses: it simply detracts from the a page about projections. The other really important information is the distortion: this would best be shown on a separate Tissot illustration (in the projection file). The thumbnails below show contributions by User:Mdf, User:Stefan Kühn, User:Reisio and User:Strebe: these could be the basis for comments. Sadly the first image fails on almost all the above aspects and is moreover problematic for users with poor sight. (Can you find north New Zealand or Borneo?)

Peter Mercator (talk) 23:09, 11 November 2009 (UTC)

I agree the "realistic" view is a bad choice here. See my User:Strebe page for an example of a style of distortion illustration that can be produced easily for use here, given arbitrary projections. Strebe (talk) 05:28, 13 November 2009 (UTC)

## Formulae of projections

Exploring all the projection pages reveals that two conventions are in use. That of cartographers, radius (R) explicit in formulae, an that of mathematicians, unit sphere. My own preference is for the former, not least because it follows the usage of Snyder in 'A Working Manual' and 'Flattening', the two most accessible surveys. Peter Mercator (talk) 23:11, 11 November 2009 (UTC)

## New page on cylindrical projections

I would be grateful if users of this page could comment on an outine of a proposed new page on cylindrical projections at User:Peter Mercator/Draft for cylindrical projections. Please add comments there rather than on this page. Peter Mercator (talk) 23:14, 11 November 2009 (UTC)

## sinus interruption

Some map projections completely cover some convex shape. Other map projections have several more or less deep "cuts" in them, in particular the "interrupted sinusoidal projection", the Dymaxion map, and the butterfly maps.

I was hoping this article would tell me: What is the official cartographic name for these "cuts"? Is there an official cartographic name for "creating a slightly different map by slicing off a little area on one side of a cut, and gluing those slices onto the opposite side of a cut"? Why do some maps have "cuts" while others don't? When cartographers make cuts in a map, what sorts of aesthetic considerations do they use when picking the exact place for each cut -- are "try to cut only in the oceans, avoiding the continents" vs. "try to cut only in the continents, avoiding the oceans" the only 2 options? If you know the answers to these questions, would you please edit this article to answer those questions? Thank you. --68.0.124.33 (talk) 05:43, 25 June 2010 (UTC)

Thanks for the comments. The article does need more on interruptions. It contains an illustration showing interruptions along with the statement that ‘Distortion can be reduced by “interrupting” the map.’ What is there is inadequate.
To answer your specific questions, some of which would be too narrow to include in the article:
• The usual name for a cut is interruption. A map with more than the normal east/west interruption is called an interrupted map.
• There is no recognized name for the practice of changing a map by moving territories across cuts. It is a rare practice.
• Most maps do not have cuts because the mapmaker wanted the map to retain as much continuity as possible. Cuts are disruptive. Those maps that have interruptions generally focus on either the continental masses, with no concern for oceans; or, conversely, focus on the oceans with no concern for continental masses.
• You have identified the normal two factors mapmakers consider when interrupting a map. There may be others: They may “need” to interrupt at an inconvenient place in order for the topology of their projection to work. For example, they may want a radially symmetric map, yet the continents do not allow that without getting split up.
Strebe (talk) 19:39, 27 June 2010 (UTC)
Thank you, Strebe. --68.0.124.33 (talk) 01:28, 16 July 2010 (UTC)

## Categorisation

Hi. I was thinking of subcategorising the list in compromise projections, with a brief description. The list is too long, and it doesn't hang well in the reader's mind. I was thinking of something like: Projections used by National Geographic (then a list including the years adopted). Then other uninterrupted projections. Then interrupted projections (with brief descriptions). I think this would help create a hierarchy (eg Robinson and van der Grinten have been surpassed by Winkel Tripel in the minds of the cartographers at National Geographic), etc. My view is that any list with more than about 3 or 4 things in it should be categorised and made into sublist. Thoughts? Grj23 (talk) 07:24, 30 July 2010 (UTC)

Or, perhaps, by surface, since that is the classification scheme introduced above? We should not develop the subcategories based strongly on what is already there because the list in its present form is small compared to its potential. Also, the “Other Noteworthy projections” category is spurious. I will delete it and merge the content with “Compromise projections”. Strebe (talk) 17:28, 30 July 2010 (UTC)

## remove link to equidistant conic projection?

Right now Equidistant_conic_projection redirects back here, so clicking it is confusing :( 178.95.30.155 (talk) 05:01, 20 December 2010 (UTC)

Done. Thanks for finding this. Strebe (talk) 08:25, 20 December 2010 (UTC)

## Myriahedral projection

Am I just not seeing it here? 71.199.96.212 (talk) 04:15, 1 March 2011 (UTC)

Hm, it's not a distinct kind of projection in the sense discussed in this article; it's a piecewise gnomonic projection (the Dymaxion map is an example). The article does once mention interrupted sinusoidal maps, but I guess it could stand to have more about piecewise maps. —Tamfang (talk) 05:27, 1 March 2011 (UTC)
I agree that this article would be improved by a few more words on piecewise maps.
While perhaps most polyhedral maps are piecewise gnomonic projection, the Dymaxion map article specifically says "It is not a gnomonic projection". (Is it perhaps an equal-area projection like the quadrilateralized spherical cube, or perhaps something like the Chamberlin trimetric projection ?)
Meanwhile, the list of map projections lists many map projections not mentioned in this article -- including a brief mention of "Myriahedral". --68.0.124.33 (talk) 18:14, 8 March 2011 (UTC)

## Which projection IS 'best'?

This is an interesting article to me as a layperson. Is it possible to explore the 'Which map is best?' section further? For example, what projections are currently favoured by whom? One of the images suggests that "The Robinson projection was adopted by National Geographic Magazine in 1988 but abandoned by them in about 1997 for the Winkel Tripel." Is there more of this type of information available? Thanks. Richdesign (talk) 08:52, 9 April 2011 (UTC)

• Assuming that you are referring to the representation of the world, there is no such thing as "the best projection". That is because it is impossible to represent the curved surface of the Earth onto a plane without distorting the relative position of the places (directions and distances) and the shape of the objects. Even if we are interested in a specific property, such as conformality (scale does not change with direction around a point), equivalence (area proportion isconserved) or minimum error, we are still left with many possibilities. A fine choice will depend on the purpose of the map, taste and possibly ... fashion. Yes, it would be nice to expand the section "Which map is best" to talk about this subject. Maybe I can give a hand if someone takes the initiative. Alvesgaspar (talk) 09:46, 9 April 2011 (UTC)

Personally, I think the section is pandering. Imagine if the article on fonts had a section called "Which Font is Best?" with a bunch of words devoted to smacking down Arial/Comic Sans/whatever, and then no information whatsoever on what people can agree on? If anything, it needs to be yanked as completely uninformative. Tmcw (talk) 15:37, 29 November 2011 (UTC)

It doesn’t look like pandering to me; it looks poorly written and uninformative. Yanked? Possibly. Rewritten? Much better. Strebe (talk) 18:42, 29 November 2011 (UTC)
Okay, I made a rudimentary stab at fixing the deplorable state of that section. It could be fleshed out much, much more with examples and what reasons might come into play for choosing each of the examples. Meanwhile, the article doesn’t even have a useful explanation of distortion, which means it’s not an article on map projections. Strebe (talk) 22:39, 29 November 2011 (UTC)

## “Infinite”

I do not think these efforts to inject “infinite” into the lede are helpful. The latest, “The family of possible map projections is infinite”, is definitely going in the wrong direction. “Family” is not defined and “family is infinite” means nothing. Technically, “the count of members of the set of possible map projection is infinite”, but this is not an article on mathematics. In particular the lede needs to avoid jargon while being correct. The original objection based on orders of infinity is not relevant, not interesting, and not even correct. Just because there are higher orders of infinity does not mean Aleph 0 is “limited”, and furthermore, where is the proof of which infinity the set belongs to? Can we not mess with something simple, free of jargon, and accurate? Strebe (talk) 20:53, 19 June 2011 (UTC)

## Replace low-contrast images

I will be replacing images on the various map projection pages. Presently many are on a satellite composite image from NASA that, while realistic, poorly demonstrates the projections because of dark color and low contrast. I have created a stylization of the same data with much brighter water areas and a light graticule to contrast. See the thumbnail of the example from another article. Some images on some pages are acceptable but differ stylistically from most articles; I will replace these also.

The images will be high resolution and antialiased, with 15° graticules for world projections, red, translucent equator, red tropics, and blue polar circles.

Please discuss agreement or objections over here (not this page). I intend to start these replacements on 13 August. Thank you. Strebe (talk) 22:43, 6 August 2011 (UTC)

## XKCD webcomic page titled Map Projections

Thought people on this page might like to see this - perception of map projections in popular culture. :) EdwardLane (talk) 11:21, 17 November 2011 (UTC)

## Projection images

It might be useful to show an image showing how projections works. This site,http://content.answcdn.com/main/content/img/McGrawHill/Aviation/f0426-02.gif or this site http://engineeringtraining.tpub.com/14070/css/14070_185.htm show how the Mercator is done (projected from the center, through a point on the surface onto the wrapping cylinder.) Geoffrey.landis (talk) 02:05, 29 March 2012 (UTC)

The first image doesn’t bother to state what it is. The description in the second article is conceptual: “To grasp the concept of Mercator projection, imagine the earth to be a glass sphere with a strong light at the center,” and the diagram is simply wrong. The Mercator is not a perspective projection. The projection your verbiage describes is usually called the “central cylindric” or the “cylindrical perspective” projection. See, for example, this unfortunate gaffe. Strebe (talk) 02:26, 29 March 2012 (UTC)
Have a look at the misconception here Peter Mercator (talk) 09:53, 29 March 2012 (UTC)
It's not hard to show that central cylindric projection is not conformal. —Tamfang (talk) 02:13, 16 April 2012 (UTC)

## Lede

The lede is slightly misleading Where it says "Map projections are necessary for creating maps."

it would be more accurate to say something like "Map projections are necessary for creating any non abstract maps." As I'm pretty sure the london undergound map doesn't use map projection, but once you map it onto the 'real map of london' you obviously are using a projection of some sort.

