Talk:Map projection/Archive 2

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., , ,  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.    


 * I went ahead and copied this into the article. Fgnievinski (talk) 03:21, 21 June 2014 (UTC)

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  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:
 * $$x = f(\varphi, \lambda)$$
 * $$y = g(\varphi, \lambda)$$
 * 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)


 * 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)


 * 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)


 * 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. &mdash; 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)

youtube video
this seems quite decent at explaining why there are a variety of useful projections which are commonly used - not sure where/how one might include such in an article though - perhaps in external links ? EdwardLane (talk) 08:55, 12 July 2017 (UTC)

No geometric meaning
I am very strongly against reincluding that statement. There are many projections that do preserve some geometric property, and in fact the great majority of existing projections must preserve some geometric property to be useful (for example, latitude lines remain parallel). This statement is not sourced and is not limited to just "perspective" projections.--Jasper Deng (talk) 23:27, 5 October 2019 (UTC)


 * The statement is not about “some geometric property”; it is about interpreting the entire projection as a geometrical construction. One might argue over which definition of “geometric” to use, but the populist notion of geometry is Euclidean and projective. In fact the great majority of existing projections must preserve some geometric property to be useful (for example, latitude lines remain parallel): This statement is false. (Even if it were true, the statement from the text wasn’t about ‘some property’.) “The great majority of existing projections” do not preserve any particular property because the great majority of projections (by some reasonable definition of distinct projection and some reasonable definition of existing projection) are “compromise” projections, which means they have given up on preserving any particular thing so as not to distort something else too much. If we look at Winkel tripel projection, which is commonly used for world maps these days in both Europe and North America, we have:
 * The poles, which are points in reality, have become line segements.
 * Angles in general are not preserved.
 * Distances are not preserved anywhere, really.
 * Shapes are not preserved.
 * The uninterrupted globe now has a huge discontinuity at the left and right edges.
 * Parallels are not parallel.
 * Each meridian has a different shape than its neighbors.
 * Parallels are not equally spaced.
 * Meridians are not equally spaced.
 * In short, no apparent property at all is preserved, let alone anything “geometric”. Winkel tripel is hardly unusual in execution. I’m not wedded to the term “geometric”; I’m wedded to the concept being presented, which is that very little of the enterprise of map projections relate to projective geometry at all. Meanwhile, it is a common misperception that map projections are projective. If you have some way to say that that is likely to be understood by the casual reader who is not going to foray into the article body, then let’s see it. Strebe (talk) 00:18, 6 October 2019 (UTC)
 * In short, no apparent property at all is preserved, let alone anything “geometric”. Winkel tripel is hardly unusual in execution. I’m not wedded to the term “geometric”; I’m wedded to the concept being presented, which is that very little of the enterprise of map projections relate to projective geometry at all. Meanwhile, it is a common misperception that map projections are projective. If you have some way to say that that is likely to be understood by the casual reader who is not going to foray into the article body, then let’s see it. Strebe (talk) 00:18, 6 October 2019 (UTC)