However the text "Map projections are necessary for creating any non abstract maps." sounds horrible and would possibly still be misleading trying to think of an example of a non abtract map that doesn't use map projection, I can imagine some (though perhaps my definition of abstract map is not perfect). Also interested to note that is a redlink.

Perhaps it should say "Most maps use one Map projection to calculate where to place each object on the map's surface."

Or perhaps "Map projections are necessary for creating scale maps." which I think I'll add now as a simplest start.

Thoughts, suggestions ?

EdwardLane (talk) 10:43, 8 June 2012 (UTC)

Good to hear from you, EdwardLane. I’m puzzled by your use of “scale maps”. What does it mean? It’s nothing I’ve encountered in 25 years in cartographic circles.
I was thinking in terms of a scale model - being a model that maintains the scale, probably equal area/distance/angle is I guess is what I meant. The contrary version would probably be a topological map (and thanks for pointing me at the correct vocabulary).
“a model that maintains the scale”: But there is no such thing. Scale necessarily varies across a map.
it's ok I see that I had left myself with an over generalised definition of 'map' and that's where my confusion began EdwardLane (talk) 11:16, 18 June 2012 (UTC)
I’m going to disagree about “abstract maps”, which I would call topological maps. It is true subway maps, for example, use no conscious projection in their construction. Yet a projection is implied and can always be described for it. In fact, the interesting inversion here is that a map of a subway system could ignore the issue of projection because the earth’s curvature across its expanse is likely less than the track’s own elevation changes. And yet the map projection implicit in the topological map is precisely how you can apprehend its spatial deformation. Strebe (talk) 01:48, 9 June 2012 (UTC)
I've bolded your own text above which illustrates the problem with the original sentence, "Map projections are necessary for creating maps."
We’re jumbling up a lot of different things here. If the subway system has no curvature in all three dimensions, and if the subway map preserves all relative distances and directions, then the map needs no projection; it is merely a scaling of an abstract surface that is either flat or “developable”. (A mathematician would still call that a projection, but it wouldn’t fit within the cartographic definition of a projection.) But the subway map you describe does imply projection due to its purpose of preserving only topology without regard to distance and direction, as Tamfang writes below. The fact that the projection is highly convoluted does not matter; there is no difference in principle from any other map projection. The real difference comes next…
good explanation thanks EdwardLane (talk) 11:16, 18 June 2012 (UTC)
Notice the definition of map projection in the lede and explanation in the Background section: A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane… For simplicity of description, most of this article assumes that the surface to be mapped is that of a sphere. A subway map does not fit the definition of map in use in the article. As written, the article was correct. I will delete “scale map” now that we have discussed it. There is no good boundary on the term “map” in general—it means different things in different domains and its meaning even in cartography is not sharp—but the article imposes a rigorous one for its own purposes.
and also well clarified, perhaps a paraphrase of this wording is what I was missing where I had the word 'scale' in there. EdwardLane (talk) 11:16, 18 June 2012 (UTC)
Just to try to give a feel for how much more complicated the situation really is, even a “perfect” subway map—one which preserves relative distances and directions—in practice would end up being a map as defined in the article because coordinates of the subway system would (in practice) be referred to the normal geodetic models. They would be treated no differently than, for example, positions on hills or in valleys that are above or below the surface of the ellipsoid. In other words, despite being buried in the earth, the geographic coordinates used to map the system would end up on the surface of the ellipsoid and hence would use a classical map projection in its representation. The reason I wrote a map of a subway system could ignore the issue of projection was because these local topographical variations overwhelm any physical “need” for a projection even though in rigorous terms a projection will always be in play due to using coordinates referred to the datum. Ignoring it doesn’t make it go away! And that’s not even getting into the intermediate abstraction of the geoid… Cheers! Strebe (talk) 20:00, 15 June 2012 (UTC)
I'm happy to bow to your expertise though about topological maps 'always' having a projection it is possible to describe. If I took a list of the underground stations in alphabetical order and put them in a nice square grid based on that and then maintained the topological linkages I can't imaging any map projection that could map real world coordinates onto those. EdwardLane (talk) 11:24, 15 June 2012 (UTC)
For any finite set of points, there exists a polynomial function to map them to any layout! —Tamfang (talk) 15:45, 15 June 2012 (UTC)
A rational function might be 'nicer' in some way, but polynomials are guaranteed continuous. —Tamfang (talk) 15:46, 15 June 2012 (UTC)
Thanks Tamfang, I didn't know there was always a polynomial function to map a finite number of points, but I suppose I could probably have gone and looked for that mathematical proof. I would have thought that the lines forming the topological linkages would have been continuous rather than finite, but I'm happy to leave the word out on the basis that the term 'map projection' was defined as 'A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane'. EdwardLane (talk) 11:16, 18 June 2012 (UTC)
The stations are a finite set of points. The function that maps the stations to your square array also maps the tracks to continuous arcs. I can even promise that the angles where tracks cross are preserved (except at n-2 points, where n is the number of stations).Tamfang (talk) 17:52, 18 June 2012 (UTC)

## Distortion

Take the earth, and shrink it to the size of a globe - I don't know but maybe a scale of 1:500000 would be a nice sized globe.

Now let's ignore the fact that even the crust's thickness varies on the underside as well as on the top (mountains and things have roots), and let's pretend the mantle is a sphere.

So lets cut off the crust (down to the mantle) like an orange peel, and flatten it all out - now start cutting (interuptions) everywhere that it doesn't fall perfectly onto a flat surface (the top will not be flat). But even getting the underside to fall 'perfectly' on a flat surface is going to take an awful lot of cutting, and unless you accept a certain amount of imperfection you're never going to finish.

But let's assume you decide that anything less than a kilometer of error is good enough that's what a map ought to show if you are not distorting the 'scale' of any particular place.

But now you end up with a very strange looking orangepeel (lets imagine you've managed to keep most of the cuts in the ocean rather than the land) - so take a photo of that from above, and then put the world back together at full scale again (we may need it later).

So now you look at your photo in some graphics package, and you notice lots of little white bits that make it hard to read, and if you stretch the image a little bit in places you can make it all join up and look more like a normal map, and if you want it to cover the whole page nicely then you need to stretch it a lot in certain spots, but think you can get away with filling in some of the space with seas, no one will notice that unless they are measuring how far away one country is from another (hmm that might matter).

Does that sound about right for getting ones head around the concept is anything obvious missing? Before I try converting that rather silly train of thought into something encyclopedic sounding EdwardLane (talk) 11:20, 8 June 2012 (UTC)

• Let me first ask you a candid question: did you haver study the theory (and story) of map projections? If not, let me congratulate you for your approach. But all of what you suggest has been already said, and tried, a long time ago! A classic example of an interrupted map projection of the type you propose is this one. But there are many more possibilities (an infinite number of them, btw). A good book to start: John Snyder (1994): "Flattening the Earth: two thousand years of map projections". Alvesgaspar (talk) 19:00, 8 June 2012 (UTC)
• Never formally but you learn stuff as you go along, and whilst no one has told me the sotry I guess I was fairly confident that was roughly the thought process you would have to go through and thus a reasonable starting place for the discussion. EdwardLane (talk) 10:55, 15 June 2012 (UTC)
I figured that Goode homolosine was not actually a perfect (just very close to) equal area projection. But I guess I may be wrong about that, so I'm happy to take that as the starting point. What I'm focussing on however is that there should be a section in this article on Map distortion and we need to explain clearly what it means in terms of direction/area being distorted (more on Tissot index and all that sort of stuff). I'm trying to imagine someone animating the distortion starting with a Goode homolosine projection, and 'stretching it' to fit a Mercator projection which would show the changes in area nicely. And then going back the other way, showing the conformal lines being distorted/interrupted.

EdwardLane (talk) 10:55, 15 June 2012 (UTC)

You are absolutely right to say the article needs a better, more focused treatment of distortion. It is scandalous that the first mention of the Tissot ellipse is down in the “See also” section, for example. Rather than reinventing the wheel (WP:OR concerns as well as didactic problems with your approach) we should refer to existing texts in the treatment of distortion. Slocum/ McMaster/Kessler/Howard’s Thematic Cartography and Geographic Visualization (2nd ed., not 1st), for example, gives an unusually thorough treatment suited for lay audiences. Strebe (talk) 20:07, 15 June 2012 (UTC)
Go for it - I'm just reinventing the wheel as I didn't know where the nice bits of text to point at are, (and I'm cautious that I avoid copyvio infringements). And yes it would have been nasty OR at the current state if I'd stuck that in the article, but once the I'd made sure I'd understood the idea properly I'd have cobbled text more encyclopedic text together and at the same time I would have looked for references. EdwardLane (talk) 11:25, 18 June 2012 (UTC)

## Map projection vs Map arrangement

Just carrying over a comment from the list of map projections talk page. I think we need to try and make a couple of graphics - maybe these two with 3 or 4 examples in each?

One map projection multiple arrangements and One arrangement multiple projections

I think that could help resolve the perennial questions about 'upside down maps' and also the specific one in the link about 'double hemisphere maps' EdwardLane (talk) 11:27, 11 February 2013 (UTC)

## Grammatical ambiguities

(Copied from my Talk page.)

"The surface of a sphere, or another three-dimensional object".

is that meant to be "(the surface of a sphere), or another three-dimensional object"?

or is it meant to be "the surface of (a sphere, or another three-dimensional object)" ?

Clearly, it is meant to be the second, but the IP user parsed it the first way, and thence concluded that it was erroneous and in need of correction, and became upset when you reverted it to the 'incorrect' version. My edit removes the grammatical ambiguity. Okay? DS (talk) 00:24, 5 March 2013 (UTC)

First, you need to move this discussion to the article’s talk page, not mine. I will copy and past all this there.
Second, the phrase you changed was not as you wrote above. You’ve added a comma that didn’t exist and you’re using “another” instead of “other” and you’ve changed “body” to “object”. The full sentence was, “A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane.” There is no defensible way to read that as, “A map projection is any method of representing the surface… or other three-dimensional body on a plane.” It cannot be read that way because “the surface” otherwise does not refer to anything. The reader simply does not understand English or the topic well enough, as is clear from “his” edits that produced clearly incorrect results. Your “correction” does not resolve anything. If I can misread the original the way the objecting editor did, then I can misread your “correction” as well. I do not agree that just because some random person amongst thousands misread the text, that something is wrong or ambiguous, especially when his “correction” was clearly wrong. Strebe (talk) 01:07, 5 March 2013 (UTC)

I am a native English speaker and a mathematician, so I think I both "understand English [and] the topic well enough". Do not resort to personal attacks. My correction was perfectly justified, as any geometry textbook will make clear to you. A (common) sphere is 2-dimensional, although it often is, but need not be, embedded in higher-dimensional space. Even in these cases it is simply wrong to say that a sphere is 3d.

The sentence to which I objected was: "A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane." This means, by the law of disjunction, [A map projection is any method of representing the surface of a sphere on a plane] AND [A map projection is any method of representing non-sphere 3d bodies on a plane]. But a sphere is not a 3d body. So the second conjunct is false so the conjunction is false so the proposition is false.

Moreover, this is very bad definition in general, because there is no reason to be arbitrary and talk of projections from 3d geometries. It does make sense to talk about spheres, of course, since this is how we commonly use projections (viz. to make maps). But really the rest of that definition should be changed to make more general. I'll hold off on that until we get some more consensus.

Recall Wittgenstein: "Whereof one cannot speak, thereof one must remain silent." — Preceding unsigned comment added by 184.186.8.148 (talk) 04:31, 5 March 2013 (UTC)

It’s not everyone else’s problem that you deal with surfaces and not volumes, so don’t make it everyone else’s problem. A sphere is a three dimensional body. Asserting otherwise is ludicrous. It’s a body. The text said “body”. You cannot make “body” mean the surface, so stop trying. Your application of the rules of symbolic logic on English is pointless as well. English “or” does not precisely mean a disjunctive OR; nor can you just throw in parenthetical groupings that suit you. Your interpretation of the original verbiage fails because you arbitrarily (and apparently tendentiously) adopted a lexical reading unsupported by the semantics. And no, your agenda to generalize the article is pointless as well; the article is about map projections, not about projections or differential geometry at large. Expanding the scope or even the definition to anything beyond roughly spherical bodies is some other article, not this one. The article needs a lot of work, but not in that direction. Strebe (talk) 05:28, 5 March 2013 (UTC)
And by the way, DS, it is now abundantly clear that the other editor would not be placated by your change, since “ambiguity” is not his complaint. Strebe (talk) 05:32, 5 March 2013 (UTC)

A sphere is not a three dimensional body. That is silly. Think about how many coordinates it takes to define a point on the surface of the Earth. Two. Cf., e.g. the Wolfram Math Encyclopedia: "Regardless of the choice of convention for indexing the number of dimensions of a sphere, the term "sphere" refers to the surface only, so the usual sphere is a two-dimensional surface. The colloquial practice of using the term "sphere" to refer to the interior of a sphere is therefore discouraged, with the interior of the sphere (i.e., the "solid sphere") being more properly termed a "ball."". This is standard in mathematics. — Preceding unsigned comment added by 184.186.8.148 (talk) 21:27, 5 March 2013 (UTC)

• I have reverted the edits made by anonymous user for the last time, based on the present discussion. Now I am also convinced that these changes are not being made in strict good faith and will propose more drastic measures if the problem persists. -- Alvesgaspar (talk) 22:14, 5 March 2013 (UTC)
“A sphere is not a three dimensional body. That is silly.” You are silly for calling it silly, and you know you are silly for calling it silly. That makes you a troll. You’re using a different definition of sphere. That’s fine, but it doesn’t belong here. It doesn’t matter what Wolfram says or what mathematical convention has evolved into. That’s not this field. This field is cartography and its relationship to geodesy. In both, “sphere” is a solid, and the literature is replete with the phrase “surface of the sphere”. As for generalizing to any curved surface, that too is silly; the entire article is written and illustrated around the sphere and geared toward cartography. Stop trolling. Strebe (talk) 03:06, 6 March 2013 (UTC)

Do not resort to personal insult. Words matter. Things are true, and they are false. One can easily verify that a common sphere is 2d. I recommend that you do so. — Preceding unsigned comment added by 184.186.8.148 (talk) 04:32, 6 March 2013 (UTC)

Oxford American Dictionaries: sphere |sfi(ə)r|
noun
1 a round solid figure, or its surface, with every point on its surface equidistant from its center.
• an object having this shape; a ball or globe.
• a globe representing the earth.
From John P Snyder, An Album of Map Projections, US Geological Survey Professional Paper 1453, 1989:
Great circle: Any circle on the surface of a sphere…
Latitude (geographic): Angle made by a perpendicular to a given point on the surface of a sphere or ellipsoid…
Parallel: Small circle on the surface of the Earth formed by the intersection of the surface of the reference sphere or ellipsoid…
Perspective projection: Projection produced by projecting straight lines radiating from a selected point (or from infinity) through points on the surface of a sphere or ellipsoid…
Small circle: Circle on the surface of a sphere…
A projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid…' (p.5)
If we assume for simplicity that a globe, which is a sphere… (p.5)
You are obstinately misapplying terms from another domain. You are trolling. You are wasting everyone’s time, including your own. Go away. Strebe (talk) 06:04, 6 March 2013 (UTC)

No, you "[g]o away". And while you're gone take a basic class in geometry. You'll see your error. E.g.:

(1) http://www.youtube.com/watch?v=5j0ZxkcVwhk ("Two-dimensional surfaces: the sphere") (2) "Regardless of the choice of convention for indexing the number of dimensions of a sphere, the term "sphere" refers to the surface only, so the usual sphere is a two-dimensional surface." (http://mathworld.wolfram.com/Sphere.html) (3) WIKIPEDIA: "Just as an ordinary sphere (or 2-sphere) is a two-dimensional surface that forms the boundary of a ball in three dimensions" (http://en.wikipedia.org/wiki/3-sphere). (4) Princeton: "[A] 3-sphere is a higher-dimensional analogue of a sphere" (http://www.princeton.edu/~achaney/tmve/wiki100k/docs/3-sphere.html) — Preceding unsigned comment added by 184.186.8.148 (talk) 07:09, 6 March 2013 (UTC)

Gentlemen, pace. Can we terminate this debate and simply agree on a satisfactory and simple first sentence. At the moment it is:
A map projection is a systematic transformation of points on a sphere or an ellipsoid to points on a plane.
This is fairly satisfactory but minor improvements are possible. For example one might wish to stress the cartographical rather than the the mathematical with
A map projection is a transformation of the geographical coordinates of points on the surface of the Earth, as approximated by a sphere or reference ellipsoid, to coordinates on a plane.
In any case, let's stop the discussion of mathematical usage and common usage. Certainly avoid the word body which started the rot.
Peter Mercator (talk) 11:15, 6 March 2013 (UTC)
• I agree with the text suggested by Peter. It is a good idea to emphasize the point that the object (domain) of a map projection is a reference surface, not the surface of the Earth. -- Alvesgaspar (talk) 12:02, 6 March 2013 (UTC)
It is not our job to construct a definition. I supplied one from an authoritative source. No one else has. The IP editor mangled it, deleted the citation, and rendered the reference broken, which is how the situation stands. There was nothing wrong with “body”; its purpose was to make clear that the topic is representing surfaces of three- (not two-, not four-) dimensional objects on a plane as well as to suggest bodies (primarily celestial) beyond just the earth. The convention in map projection literature is that “sphere” refers to the entire body, not just the surface. A reason for that (besides the fact that historically “sphere” has always meant the entire ball [it derives from Greek σφαίρα (sphaira) = ball]; the geometric usage the IP editor insists on is recent and narrow) is because datum transformations must also include height above or below the reference ellipsoid and must consider offsets and rotations in 3-space, and also because geodesy in general deal with three coordinates, not two. It’s also true that the spherical or ellipsoidal approximation for the geoid is sometimes required or chosen to be volumetric, not authalic. Strebe (talk) 16:51, 6 March 2013 (UTC)
• Let me quote the definitions given in the "Glossary of Mapping Sciences" (1994), p. 321: (1) A pair of functions relating coordinates of points on a specified surface (usually a rotational ellipsoid) to coordinates of corresponding points on a plane. Equivalently, a relation between a coordinate system on a specified surface and a coordinate system on a plane; (2) any systematic method of representing the whole or a part of the curved surface of the Earth [or of any other body, I would say] upon another, usually flat, surface. I prefer the second definition which is less mathematical and more appropriate to a general encyclopaedia. -- Alvesgaspar (talk) 19:06, 6 March 2013 (UTC)

## RFC: Is a common sphere (like the surface of a soccer ball) a two-dimensional or a three-dimensional object?

Is a common sphere (like the surface of a soccer ball) a two-dimensional or a three-dimensional object?184.186.8.148 (talk) 07:18, 6 March 2013 (UTC)