 * Citations:
 * “Indeed, many projections have simply no geometric or physical interpretation, and are described purely by mathematical formulae.”
 * “It is evident, from our definition, that we use the word Projection in a sense much wider than that which geometry gives it. The majority of map projections are not projections at all in the geometric sense.”
 * “In cartography projection by no means only implies perspective or geometrical projection.”
 * “Classification of Projections… Perspective Projections. A first group in a general classification might well be the strictly geometrical projections, namely those derived from the ‘generating globe’ by processes which are, in fact, ‘projection’ as it is popularly understood.… Non-Perspective Projections. An appropriate second group embraces projections which are, in effect, derived from their perspective counterparts by suitable modification.… Conventional Projections. A third group includes those projections which are purely conventional in form, and which the idea of ‘projection’, as generally understood, is not apparent.… Included in this group are some very valuable projections, especially those designed to show the whole world on one map.”
 * &c. The disavowel that projections are limited to “geometric” is common in the literature. Use of the term “geometric” in all these cases, while not explicitly defined, is clearly the same usage intended by the article text you have deleted. Strebe (talk)
 * "populist notion of geometry is Euclidean and projective" – Your assertion that "geometric" here only means Euclidean geometry is absurd in face of how this topic is decidedly one in non-Euclidean geometry (specifically differential geometry on a spheroid-like surface). Find a better word than "geometry", which to a mathematician is emphatically not limited to just Euclidean geometry. From that point of view, every projection is a geometric construct as it concerns the geometry of a differentiable manifold (I'm sure you would loathe an orientation-reversing mapping showing California east of Nevada). Your sources do not appear to make this kind of distinction. A projection might not be "geometrical" in the sense of these articles, but it is plainly wrong to assert that these projections have nothing to do with geometry. We are not writing for just primary school students toiling with compass and straightedge constructions.--Jasper Deng (talk) 02:12, 6 October 2019 (UTC)
 * "populist notion of geometry is Euclidean and projective" – Your assertion that "geometric" here only means Euclidean geometry is absurd in face of how this topic is decidedly one in non-Euclidean geometry (specifically differential geometry on a spheroid-like surface). Find a better word than "geometry", which to a mathematician is emphatically not limited to just Euclidean geometry. From that point of view, every projection is a geometric construct as it concerns the geometry of a differentiable manifold (I'm sure you would loathe an orientation-reversing mapping showing California east of Nevada). Your sources do not appear to make this kind of distinction. A projection might not be "geometrical" in the sense of these articles, but it is plainly wrong to assert that these projections have nothing to do with geometry. We are not writing for just primary school students toiling with compass and straightedge constructions.--Jasper Deng (talk) 02:12, 6 October 2019 (UTC)


 * You’ve demonstrated your bad faith here by jumping straight to “absurd”. I gave reputable citations. You gave none. I explained the context for the text. You explained the context for mathematicians. This is an encyclopedia article for people who likely have never heard of differential geometry and who want to know about cartographic projections, not an article for differential geometers who think they own all the words and concepts they use and who already know about projections. I’m done with you. I have reverted the text, and if you wish to fight about it, then this will go into arbitration. Strebe (talk) 02:53, 6 October 2019 (UTC)
 * You won’t WP:AAGF and last time I checked, arbitration is the last, not first or second, step of dispute resolution. I’m taking this to WP:DRN. You seem ignorant of the math of projections and projections are a common real-world example for differential geometry classes, thus our audience includes them too.—Jasper Deng (talk) 03:35, 6 October 2019 (UTC)


 * Then check again: The first step is third opinion in situations like this. Strike one. If you’re interested in my ignorance of map projections, do a little homework on my publications. Strike 2. You are the one who broke into insults and continue to with your amusing speculations about my map projection knowledge, violating WP:CIVILITY and WP:AAGF. Strike 3. Your claims of edit warring are topsy-turvey, since you have just violated WP:3REVERT—and I haven’t. Strike 4. Your complaint that I called your edit wrong are false. What I said was false was your unqualified claim in your edit comment that “distance-preserving map still apply”. Maybe you knew what you were talking about, but no one else could, because no such map exists without qualification. Strike 5. Strebe (talk) 05:36, 6 October 2019 (UTC)
 * Wrong. WP:Arbitration explicitly states that arbitration is the last dispute resolution step. I don't care about your publications. WP:EXPERT is not a trump card. And I have not violated 3RR. I have undone your reinsertion of that content exactly two times (or three counting my initial edit), and I started the dispute resolution process, whereas you chose to continue the edit war. A curved space is not isometric to flat space, but the projection centered on a particular point, with every other point's distance to it preserved, exists.
 * And in any case, you have conveniently ignored how none of your sources make the bold claim that there is absolutely no possible geometric interpretation of a typical map projection. That is ridiculous and every differential geometry textbook cites map projections as an example of an application of differential geometry (such as the text I used in my education). Just Google any such textbook and you will find such a thing. WP:DUE weight requires that interpretation to be given fair treatment.
 * "I'm gonna revert you, too bad" and "fight me" is no way to approach any dispute. I would have suggested you self-reverted first had I not been poked by your unnecessarily confrontational language above.--Jasper Deng (talk) 06:09, 6 October 2019 (UTC)