I do not think we should shy away from precise mathematical language in this article, though, as it is about a fundamentally mathematical concept--a map projection--and uses substantial mathematical notional and contains substantial mathematical discussion.184.186.8.148 (talk) 06:36, 7 March 2013 (UTC)
Agreed. There is common community consensus upon employing the vernacular of the relevant field when treating fundamentally technical subjects. In this case, it is clear that we should lead with the most general and pragmatic description of a sphere -- which necessitates some mathematical description at a bear minimum, and empirically clear distinctions -- such as between the sphere and the surface of the sphere, as this is relevant as to the dimensions they occupy and how -- in any event. And really, once you are talking about spatial dimensions, you're pretty committed to a mathematical description at that point, not really any way around it. I might also suggest though, to our more graphically-minded editors if any are present, that this is a case where the right visual could go a long way. Snow (talk) 10:26, 23 March 2013 (UTC)
The common terminology—that a sphere is three dimensional—happens to be the same as the terminology in the map projections literature, as I cited above. Strebe (talk) 16:33, 6 March 2013 (UTC)
Why not just use the same trick as the Sphere article: the first sentence BsZ cited doesn't actually say if a sphere is 2- or 3-dimensional, it just says it's an object in 3D space. If you use a phrasing like "a sphere or another object in three-dimensional space", that works no matter which definition of "sphere" the reader is assuming. — HHHIPPO 19:00, 6 March 2013 (UTC)
I'm okay with that, but one thing to be aware of is that even though the map projections we typically encounter are from curved 2d space (surface of the Earth) to flat 2d space (a road map, e.g.), there's nothing special about these dimensions. The embedding can take place in any dimension, so when you say "a sphere or another object in three-dimensional space" that's not really true--it's a sphere or other object in ANY dimensional space, or indeed not embedded at all.
The key with a projection is that you're going from curved space to flat space, and that you can't do that without losing some features (e.g. distances). What features you lose, and preserve, depends on the mapping you use.184.186.8.148 (talk) 02:42, 7 March 2013 (UTC)
The topic isn’t about “objects in three dimensional space” and it’s definitely not about “embedding” in arbitrary dimensions. Map projections are a cartographic concern that happens to use differential geometry as a tool. The field is not a subset of differential geometry or even of mathematics, despite its use of them. Strebe (talk) 04:12, 7 March 2013 (UTC)
The topic of this thread is the dimensionality of spheres. If you don't want comments on that, please remove the RFC tag. The aim of my suggestion was to avoid the need to differentiate between cartographic and mathematical definitions of terms by using a phrasing that works for both audiences. If you want to use only cartographic terms no matter if the statements are mathematically wrong, that's fine with me. But I would then suggest to mention this (like "In cartography, a map projection is..."), and also to avoid linking to the mathematical articles on any terms you use in a different way, at least in the lede. — HHHIPPO 08:42, 7 March 2013 (UTC)
With apologies to HHHIPPO and others, when I wrote “the topic isn’t about”, I meant the topic of map projections, not this RFC. Strebe (talk) 05:49, 8 March 2013 (UTC)
Concur.184.186.8.148 (talk) 18:02, 7 March 2013 (UTC)
As per others, the RfC is inappropriate for the dispute at hand. First, the parenthetical example begs the question. More to the point, if the standard cartographic/geodesic terminology used in WP:RS is mathematically imprecise (or even wrong), then simply add a note explaining the differences. Not to mention that Earth is not precisely a sphere anyway – "The shape of the Earth approximates an oblate spheroid, a sphere flattened along the axis from pole to pole..." —[AlanM1(talk)]— 09:11, 7 March 2013 (UTC)
Not sure where you get "[a]s per others, the RfC is inappropriate". You seem to be the first person making that claim.184.186.8.148 (talk) 18:02, 7 March 2013 (UTC)
• I concur with AlanM1 that this Rfc is inappropriate and useless. Everybody knows that the surface of a sphere (or any other surface for that matter) is two-dimensional. Thus what are we discussing about here? As for the concept of "sphere" (which is a different matter), I believe that defintions are supposed to serve our purposes, not the other way around... I wonder how many math manuals use the expression "the volume enclosed by a sphere" instead of "the volume of a sphere". The same goes for mathematical cartography... -- Alvesgaspar (talk) 18:48, 7 March 2013 (UTC)
So it sounds like you agree with me then, that a sphere is 2-dimensional? We need to be careful with our terminology; this is why I think it is important that the article be as precise as possible. 184.186.8.148 (talk) 04:45, 8 March 2013 (UTC)
That is not what I wrote, please read more carefully. A definition is just a convenction, not the "truth",and we use differente definitions in different contexts. Alvesgaspar (talk) 10:37, 8 March 2013 (UTC)
See, all this confusion is perfect evidence of why we need to be careful with our terminology. These words have precise meanings. This is a mathematical article and so we have to understand the underlying mathematics and the proper way in which terms are used. The earth is a 3-dimensional ball. The surface of a ball is a 2-dimensional sphere. It is not the case, despite what you say, that "any . . . surface . . . is two-dimensional". The ones we encounter in daily life tend to be, but (e.g.) a 4-dimensional ball would have a 3-dimensional surface.
The essential thing about a projection is not that we're dealing with spheres. That is how maps work commonly, but that is a purely contingent matter. The essential thing is that we are taking CURVED space (viz., in this case, a sphere) and projecting it into FLAT space (a plane). In doing so lots of interesting things happen.184.186.8.148 (talk) 23:59, 8 March 2013 (UTC)
• Well, I really don't need to be patronized by an anonymous user whose only apparent purpose is to disrupt the project and make us loose our time in the process. I may change my attitude if you log in and start using your usual username. In the meantime I don't think we can go on assuming good faith. -- Alvesgaspar (talk) 00:31, 9 March 2013 (UTC)
* There is no policy saying that a user must not use a IP address; what difference does it make? There are, however, policies against assuming bad faith, or being mean to newbies, and so on. I would ask you to abide by these.184.186.8.148 (talk) 00:48, 9 March 2013 (UTC)
The location of any point on the surface of a sphere can be expressed using two dimensions; for example, latitude and longitude. Hence, it is two-dimensional by definition. Praemonitus (talk) 04:46, 12 March 2013 (UTC)
• Neither. A sphere is a set of 1-dimensional points with distance r from the center. As the into states "is a systematic transformation of points on a sphere, a revolution ellipsoid or any other reference surface to points on a plane." A soccer ball is a ball. The Earth could be considered a ball (mathematically). The earth could also be represented as a set of points with no thickness. If the points are continuous, or are interpolated then projected, one could have a plane; if not interpolated, not. As it relates to the article - are map projections to a plane? Sometimes. Sometimes not. Strictly speaking mathematically this is impossible - but one can interpolate imperfections and achieve an acceptable result for the purposes of cartography. Patriot1010 (talk) 20:49, 15 March 2013 (UTC)
• SHRIEEEEEK!!! Folks, in all the RFCs I have been offered, I have never seen so many people on WP so well equipped to understand the basic concepts of the substance under discussion, and yet so comprehensively and variously at odds. Most of us even understand all this and we still get stuck in the same flypaper. If we waste our time and substance on trying to patch this thing up we will never get anywhere worth getting to; just a fabric of band-aids on band-aids, not even a decent web of duct tape. I don't for a moment believe that you will do what I am about to recommend, but I think it is the only thing to do that will work (short of some genius producing a product out of whole cloth that carries everyone's approval, including the readers'). The principle is not just top-down design, but careful decision-deferral at every step, building a complete new version of the article either in the talk page or someone's home page. The approach has two advantages: it limits the topic at every point, so that any contributor who introduces concepts of say, volumes when the relevant concept is surfaces, can have his contribution moved to a "Noise" subsection elsewhere, whence, if it is sound and necessary material, the editors can modify it as necessary and move it to where it is useful.
• 1) Accept two or three arbiters/editors who might or not be pals, but can cooperate without bogging down in trivialities, personalities or other executive disqualifications. If they are skilled cartographers, fine, but skilled WP editors would be more important.
• 2) Construct a top-level of titles for sections and sub-sections; it might or might not resemble or be based on the current TOC for the article, plus a single lede paragraph and an introductory, explanatory sentence or so under each heading. Polish each sentence till it is natural, technically accurate, and understandable; avoid arguments about maths & the like, not by trawling through textbooks for full formal definitions,but rather by helpful informal circumlocution; for example, instead of worrying about the fact that a sphere is a surface and a ball is its enclosed volume as well, speak of "a spherical surface" -- it might be technically redundant, but it would not entail any confusion or actual inaccuracy. At every stage of the development the article does NOT have to explain every technical point, but must have a comfortable and comprehensive structure. Every term or concept that is infrastructural would appear as a link (this has nothing to do with the usual concept of over-linking; it is an editing convenience, so don't re-start THAT fight here as well!) If a link refers to an existing article, check whether the subject is acceptably covered there; if not, take appropriate action in the remote article or compse suitable material for use in situ. If it is a red link then either write the new article to explain that term in entirety, or expand the necessary text in this one.
• 3) Do not expand any new section before it is necessary, nor explain any as-yet unwritten material before its section comes up. Those of you with program design experience will know why.
• OK, not to explain anything that no one needs or wants explained, I'll await responses if there is any interest. But an approach like this would among other things avoid unnecessary explanations such as that a sphere is "set of 1-dimensional points with distance r from the center", and trap silly questions about zero-dimensional points. The nature of a sphere should not be at issue in our article, but linked to a suitable article. Etc etc JonRichfield (talk) 09:46, 21 March 2013 (UTC)
• This RFC was started by a Single-purpose account user to make some point, or pursue some private agenda, and is useless in the scope of the present artcicle. It should be closed by now, imo. Alvesgaspar (talk) 14:25, 23 March 2013 (UTC)
• I agree that this RFC should be closed. 00:52, 27 March 2013 (UTC)
I agree also. I am removing the RFC tag. Strebe (talk) 03:48, 27 March 2013 (UTC)

## The purview of this article

On my talk page, user 184.186.8.148 alleges, “The title of the article is not ‘cartographic map projections’. It is true if that were the article your view would be correct, since cartography is the practice of making maps, which are, at least to the present day, all two-dimensional. But this is an article about map projections generally, and maps can be of any dimension.” This assertion appears to be the root of the recent disputes over scope and terminology of this article.

I dispute the assertion that this article is about something broader than “cartographic map projections” (a term which, by the way, appears in not a single book title and has little presence in the literature for the obvious reason that it is redundant). From the content, clearly the article is not about more than cartographic projections. But I also dispute that the title implies anything different or broader. The terms “map” and “mapping” and “projection” are fundamental to differential geometry, but the term “map projection” means, specifically, cartographic projections. This is confirmed in several ways:

• A search on amazon.com for books with “map projection” in the title yields about 126 distinct titles for books and reprints before the results deteriorate into gray goo. Of those, not a single one is about anything but cartographic projections.
• Wolfram’s description of "map projection" states, verbatim: “A projection which maps a sphere (or spheroid) onto a plane. Map projections are generally classified into groups according to common properties (cylindrical vs. conical, conformal vs. area-preserving, etc.), although such schemes are generally not mutually exclusive. Early compilers of classification schemes include Tissot (1881), Close (1913), and Lee (1944). However, the categories given in Snyder (1987) remain the most commonly used today, and Lee's terms authalic and aphylactic are not commonly encountered.”Thus map projections, according to Wolfram, are only about spheres and spheroids, not about hyperspheres or hyperspheroids or any other surface.
• Notice that Wolfram evokes Tissot, Close, Lee, and Snyder, and no one else. All of those authors concerned themselves specifically with cartographic projections and not projections more generally.
• Notice that Wolfram evokes Snyder’s classifications as being the most commonly encountered. John P. Snyder authored and co-authored 52 books and scholarly papers on the topic, wrote the definitive bibliography of map projections, wrote the definitive history of map projections, pioneered mathematical and computational techniques for map projections, developed many significant map projections including the Space-oblique Mercator projection, and served as the map projection authority for the United States Geological Survey from 1979 until his death in 1997. His works are definitive for the English world because he described the entire body of literature, systematized it, and synthesized from it, all for the first time.

In the domain of pure mathematics “mappings” or “projections” are occasionally referred to as “map projections”, but they do not form any substantial body of literature under that name.

I propose:

1. That the purview of the article remain cartographic projections, without expanding the scope into projections in general;

2. That the nomenclature prevalent in the map projection literature be used for the article;

3. That disputes in nomenclature and definitions be resolved by appeal to the map projection literature;

4. That we wind down discussions of how terms are used in other domains and how other domains treat the mathematics and nomenclature of map projections so that this talk page can focus on its purpose of improving the article.

Strebe (talk) 07:49, 8 March 2013 (UTC)

Right, notice that you've made my point for me. You quote Wolfram: "A projection which maps a sphere (or spheroid) onto a plane". That is precisely what I have wanted. You are the one who insisted on the (incorrect) phrase "surface of a sphere". (Cf. Wolfram's "sphere" page.) I believe that we should limit this article to the domain you suggest, but only if we are precise in our language. We can assume we're talking about 2-dimensional objects; I have no objection to that. But you still must talk about projecting FROM a sphere TO a plane, NOT from the surface of a sphere TO a plane, because that is incorrect.184.186.8.148 (talk) 00:03, 9 March 2013 (UTC)
I invite the reader to notice that 184.186.8.148’s comments bear no relevance to the question of the definition of “map projection”, and therefore to the question of the purview of this article. Also, that they bear no relevance to the question of who and what are authorities on the nomenclature of map projections. Until those questions are answered, the matter of Wolfram’s definition of “sphere” is also irrelevant. Strebe (talk) 02:41, 9 March 2013 (UTC)
My comments are not just relevant but salient. "Map projection" in its most general meaning is far broader than the projections that you cite--namely, those that go from a sphere to a plane. I have never wanted to rewrite the article to broaden its discussion (though I think a sentence or two discussing the broader mathematical concept would be useful). I have only wanted to ensure that NO MATTER HOW WE DECIDE ON CONTENT we do not make factually false claims; such as, for example, that a sphere is 3-dimensional. That was the error that originally got me involved in this article.184.186.8.148 (talk) 22:59, 11 March 2013 (UTC)
This puzzling statement implies 184.186.8.148 believes there is only one definition for “sphere”. However, that has been demonstrated repeatedly to be false, and it has been demonstrated repeatedly that the definition 184.186.8.148 subscribes to is not authoritative for this article because it conflicts with the definition commonly used in the field of map projections as well as with dictionary usage. Strebe (talk) 00:44, 12 March 2013 (UTC)
I see no problem with making it clear that the projection is FROM the surface of a sphere TO a plane. The meaning of this statement is quite clear (and removes doubt in the context of Merriam & Webster and others defining a sphere as a 3D object bounded by a set of points equidistant from a center). I also acknowledge that this is being discussed over there. -- Scray (talk) 02:09, 12 March 2013 (UTC)
I do not believe that "there is only one definition for 'sphere'". I believe that there is only one CORRECT definition for sphere, which is the one used commonly in mathematics. I do not dispute that the term is used more broadly, and to refer to other geometries, in colloquial usage and (I'm taking your word for it) in the cartographic literature. To my mind, this latter usage is incorrect.184.186.8.148 (talk) 07:39, 12 March 2013 (UTC)

## Another snobish edit

I have reverted another edit by 184.186.8.148, who had replaced, in the first line of the artice, "... on a sphere or an ellipsoid" by "on a sphere or other ellipsoid". This is a snobish and useless change whose only effect would be to confuse the non-mathematical readers (that is most of them). May I remind all that this is an article of a general encyclopaedia, not a Bourbakian paper? -- Alvesgaspar (talk) 11:22, 9 March 2013 (UTC)

Comment Coming over in response to RFC bot, I think the wording "or other ellipsoid" to be clear and instructive. Statements like this, to a non-mathematician, might bring one up short, and clicking the blue link for ellipsoid they might learn something. If they don't notice, then no harm. Leaving "or an ellipsoid", if factually incorrect (I'm not a mathematician, but it seems to be incorrect) would be counter to our encyclopedic mission. It seems to me that this sort of tension is at the heart of the current friction. BTW, calling the edit "snobish" [sic] seems explicitly counter-productive. -- Scray (talk) 01:04, 11 March 2013 (UTC)
Saying "a sphere or other ellipsoide" is equivalent to saying "a circle or other ellipse" or "a square or other rectangle", which is hardly instructive in an article about map projections. If it were, the literature on the subject (including the books intended for colleage education) would certainly adopt the form, which is certainly not true. Please refer to the definitions used by the authorities in the field (some of them cited above) and remember that this article is about map projections, not elementary geometry. -- Alvesgaspar (talk) 01:23, 11 March 2013 (UTC)
I reject the usage “or other ellipsoid”. While a sphere is a degenerate ellipsoid, the general pattern of usage is not common in English usage, as Alvesgaspar points out; nor is it common in the map projection literature, as Alvesgaspar also points out. There is a strong reason the two are kept distinct in the map projection literature: In terrestrial mapping, spherical models are used in distinctly different contexts than ellipsoidal models, and there is no smooth transition between them. Spherical models are used in small-scale mapping; ellipsoidal models are used in large-scale mapping. If you say “ellipsoidal model” in geodesy, the earth sciences, cartography, or map projections, you distinctly mean not a spherical model. The practical mathematics differ drastically between the two; the applications differ drastically between the two. This is an example of why you must not enforce terminology and practices from one field onto another. That is not our job as encyclopædia editors. It is our job to report what the literature says. Strebe (talk) 01:35, 11 March 2013 (UTC)
I see what you mean, but I noted the two choices (the current language and the text that was reverted), and the usage quoted above from Wolfram, "sphere (or spheroid)." I have the impression (I stated that I'm no expert) that Wolfram's "(or spheroid)" is meant to remind readers that the Earth is not a perfect sphere, and that the construction "or other ellipsoid" is more correct (and closer to WOlfram's intended meaning) than "or an ellipsoid", which Avesgaspar restored. -- Scray (talk) 05:40, 11 March 2013 (UTC)
Wolfram uses the phrase “or other ellipsoid” because a sphere is a special case of an ellipsoid. In pure mathematics you would not normally divorce a special case from the general case by using “or” between them because mathematics generalizes to the extent possible. In applied mathematics and in general English you often do divorce the special case from the general case because often the distinction is important. Strebe (talk) 06:40, 11 March 2013 (UTC)
Either you're not reading what I'm saying very carefully, or I'm really lost. As quoted above (by you), Wolfram does NOT say "sphere or other ellipsoid"; rather, "sphere (or spheroid)". Are you now referring to some other part of Wolfram's text? I will assume that we're talking about the same quotation - in which case, please re-read my last comment. I think Wolfram's statement is meant to clarify sphere as meaning to include spheroids like Earth, rather than to distinguish them. Just want to get on the same page, here. -- Scray (talk) 06:57, 11 March 2013 (UTC)
No, my mistake. I have no quibble with Wolfram’s usage; that accords with what one might see in a text on map projections. It’s when the same idea gets phrased as “or other ellipsoid” that it diverges from the emphasis of the map projection literature. I do not read “sphere (or spheroid)” to mean “sphere or other ellipsoid”; I read it to mean, “sphere (or sometimes oblate ellipsoid instead)”. But either one works. How Wolfram phrased it sidesteps emphasis, which is a good idea in a mathematical context. Strebe (talk) 15:50, 11 March 2013 (UTC)

Scray's points here all seem like sound ones to me.184.186.8.148 (talk) 22:56, 11 March 2013 (UTC)

## Definition of “map projection”

We should get an airtight, cited definition for “map projection” in place so that we don’t have to debate the scope of this article and its nomenclature. If a new debate crops up we can point to the reference and point to the discussion already resolved. I have all the major and minor texts on map projections in my library, but don’t have access to my library for now. I suggest we discuss the definitions from the major English texts and select one. We can decide after that how to expand on it if we need to. I consider the following texts to be “major” in that they influenced later texts. They are in reverse order of publication date.

• J.P. Snyder, An Album of Map Projections or Map Projections—A Working Manual
• D.H. Maling, Coordinate Systems and Map Projections
• J.A. Steers, Introduction to the Study of Map Projections
• Deetz & Adams, Elements of Map Projection
• Arthur Hinks, Map Projections

Deetz & Adams and Steers went through many editions, but I don’t recall changes in definitions. Maling had two editions, the second one considerably expanding the book, but I don’t recall changes to the early material.

Definitions I have on hand:

1. John P Snyder, An Album of Map Projections:
A (map) projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane.' (p.5) (“Map” is omitted there because the full term “map projection” appears at the end of the preceding sentence.) This book does not target any particular audience.
2. John P Snyder, Map Projections—A Working Manual:
A map projection is a systematic representation of all or part of the surface of a round body, especially the Earth, on a plane. (p. 3) This book is largely for a technical audience. (This definition is repeated in Flattening the Earth, which is a history agnostic to audience.)
3. Arthur Hinks, Map Projections
Hence if we can find a way of representing the parallels and meridians upon our sheet, we can lay down the points in their positions relative to these lines, and make our map. Any such representation of meridians and parallels upon a plane is a map projection… The number of possible ways of constructing a projection is infinite, even if we restrict our definition to the statement that any orderly construction of meridians and parallels may be considered a projection. (pp 1–2) This book is intended to be easy on math.
4. D.H. Maling, Coordinate Systems and Map Projections
…Any systematic arrangement of meridians and parallels portraying the curved surface of the sphere or spheroid upon a plane. This book is for a technical audience.