 * I never argued that arbitration is the first step. You chose to ignore what I actually stated, which was that third opinion is the first step. Straw man argument.
 * I am not using my publications in any sense that WP:EXPERT applies to because it’s your libel that I refuted with them, not a technical argument. Another straw man argument.
 * You have three reversions. I have two reversions. You state that I chose to continue the edit-warring. You have some interesting math and deductive skills there.
 * I gave a good account of why I called your distance statement incorrect. You ignored my explanation and proceeded to explain how you were right by adding in crucial concepts that you didn’t say originally. Straw man argument. Again.
 * My citations stand on their own. By your reasoning, those citations surely include differential geometry in the definition of “geometry” that they use. And yet, they do not. The meaning invoked by their texts precludes differential geometry and is consistent with the usage the article had before your reversions.
 * What differential geometry textbooks have to say about map projections isn’t relevant to this conversation. Straw man argument. Again.
 * So, what we have here, is Jasper Deng screaming about my edit-warring when he’s the dominant edit-warring party. We have Jasper Deng questioning my credentials, and then, when I suggest he check my credentials, trotting out the irrelevant WP:EXPERT. We have Jasper Deng leading the WP:CIVILITY violations charge with assertions of “absurd”ity and following it up with libel and a series of straw-man arguments. We have Jasper Deng claiming WP:SYNTH on citations that cannot, by any contortion of reading or logic, support their definition of “geometry”, while, meanwhile, providing no citations of their own of any kind, let alone from the field of map projections. This don’t look good.


 * The sad thing is, I don’t disagree with Jasper Deng’s technical statements. They just don’t apply here. Map projection is not a proper subset of differential geometry. It has its own literature and terminology. “Geometry” doesn’t mean the same thing that differential geometers use in their field. The usage in this article, however, is consistent with the usage in the field of map projections, as I have cited, and consistent with lay notions of geometry. That said, it wouldn’t bother me to replace “direct” with “classical” in the disputed text:
 * Before: …which are defined only in terms of mathematical formulae that have no direct geometric interpretation''.
 * After: …which are defined only in terms of mathematical formulae that have no classical geometric interpretation''.
 * I don’t think the new text means anything to a layperson, but it probably doesn’t get in the way and probably accords with how modern geometers of any persuasion (not just differential geometers) would talk about it. But I definitely disagree with simply eliding the sentence in order to placate the sensibilities of a different field’s practitioners. The reason the sentence is important is because teachers frequently run into the erroneous belief that map projection is literally a consequence of projective geometry. Strebe (talk) 07:18, 6 October 2019 (UTC)
 * " I have reverted the text, and if you wish to fight about it, then this will go into arbitration" So you recant your mention of "arbitration" here? Because after 16 years here you'd better know the meaning of that in a DR context. I have exactly two reverts, because my first edit didn't undo your edit (unless you're the author of that exact text, which I don't see evidence of at first glance). If you didn't want to continue the edit war, then you shouldn't have touched the article again. It takes two to edit war. Unless you are going to recant that statement, there is no straw man here. And no, mathematicians have no problems calling absurd claims absurd. I'm not saying you are absurd, but I am attacking the idea.
 * I thought I was clear when I said "distance-preserving map" in my edit summary, since I am perfectly aware that curved space isn't isometric to flat, so I thought anyone would know I was implying something less powerful.
 * I do not deny your citations. However, your quotes from them are not definitions, and your citations are not the final word. If you Google the exact terms "map projection" "Riemannian geometry", your results are plenty of papers and texts explaining this application. One of them even explicitly names this a problem in geometry. No (pure) math sources restrict geometry to Euclidean geometry. In fact, ever since we've known the world is not flat, geometry, whose root means "study of the earth", has been concerned with non-Euclidean geometries too. Therefore, it is undue weight to say even your revised text, especially as the linked article contradicts this restrictive definition. I would have revised it, but since your quotes don't even define, rigourously, the meaning of "geometry", they are not any grounds to override the definition of "geometry" as provided in that article. If you want to use a more restrictive definition, then you had better provide for an explanation for this restricted use, rather than linking an article (geometry) whose given definition contradicts you. That definition, since it is not the prevailing academic definition of "geometry", cannot be assumed to be such even if this specific field uses it. What if in my fictional study of Jasperometry, peer-reviewed sources defined metal as (native elemental) gold, and an article on Jasperometry said "aluminium ore is not metal ore"?
 * The fact that the statement can even be misinterpreted (with respect to either of our views) also shows that it's too imprecise to begin with. If it is to be reintroduced, it needs to be made much more precise, or at the very least a footnote must be added to clarify.--Jasper Deng (talk) 07:30, 6 October 2019 (UTC)