Strebe (talk) 06:51, 15 March 2013 (UTC)

• My preference goes to the first but I don't have any strong feelings about this. In my opinion it is better to define the domain of the projection as the latitudes and longitudes of locations than as the meridians and parallels. The idea that the positions of the points on the projection are determined (interpolated?) relative to those meridians and parallels, like Hinks says, is strictly wrong. -- Alvesgaspar (talk) 19:52, 17 March 2013 (UTC)
My preference is also with #1. It seems like the least arguable of the definitions, and I agree with your point about parallels/meridians versus latitudes/longitudes.
Within the domain of map projections the coordinate system is always lat/lon regardless of the reference surface, so Definition #1 specifying lat/lon makes it quite clear we are dealing with cartographic projections. I think I understand why Snyder went with #2 sometimes; it was to avoid limiting the reference surface to strictly spherical or ellipsoidal, but the unfortunate side effect of that is that “round” is poorly defined; nor does it characterize irregular bodies in general, which defeats the purpose of using the term “round” instead of “sphere or ellipsoid”. If we go with Definition #1, it is reasonable to point out that the field has been extended to irregular bodies, referencing Stookes and others, and of course also reasonable to point out that projections are a much broader topic in mathematics. Strebe (talk) 00:37, 18 March 2013 (UTC)

## Fuller Projection

[Moving new inquiry to its own section]

Why is the Fuller projection not listed? — Preceding unsigned comment added by 173.51.214.90 (talk) 16:51, 5 April 2013 (UTC)

It is mentioned in the article (even though the article is not a list of map projections). It is also listed in List of map projections. Strebe (talk) 00:37, 6 April 2013 (UTC)

## Possible Reorganisation

I am itching to reorganise this article, as I feel it could be much improved with some careful changes, but am naturally hesistate as it is clearly a well tended article. It seems to me there are two basics areas to cover:

1. the practical use of map projection - the key characteristics of different projections, measuring distortion etc.
2. the theory behind map projections - projectable surfaces, reference surfaces etc.

which appeal to different types of user, and might form a good basis for structuring the article. The section on which map projection is best could be retitled "selecting a map projection". It also ought to cover aspects such as the outline of the map. Then in the later stages rather too many examples in some cases (we have the list of map projections) and too few in others. I have made a modest start by reordering the paras in background section to what I hope will be seen as a more logical order. Treading carefully for now! Marqaz (talk) 00:18, 17 April 2013 (UTC)

The article needs a lot of work. I agree the myriad examples of projections without much context is better handled by List of map projections. I’m less certain about the practical versus theoretical division because I don’t know how to talk about measuring distortion or characteristics of projections without talking about developable surfaces, reference bodies, or how distortion is characterized. I think “Which projection is best?” is fine as the section title; it fits the purpose and text, and it directly responds to people who come to the article not wanting to know all about projections, but rather to who come to know a) Which projection is best? —for whom the answer is, there is no unqualified answer; or b) Which projection should be used in this circumstance? —for whom general answers are given. Strebe (talk) 02:22, 18 April 2013 (UTC)

## Wikipedia de-facto standard map projection - what is it called?

All over wikipedia, a non-standard map projection is used, that is neither equirectangular nor equal-area. Here is an example but there are many more all over the place. [[4]] What is this projection called? Since it is a wikipedia standard it should be mentioned in the article. What is the formula to convert this thing to equirectangular? Is it the [Winkle times 3 or whatever]? Would be nice if wikipedia used equirectangular projection for global maps because then they could be used as textures on spheres, but that is a different issue altogether. Apparently wikipedia generates its maps using this http://lert.co.nz/map/ — Preceding unsigned comment added by 2001:15C0:66A3:2:2814:F976:C38:6120 (talk) 06:28, 25 October 2013 (UTC)

I wouldn’t say that is a "standard" on Wikipedia; it’s just common in the kind of map you’re looking at. Contributors use whatever tools are at their disposal, and construct their maps using whatever projection is apt, is dictated by the tool, or arises out of whim if they don’t know or care about projections. That particular projection is not a Winkel tripel. It is probably a Robinson, but I would have to be someplace other than on a cellphone sitting on a bus to confirm. It would be a shame if most world maps were on the equirectangular. That projection is poor for most cartographic purposes. Maps ought to be made for people’s understanding rather than for ease of some software’s processing. I’m puzzled why you want to put the map back onto the sphere. The whole purpose projecting is to get it off of the sphere! Strebe (talk) 16:41, 25 October 2013 (UTC)
[ec] First, the maps in WP are not generated by some top-down authority as anon's remarks seem to suggest. They are contributed by ordinary users, and we have little control over what projections or tools are used, or -- critically -- how well the cartographic properties and sources are documented. The Maps Project supplies links to various tools, but I don't know that the Flash tool posted at lert.co.nz by gunn.co.nz is one of them (or where Gunn got the Flash tool). So the notion that this is an "official" projection of WP in any sense is mistaken on several points. This tool (from Gunn or elsewhere) may well be where Alinor (talk · contribs) makes his or her maps, but there's no documentation, so it's hard to tell.
Anon calls the projection "non-standard", but there is no "standard" projection. There are common ones and rare ones, but the choice depends on the intended use of the map. Without the graticule it's difficult to know for sure (the Flash tool isn't saying), but just eye-balling it, it looks very similar to the Robinson projection, which is widely used. It could also be any of several similar pseudocylindrical map projections, like the Times Projection, Wagner 4, Kavraiskii 7, or Baranyi 4. The latter two are unlikely unless the Flash tool comes from Eastern Europe -- but we don't know.
There's a reason that maps are not all equal area projections. Projections serve a variety of purposes. Anon would like to use them as background projections, but the creators of the maps obviously had different goals. Neither equal area nor conformal maps give an intuitive feel for land masses as they sit on the globe, and that is why the burgeoning stable of pseudo-cylindrical maps developed. What anon is really asking for is that the mapped data be available without being tied to a specific projection -- a laudable goal, but one we're not likely to achieve any time soon!
-- Elphion (talk) 17:26, 25 October 2013 (UTC)

## Non-mentioned map projection

One non-mentioned map projection is that projection that takes the direction of travel to be north, which is east for rotation (but not necesarily for solar orbit). That projection has NS oriented WE, including the space orienations, where E&W are lattitude longtitude reversed (90° greenwhich rotation: top is north). That orientation causes a ´race´ tire orientation, where the north & south poles are hubcaps. Anyone around with such a map? — Preceding unsigned comment added by 190.204.18.169 (talk) 15:50, 18 February 2014 (UTC)

This transverse Mercator projection is mathematically the same as a standard Mercator, but oriented around a different axis.
Sounds like a transverse projection (like the Transverse Mercator projection) rotated 90 degrees? -- Elphion (talk) 16:49, 18 February 2014 (UTC)

A T and O map map made with modern cartography -- east toward the top
We'd like to help you fill in the missing details in this article, but that description is difficult to follow.
Are you maybe talking about a map with the orientation used by most of the earliest maps (east toward the top) or some other map#Orientation of maps?
Are you maybe talking about maps that show two circles side-by-side (hemispheres), like the side view of the tires on a race car?
 Western hemisphere. Eastern hemisphere
or
 Northern Hemisphere from above the North Pole The Southern Hemisphere from above the South Pole
--DavidCary (talk) 16:13, 14 May 2015 (UTC)

## Geoid, and why it is not used as a datum

I made this reversion for the stated reason. To elaborate, the geoid as a model is not about elevations as referred to an ellipsoid. That would mean the model is the ellipsoid. If the geoid itself were the model, mean sea level becomes the model. It would be a more complex surface but still use longitudes and latitudes across that surface, and would still have elevations measure from that. For example, typical hills and valleys have no effect on the geoid, and so they would have elevations to pinpoint positions on them more accurately than just latitude and longitude, whereas ocean surfaces define the geoidal model and therefore would always have 0 elevation—unlike an ellipsoidal model. Strebe (talk) 01:18, 9 June 2014 (UTC)