 * “So you recant your mention of "arbitration" here?” It’s very odd that you keep pursuing this. No, I do not recant. What you might consider recanting is the claim that I said it’s a first resort. That’s not in there. I see why you read it that way, but that’s a misinterpretation. Did it ever occur to you that I meant it as the last resort? As in, “If you want to fight it all the way to the Supreme Court, then go right ahead.”? Why did you ignore my statement that WP:3 is the first resort? And why is this business about arbitration important anyway if you know we’re a long way from it?


 * “If you didn't want to continue the edit war, then you shouldn't have touched the article again. It takes two to edit war.” You are the one complaining about edit-warring, not me. YOU. YOU. YOU. Do not confuse me with YOU. All I have commented on about edit-warring is your hypocrisy in the matter. You’ve been bleating all along about my edit-warring when you are the one with the last revert. That’s hypocrisy.


 * “I thought I was clear when I said "distance-preserving map" in my edit summary, since I am perfectly aware that curved space isn't isometric to flat, so I thought anyone would know I was implying something less powerful.” Your defense here seems to be, “I thought everyone knew what I meant because I knew what I meant.” Look, I don’t doubt now that you knew what you meant when you wrote it, but I also don’t see how you can expect anyone else to have known that.


 * “The linked article contradicts this restrictive definition.… If you want to use a more restrictive definition, then you had better provide for an explanation for this restricted use, rather than linking an article whose given definition contradicts you.” Well, let’s see what that article says about classical geometry:"Classical geometers paid special attention to constructing geometric objects that had been described in some other way. Classically, the only instruments allowed in geometric constructions are the compass and straightedge. Also, every construction had to be complete in a finite number of steps. However, some problems turned out to be difficult or impossible to solve by these means alone, and ingenious constructions using parabolas and other curves, as well as mechanical devices, were found."


 * And this:"Euclidean geometry is geometry in its classical sense. As its models the space of the physical world, it is used in many scientific areas, such as mechanics, astronomy, crystallography, and many technical fields, such as engineering, architecture, geodesy, aerodynamics, and navigation. The mandatory educational curriculum of the majority of nations includes the study of Euclidean concepts such as points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, and analytic geometry."


 * Classical geometers, and what they do: Euclidean geometry. Euclidean geometry, and how it’s what geometry means to so many fields today. That makes you pretty much exactly wrong. But you do persist in your imperious bossiness, don’t you. Strebe (talk) 09:10, 6 October 2019 (UTC)

Sorry, if you are going to WP:SHOUT at me I’m not going to spend more time attempting to converse with you. Ad hominem is not a way to discredit the fundamental problem that this is a vague statement (what is an “interpretation”?). At this point your arguments are so fallicious it’s not even funny. Chillax, and wait for DRN to do its job.—Jasper Deng (talk) 09:30, 6 October 2019 (UTC)

Currently, the article says that "most" projections "are usually defined in terms of mathematical formulae that have no direct geometric interpretation". I find this statement too vague to be meaningful. What must a geometric interpretation satisfy in order to be "direct"? Is a formula for transforming coordinates somehow illegitimate? How many projections are "most"? XOR&#39;easter (talk) 17:33, 6 October 2019 (UTC)


 * This is not a context for which unbounded precision is needed because its purpose is to debunk a common notion that, itself, has no precision, let alone accuracy. For any reasonable interpretation of “direct”, the statement is accurate and meaningful to a wide audience. “Direct” suggests “not abstract”, “not complicated”, “not exotic”. Pedantry beyond need destroys readability. If your statement is sincere that you do not find the text “meaningful” (as opposed to “not precise enough for me to base a mathematical proof on”) then please explain further. “Most” means, literally, “most”, by any reasonable definition you might use. Why does “illegitimate” come into the conversation here? How does the text imply any such thing? Also, I did propose “classical geometric” as a replacement if, for reasons I don’t yet understand, “direct” is objectionable. Strebe (talk) 18:54, 6 October 2019 (UTC)
 * For any reasonable interpretation of “direct”, the statement is accurate and meaningful to a wide audience. I must not be part of that wide audience, because now I'm even more confused. Whatever applies to "most" map projections is, by definition, not "exotic". I don't know what "not abstract" would mean when applied to mathematics; even applied math is abstract to some extent. And "classical geometric" would be worse: that sounds like saying most map projections are not expressed as a ruler-and-compass construction &mdash; probably true, even more probably irrelevant. XOR&#39;easter (talk) 20:36, 6 October 2019 (UTC)


 * Whatever applies to "most" map projections is, by definition, not "exotic" Your argument amounts to, “Most map projections are not exotic; therefore, whatever description is used for them is not exotic; therefore, if I succeed in describing most map projections in terms of bacon, this description would not be exotic.” Of course the interior of any map projection is described by differential geometry, and of course differential geometry is a (modern) form of geometry, but if your thesis is that differential geometry is not exotic to most readers, then obviously my citations disagree. I would be happy to conduct a Mechanical Turk study to this effect if you wish to seriously press this point, as long as you pay for it and my time if you are demonstrated wrong. I don't know what "not abstract" would mean when applied to mathematics; even applied math is abstract to some extent. This would be an example of pedantry beyond utility, and, honestly, feels like trolling. Abstraction comes in degrees. I am quite certain that you understand this, and I am quite certain that you understand the that applicability of a statement depends upon the degree to which it holds, not to false dichotomies about its binary truth value outside of a mathematical or formal logic proof. Therefore protestations that “I don't know what "not abstract" would mean” ring hollow. And "classical geometric" would be worse: that sounds like saying most map projections are not expressed as a ruler-and-compass construction &mdash; probably true, even more probably irrelevant. If you wish to press this belief in the connotation of classical geometry, I suggest you take that up on Talk:Geometry so that you can get the passages from it that I quote above removed. Good luck.


 * I am interested in a text that helps eliminate misconceptions that people hold about map projections. So far you and Jasper Deng have elected to present a blizzard of highly strained arguments, rather than building anything. If you have some pithy explanation for what the disputed text intends to convey that most people would understand, perhaps you should consider tendering it, rather than everything else you’re doing that amounts to “not helpful”. Strebe (talk) 21:47, 6 October 2019 (UTC)

Isn't it the case that all map projections with the additional property that latitudes become horizontal lines and longitudes become vertical lines DO have a direct geometric meaning: They can be obtained by projecting from the center of the earth onto some particular surface of revolution and then perpendicularly onto a cylinder? I don't see the relevance here. The more important idea is what the lead already says: that most map projections are designed to preserve some important properties of the surface (area, angles, connectivity of land masses...) but that they cannot preserve all such properties. Whether the projection is defined by geometric construction or by mathematical formula does not seem to be an essential property of the projection; the same property can be defined multiple ways. —David Eppstein (talk) 21:44, 6 October 2019 (UTC)