The current version reads: "This model [the geoid] is not used for mapping because of its complexity, but rather..." First, this article is not about the geoid, so the whole part after the comma ("but rather..." and on) doesn't need to be fixed, it should simply be discarded. Second, "for mapping" is ambiguous as to whether it's meant data collection or depiction, so it should be replaced with "in map projections" for a narrower scope. Third, "because of its complexity" doesn't say much; it could be made more informative as follows: "because (a) the geoid affects primarily the vertical position (altitude), which is normally not input to map projections -- they are formulated in terms of latitude and longitude; (b) the effect of the geoid on horizontal positions -- the deflection of the vertical -- is often negligible, just a few percent of a degree, so inputting astronomical latitude and astronomical longitude would not make a significant difference in the output map-projected coordinates; (c) map projections are not as formulated as flexibly more general surface development methods, such as forms of UV mapping in texture mapping." Could you please address each point above separately (first, second, third; and a, b, c). Thanks. Fgnievinski (talk) 17:57, 10 June 2014 (UTC)
First, this article is not about the geoid… The section is about choosing the model for the shape of the earth. The remainder of the paragraph you object to states why the geoid is not used but also how it relates to the model that is used (the ellipsoid). How much detail is good there can be debated. Second, "for mapping" is ambiguous… There was a time when maps were the storage medium for data collection, and in those days, mapping included a more or less formal survey. That’s no longer true, and mapping does not mean data collection. However, presumably your objection could be met by changing in mapping to for maps. As for (a) and (b), I think a synthesis of our opinions are that the geoid as a model yields only tiny increases in fidelity of the latitude and longitude assignation but does so at great cost in complexity. (c) Please explain the relevance of this observation to the discussion. Strebe (talk) 02:50, 11 June 2014 (UTC)
Point (c) is related to your previous statement, that "If geoid were the underlying model, it would change characterization of conformality and equivalence, just as ellipsoid over sphere does." which I agree with, but I insist that a map projection based on the geoid has never introduced, and if it were to be introduces, it'd be akin to uv mapping technique. Fgnievinski (talk) 14:22, 11 June 2014 (UTC)
So I'm proposing the following: "A third model of the shape of the Earth is the geoid, a more complex and accurate representation of the Earth's actual shape, which superimposes variations above and below the ellipsoid. These undulations would change the characterization of conformality and equivalence. In principle, the geoid could be used as an Earth model for map projections -- not unlike the surface development methods employed in UV mapping. In practice, though, map projections neglect the variations in ellipsoidal elevation (be them of the geoid or of the actual land surface). In between these two extremes, one could arguably input astronomical latitude and astronomical longitude to evaluate the map projections, but deflection of the vertical is likely negligible (just a few percent of a degree), although the exact discrepancy in the output map-projected coordinates is unknown." Fgnievinski (talk) 14:22, 11 June 2014 (UTC)
Since the purpose of this paragraph is to explain why the geoid is not used in computing map projections, this statement is not appropriate: In practice, though, map projections neglect the variations in ellipsoidal elevation (be them of the geoid or of the actual land surface). It merely says they’re not used because they’re not used. I like the first half of your proposal. The latter half is too speculative and written in too speculative of language. Someone will immediately demand citations. I propose instead:
A third model of the shape of the Earth is the geoid, a more complex and accurate representation of the Earth's actual shape. A geoidal model superposes variations above and below the ellipsoid's surface, corresponding to mean local sea level. These undulations would change the characterization of conformality and equivalence and therefore would introduce changes in the mapped graticule in comparison to an ellipsoidal model on projections that preserve conformality or equivalence. In principle, the geoid could be used as an Earth model for map projections, similar to the surface development methods of UV mapping. In practice, though, for bodies as relatively smooth as the Earth, the enormous increase in mathematical complexity yields little practical benefit. However, such techniques are sometimes needed when mapping small, irregular bodies such as asteroids. Strebe (talk) 05:31, 16 June 2014 (UTC)
Glad to see some convergence in the ideas. I had to rectify some of the wording about the geoid. Also, the parts about "yields little practical benefit" cannot be backed up without going into original research here. Not to mention "are sometimes needed", which I've also trimmed below. Fgnievinski (talk) 02:43, 18 June 2014 (UTC)
A third model of the shape of the Earth is the geoid, a more complex and accurate representation of the Earth's actual shape. It superposes undulations up to 100-m above and below the ellipsoid's surface, and is defined as the gravity equipotential that best fits mean sea level (which deviates permanently from the geoid by up to 2 m, see ocean surface topography). The geoid would change the characterization of conformality and equivalence and therefore would introduce changes in the mapped graticule in comparison to projections that preserve these properties based on an ellipsoidal model of the Earth. In principle, the geoid could be used as an Earth model for map projections, similar to the surface development methods of UV mapping. In practice, though, this is not normally done. Fgnievinski (talk) 02:43, 18 June 2014 (UTC)
It’s bad form to make a statement like “in practice it is not normally done” without supplying a reason since of course “Really? Why?” is the first thought that comes to mind. Any geodesist would readily agree; it just goes without saying, so they don’t. The field of planetary geodesy starting with Stokes does in fact concern itself with geoidal models for small bodies, since ellipsoidal and even triaxial ellipsoidal models are not good approximations in many cases. It would be a shame not to mention these in conjunction with UV mapping. These models yield complicated coordinated systems, but the alternative is worse. In the case of the earth, the alternative is deemed better for its simplicity. I’m fairly sure I can find a explicit reference for this, but I’m deprived of my library for the time being. (See for example this or this, slide 3.) I think we can drop the bit about equivalence; no one cares about that for large enough scales for a geoidal model to mean anything. Conformality, on the other hand, is still important. Strebe (talk) 06:14, 18 June 2014 (UTC)
Truth is, we don't know for sure why the geoid has not been used. I suspect it's just historical inertia. Maybe someone one day will come and show that it's significantly more accurate for certain applications and that it's not that complicated to use it. So shall we stick to the facts. As for the asteroids, I'll concede if you find a reference where it's been actually used. I don't think it has. Fgnievinski (talk) 22:31, 18 June 2014 (UTC)
No, I gave two references that state the geoid is too complicated. Those are the facts. Of course inertia has something to do with it, but if using the geoid as a model for projecting from were valuable enough then of course inertia would not prevail. All you are really saying is that the geoid is too costly for the benefit. As for planetary bodies, I did not mean UV mapping is used for them; I meant that geoidal models are used for them. There are dozens of papers on this. here, here, here, here… UV mapping itself is not terribly interesting unless you pair that with preserving some metric of the mapped area. If you’re not trying to preserve anything particular then you might as well project an ellipsoid onto the irregular body to establish horizontal coordinates. To map coordinates, project from the ellipsoid onto a sphere, and from the sphere onto a plane. They do that, too. Strebe (talk) 06:38, 19 June 2014 (UTC)
No, no, no -- these first two references don't mention map projection in conjunction with the geoid at all. That the geoid is more complicated than the ellipsoid is a well-sourced fact, but that the geoid is not worth for map projections, that remains unsourced. In fact, it cannot possibly be absolutely true, as it'd take a single exception -- even a restricted and esoteric usage case -- to render that generalizing claim false. We can say for sure that the geoid is not normally used, not that it will never find its use on Earth projections. Fgnievinski (talk) 02:07, 20 June 2014 (UTC)
Now, you blew my mind with the references about asteroids. Truth be told, I thought that was highly speculative! So here's my latest proposal. Fgnievinski (talk) 02:07, 20 June 2014 (UTC)
A third model is the geoid, a more complex and accurate representation of the Earth's actual shape. It superposes undulations above and below the ellipsoid's surface, and is defined as the best equipotential surface approximation to mean sea level (which has smaller permanent deviations from the geoid, see ocean surface topography). The geoid would change the characterization of conformality and equivalence and therefore would introduce changes in the mapped graticule in comparison to projections that preserve these properties based on an ellipsoidal model of the Earth. In principle, the geoid could be used as an Earth model for map projections, similar to the surface development methods of UV mapping. In practice, though, this is not normally done for the Earth, as its shape is very regular -- only hundred-meter level geoidal undulations over more than six thousand kilometers Earth radius, or about 0.001% relatively speaking. However, it is not uncommon to use the geoid (and even more complicated, smoothed topography models) as the body shape model underlying map projections for more irregular bodies, such as asteroids.[1], [2], [3], [4][5] Fgnievinski (talk) 02:07, 20 June 2014 (UTC)
We need to simplify the verbiage; most people who don’t already understand what’s being said are going to find it too hard and has too many parenthetical digressions. Also, it’s not true that the geoid superposes undulations above and below the ellipsoid. You do not need an ellipsoid in order to model the geoid, and in fact, it’s better to derive a best-fitting ellipsoid from the geoid, since that’s actually what happens. It’s more accurate to say that an ellipsoid subtracts the geoid’s undulation to arrive at a simpler surface. Also there’s already an article on the geoid, so, except for its relationship to map projections specifically, we do not need to go into this kind of detail. Also, I’m dropping mention of UV mapping. The relationship of geoidal models to UV mapping is superficial and WP:OR. You need to cite that to include it.
A third model is the geoid, a more complex and accurate representation of Earth's shape. It is calculated as mean sea level, which means the shape the earth would have if its gravity were the same everywhere but there were no winds, tides, or land. Compared to the best-fitting ellipsoid, a geoidal model would change the characterization of important properties such as distance, conformality and equivalence. Therefore in geoidal projections that preserve such properties, the mapped graticule would deviate from a mapped ellipsoid's graticule. Normally the geoid is not used as an Earth model for projections, however, because Earth's shape is very regular, with the undulation of the geoid amounting to less than 100 m from the best-fitting ellipsoidal model out of the 6.3 million m Earth radius. For small, irregular planetary bodies such as asteroids, however, models analogous to the geoid are used sometimes.[6][7][8][9][10]
I went ahead and copied this into the article. Fgnievinski (talk) 03:21, 21 June 2014 (UTC)

References

1. ^ Cheng, Y.; Lorre, J. J. (2000). "Equal Area Map Projection for Irregularly Shaped Objects". Cartography and Geographic Information Science. 27 (2): 91. doi:10.1559/152304000783547957.
2. ^ Stooke, P. J. (1998). "Mapping Worlds with Irregular Shapes". The Canadian Geographer/Le Géographe canadien. 42: 61. doi:10.1111/j.1541-0064.1998.tb01553.x.
3. ^ Shingareva KB, Bugaevsky LM, Nyrtsov M. Mathematical Basis for Non-spherical Celestial Bodies Maps. J. of Geospatial Eng., V. 2, 2, Des. 2000, pp. 45-50. [1]
4. ^ Nyrtsov, M.V. (2003), THE CLASSIFICATION OF PROJECTIONS OF IRREGULARLY-SHAPED CELESTIAL BODIES, Proceedings of the 21st International Cartographic Conference (ICC), Durban, South Africa, 10-16 August 2003, pp.1158-1164. [2]
5. ^ Clark, Pamela Elizabeth; Clark, Chuck (2013). "Constant-Scale Natural Boundary Mapping to Reveal Global and Cosmic Processes". SpringerBriefs in Astronomy: 71. doi:10.1007/978-1-4614-7762-4_6. ISBN 978-1-4614-7761-7. |chapter= ignored (help)
6. ^ Cheng, Y.; Lorre, J. J. (2000). "Equal Area Map Projection for Irregularly Shaped Objects". Cartography and Geographic Information Science. 27 (2): 91. doi:10.1559/152304000783547957.
7. ^ Stooke, P. J. (1998). "Mapping Worlds with Irregular Shapes". The Canadian Geographer/Le Géographe canadien. 42: 61. doi:10.1111/j.1541-0064.1998.tb01553.x.
8. ^ Shingareva, K.B.; Bugaevsky, L.M.; Nyrtsov, M. (2000). "Mathematical Basis for Non-spherical Celestial Bodies Maps" (PDF). Journal of Geospatial Engineering. 2 (2): 45–50.
9. ^ {{cite journal | last1 = Nyrtsov | first1 = M.V. | year = 2003 | month = 8 | title = The Classification of Projections of Irregularly-shaped Celestial Bodies | journal = Proceedings of the 21st International Cartographic Conference (ICC) | pages = 1158–1164 | url = http://icaci.org/files/documents/ICC_proceedings/ICC2003/Papers/141.pdf
10. ^ Clark, Pamela Elizabeth; Clark, Chuck (2013). "Constant-Scale Natural Boundary Mapping to Reveal Global and Cosmic Processes". SpringerBriefs in Astronomy: 71. doi:10.1007/978-1-4614-7762-4_6. ISBN 978-1-4614-7761-7. |chapter= ignored (help)

## Article should be Cited for having multiple issues

#### No history

This Article does not appear to have a history section where one would obviously be present. Considering the importance of the article, the vast wealth of history on the subject, plus the importance of the development of maps throughout many civilizations, I believe this problem needs to be addressed.