 * Isn't it the case that all map projections with the additional property that latitudes become horizontal lines and longitudes become vertical lines DO have a direct geometric meaning: They can be obtained by projecting from the center of the earth onto some particular surface of revolution and then perpendicularly onto a cylinder? If I understand what you are describing here, then yes. That does not seem “direct”, and in any case, projections of the class you describe are not “most projections”. The reason the text about direct geometric interpretation is in there is because, as noted a few times in this sadly lengthy “debate”, the misconception is common that a map projection corresponds to a physical projective “image”. Strebe (talk) 21:55, 6 October 2019 (UTC)
 * In wording like "that does not seem direct", it seems that you are arguing from personal intuition rather than reliable sources. We need reliable sources to include editorializations like this in the article. —David Eppstein (talk) 22:06, 6 October 2019 (UTC)
 * Agree with David Eppstein. All the discussion of whether this vague claim is correct is ultimately beside the point -- it's unsourced.  Per WP:V, "any material whose verifiability has been challenged ... must include an inline citation that directly supports the material." --JBL (talk) 22:38, 6 October 2019 (UTC)
 * It is also worth noting that this point (do "most" map projections have "direct geometric meaning"?) was an unnecessary digression in the paragraph in which it appeared. I have rewritten the remaining sentences to put the emphasis where it belongs. --JBL (talk) 22:42, 6 October 2019 (UTC)
 * I like the phrasing in JBL's edit. XOR&#39;easter (talk) 22:55, 6 October 2019 (UTC)
 * I also like this revision. I think we have a consensus here. I also apologize if I seemed rude with Strebe above, however I have little patience for hand-waving content.--Jasper Deng (talk) 23:10, 6 October 2019 (UTC)
 * New version is ok with me too. —David Eppstein (talk) 00:53, 7 October 2019 (UTC)


 * All the discussion of whether this vague claim is correct is ultimately beside the point -- it's unsourced. The rewrite is still unsourced. Please explain why the four citations I provided early in this debate do not count as sources. Every one of those citations uses “geometry” in the meaning that the text used to. Every one of the categorically disavows that most map projections are merely geometrical. How could this be more clear? “It is evident, from our definition, that we use the word Projection in a sense much wider than that which geometry gives it. The majority of map projections are not projections at all in the geometric sense.” Hence, merely stating that projections are not “perspective” is WP:SYNTH for ignoring what the texts in the field of map projections actually say about geometry and perspective. We have to suppose that these texts state these things for reasons that make sense for the broad audiences they address.


 * I proposed “classical geometric interpretation” in place of “direct geometric interpretation”, which I am fairly sure wouldn’t interfere with a broad audience’s understanding while making clear to mathematicians what kind of geometry we are talking about. However, this was savaged by Jasper Deng in a way that looks flatly wrong, given what Geometry has to say about the topic, and was otherwise ignored. Now we have a round of approval for the new text that is (a) unsourced; and (b) ignores what the sources actually say. How could the current state be satisfactory? Strebe (talk) 01:24, 7 October 2019 (UTC)
 * The source says they are not projections. You say they have no direct geometric interpretation. Whatever you might mean by that phrase is unclear because you've shot down every attempt here to guess at what's in your head, but it appears to be a different meaning than what is in your source. —David Eppstein (talk) 04:12, 7 October 2019 (UTC)


 * This dispute stems from two causes: (1) “Geometry” has several definitions, whereas the article doesn’t (and shouldn’t) engage different definitions; and (2) The problem that the disputed verbiage means to address does not admit precision because the misconception it addresses has no precise boundary. Nobody else here has bothered to address either of these causes.