#### Bold claims

The beginning statements lack citations and make bold claims.

#### Background Section is an imposter!

The "Background" section clearly does not give "background" of any kind. This section should be moved to a more appropriate section and re-titled.

This article needs help!

Xavier (talk) 2:22am, Sunday, November 1st, 2015 (UTC)

I think you're being over-dramatic here, and I don't think the article deserves tagging. I read the lead carefully and see no "bold claims"; the one you chose to tag with {{cn}} is the elementary mathematical observation that there are infinitely many functions mapping the sphere to a plane. I agree that "Background" is not an ideal title, but what would you call it? And it is placed exactly where it should be, to discuss the framework on which all the other sections depend. I agree that a brief discussion of the history of projections would be useful, but (a) that's hardly reason to tag the article; (b) the article is already quite long, so any such discussion would have to be very brief; and (c) the history of the various projections is better discussed at their respective articles. There is, of course, the article History of cartography, which we could link to in the "See also" section. -- Elphion (talk) 13:42, 1 November 2015 (UTC)
PS: Thanks for listing your concerns here rather than just tagging the article as a drive-by shooting! -- Elphion (talk) 13:52, 1 November 2015 (UTC)
Thank you for clarifying the issue. I am a new member to Wiki and I have a lot to learn. On the bold claim subject I would agree with you but, I still feel the claim needs a citation. If this claim is such an elementary fact than there should be plenty of citations to find on the matter.
Xavier (talk) 9:36am, Sunday, November 1st, 2015 (UTC)
Furthermore, I would argue that there IS a finite limit to the number. Until it has been proven it cannot be fact. So, where is the proof? Is that not what citations are for?
--Xavier (talk) 17:46, 1 November 2015 (UTC)
Drama. It’s not a matter of “proof”. It’s a matter of definition. A map projection is has this structure:
${\displaystyle x=f(\varphi ,\lambda )}$
${\displaystyle y=g(\varphi ,\lambda )}$
φ is latitude; λ is longitude. The f and g are any continuous function. There is no limit to the number of continuous functions because you can create them at will. Strebe (talk) 07:57, 3 November 2015 (UTC)

[outdent] For example think of any projection that maps a hemisphere to a disk (stereographic projection for example). Consider just the points of that hemisphere, mapped to the disk. Keeping the circumference of the disk fixed, distort the interior of the disk by grabbing the center point C of the disk and moving it to any other interior point C' of the disk, dragging the rest of disk with it as if the disk were stretchable. There are infinitely many points C' to move the center point to, and each one of those mappings changes the relationship of the center (C/C') to the circumference, and is therefore a new projection (a new map of the hemisphere to the disk). This could be made into a formal proof by exhibiting a suitable distortion function (e.g., linear interpolation of the segments CP joining C to boundary points P to the segments joining C'P joining the new position of the center to the same boundary points. -- Elphion (talk) 12:47, 3 November 2015 (UTC)

@Elphion: I understand what you are saying but, this is a matter of citation. I do not like seeing bold claims such as this one without a citation. While your explanation is very thorough, I do not see much indication in the actual article. I am not concerned with proof as much as I am with just having a citation. That is all.
P.S. On that note, it seems to me that the statement is pure speculation from someones opinion rather than having gotten it from a source. Or even a reliable source for that matter.
--Xavier (talk) 17:45, 3 November 2015 (UTC)
Furthermore, if a citation is to not be used than an explanation should at least be customary.
--Xavier (talk) 17:55, 3 November 2015 (UTC)
Alright! Now we are talking! Citation added.--Xavier (talk) 18:02, 3 November 2015 (UTC)

Well, one needs to draw the line somewhere. Would you require citation for "The sky is blue" or "Balls fall under the influence of gravity"? That there are an infinite number of projections is so obvious that only Snyder (of the several books on projections that I checked) takes the ink to actually say that -- and not even Snyder bothers to back it up with any argument. (Thanks to Strebe, who added the citation before I could.) Not every sentence really requires citation; else the articles would be so cluttered that they would be hard to read (or at least hard to edit). -- Elphion (talk) 18:38, 3 November 2015 (UTC)

@Elphion: You are very correct however, in this case I do not know anything about map projections, so this fact is not obvious to me. This is why I requested a citation. I only requested one citation which does not appear to "clutter" the page, as you put it. Plus, it would appear that someone else agrees with my point. This case is closed.
--Xavier (talk) 18:49, 3 November 2015 (UTC)
Sorry guys but the citation is useless as is because no page is indicated. Furthermore, and as Strebe explianed, it is unnecessary. Stating that there are infinite map projections is just as trivial as saying that there are infinite functions ... or numbers. Alvesgaspar (talk) 19:50, 3 November 2015 (UTC)
Since this has become a trivial point, I vote to have the comment removed altogether.
--Xavier (talk) 20:05, 3 November 2015 (UTC)
I restored the citation, which I submitted originally with page number. I don’t know why Xavier removed just the page number. I don’t mind having the statement cited now that the work of citing it is done. The book is already referenced any number of times (and now properly reused); no harm in referencing it yet again. My original resistance was because I doubted I could find a reference easily, given how trivial the observation is. Strebe (talk) 21:19, 3 November 2015 (UTC)
@Strebe: Thank you. I removed the page number because I thought it was a typo. Plus, you had added an extra "}}" syntax at the end. I am new, what is a "page number"?
Xavier (talk) 21:33, 3 November 2015 (UTC)
(answered at user talk:Xavier enc) -- Elphion (talk) 22:03, 3 November 2015 (UTC)

## Azimuthal/Retroazimuthal

I think the distinction between azimuthal and retroazimuthal should be clarified. No~w the article seems to be saying that one preserves directions from a central point, while the other preserves directions to a central point, but that sounds like the same thing. MathHisSci (talk) 21:20, 17 April 2016 (UTC)

But it's not the same thing at all. The explanation properly belongs in a separate article because it's quite involved and would require diagrams for a lay audience. I don't know of any secondary source that gives a useful lay explanation, now that I think about it, and so providing one in Wikipedia would be WP:OR. Anyway, it definitely wouldn't belong in this article. Strebe (talk) 01:30, 18 April 2016 (UTC)

## Recent broken edits

In this edit, User:Isambard Kingdom has reintroduced many problems.

• There are syntactical errors left over from edits by User:Pleasantville, such as "Because of the many uses maps" and conjunctions without commas starting out sentences.
• There are incoherencies left over from the edits by User:Pleasantville. To wit, "types of data" and the other uses of "data" are garbled. "Data" is not plural of "datum" in this context, and even "types of datums" is not at all what is meant by the text.
• User:Isambard Kingdom has reintroduced the non-English "they can viewed easily".
• User:Isambard Kingdom considers globes only as a subset of maps rather than exclusive to, which is neither normal usage nor standard usage in the geographic and map projection literature. Mathematically "globes are a subset of maps" is true, but language is more flexible than that. This edit is useless pedantism.
• This refusal to consider globes in juxtaposition to maps apparently then inspired the deletion of the rationale for map projections. The first paragraph in "Background" now bears no relationship to the second and has no purpose on its own.
Map projections can be designed to accommodate a range of scales. They can viewed easily on computer displays. They can facilitate measuring properties of the mapped terrain. They can show larger portions of the Earth's surface at once. — Erm. "larger" than what?
However, Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without distortion. The same applies to other reference surfaces used as models for the Earth. Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. Every distinct map projection distorts in a distinct way. The study of map projections is the characterization of these distortions. "However," what? The first paragraph talks about map projections as a given, and then the second paragraph, apparently ignoring the first paragraph, syntactically states a connection to it with "however" without providing any reason for that connection, and then goes on to claim that map projections distort--without ever even establishing any connection to maps. This is a mess without motivation or clear meaning.

The text as it stands is incoherent. I am reverting this again. I would appreciate some reasonable cooperation at addressing these concerns here, on the talk page, where that is supposed to be done. Strebe (talk) 23:15, 10 March 2017 (UTC)

## Equal-area question

Does averaging the coordinates of two different equal-area projections make another equal-area projection? If yes, do they have to have the same area scale? — Preceding unsigned comment added by 2A01:119F:2E9:2F00:8C70:6F61:25A8:4750 (talk) 17:56, 22 March 2017 (UTC)

No. Linear combinations of equal-area projections (including “averaging”), does not, in general, result in an equal-area projection. Strebe (talk) 22:06, 22 March 2017 (UTC)
Is there any way to combine equal-area projections in a way that will make another equal-area projection? 2A01:119F:2E9:2F00:4082:9261:D40D:C418 (talk) 15:49, 23 March 2017 (UTC)
There are many area preserving transformations. For example, you could apply the transformation implied by transforming known projection A to known projection B, and apply that transformation to known projection C, resulting in a new projection D.
Please understand that these kinds of conversations are properly conducted in other forums, such as the Mapthematics forum on map projections. Wikipedia talk pages are only for discussing how to improve the associated article.Strebe (talk) 16:36, 23 March 2017 (UTC)