 * The source I think you refer to says that map projections are not projections in the geometric sense. The author conveys there that “geometry” has a concept of “projection”, but that most map projections do not fit that geometric conception. These authors’ definition of “geometry” cannot be the same definition of “geometry” that Jasper Deng wishes to impose because, in Jasper Deng’s expansive definition of “geometry”, the term projection is also expansive, and of course includes map projections.


 * The authors I cite felt that their use of the term “geometry” was good for the purpose. We can assume that their audiences were not differential geometers, but we can also assume that their audiences were trained in most of the mathematics that could show up in a high school curriculum: the mathematics in all of those texts are at least at that level. None of the authors defined “geometry”; they seemed to know how their audience would understand it. That conception of geometry isn’t necessarily precise, and does not need to be, because the audience itself would not have a precise conception of geometry. It was sufficient to warn that projections are not “geometric”. Eight years ago, when the disputed phrase here morphed from a previous description of “direct physical interpretation”, the term “direct” was retained because leaving the term naked as “geometry” could invite objections such as Jasper Deng’s.


 * As editors, we are obliged to stick to the sources. We are obliged to reconcile specialist and lay conceptions and terminology. I do not care about “direct” specifically. I have repeatedly asked for alternatives. I proposed “classical”, but rather than respond to that, you responded with hostility, apparently still referring to “direct”. I do not care about “direct”. I believe it is a workable solution, for the reasons I gave. It’s not important that its meaning be precise because the problem the disputed sentence addresses—people’s common misconception about how projections work—is not precise. Meanwhile, the misperception is real, and educators repeatedly run into it, as can be inferred by the fact that these varied sources all feel the need to disabuse their audience of whatever “geometric” thinking they might have about the topic.


 * In summary, I agree we cannot use just the term “geometry” the way all of these cited authors do. But the problem isn’t with the authors. It’s with a gaggle of editors here who do not seem able to engage with multiple, reasonable, correct definitions for the same term. We need to resolve that. Long ago, I wrote “distinct”. Some editors have now express hatred for that but have failed to come up with a good qualifier. Instead, they modified the text to claim that most projections are not “perspective” with the rationale that the older text was not sourced. And yet, they did not source their change. And, it contradicts the only things that have been sourced. And they clapped each other on the back and went home. How long will this go on? Can I get any of you to do your job as Wikipedia editors, engage the sources, grapple with the problem of lay audiences versus specialist terminology, and work out something usable here? Or can I just expect an endless barrage of sabotage and sophistry?


 * Here’s another one for you, just for fun. There’s no end to them. Notice the distinct use of “geometric” and “perspective”. This also contradicts the current state of the text, which states only perspective.
 * “To a cartographer a projection is not necessarily perspective or geometric, and, since the most useful projections are generally non-persepctive, we must understand the term as applying to any method of representing the meridians and parallels on a flat sheet of paper.”
 * Strebe (talk) 07:55, 7 October 2019 (UTC)
 * You are trying to stitch together unimportant asides in a bunch of sources into your own, different, also unimportant aside in this article. I don't understand why; the form in which I have left the sentence maintains the essential idea (that map projections are various, and not necessarily point projections) without the contentious digression.  Skimming through what looks like thousands of words you've written here in the last few days does not give me any sense of why I should believe the digression is valuable to a reader.  (And, in advance: thousands more words will not accomplish that, either.  Maybe if you can fit it into a single short paragraph.)  Ultimately, no one is required to personally satisfy you that the present way is better, and there seems to have developed a pretty good consensus in its favor fairly quickly.  If you are dissatisfied with this you can always look at WP:DR.  --JBL (talk) 11:31, 7 October 2019 (UTC)


 * Who are you to decide whether it’s “important”? Are you WP:RELIABLE? What exactly is going on here? I have, again, requested that you and others examine the sources. You have, again, failed to do this. The sources all strive to disabuse its audience of the notion of map projections being a geometrical construction. Apparently this was important to them. It recurs. But now you assure me, as a reliable source, that the matter is unimportant, and you claim that I “stitch” together something that’s plainly right there in each source, with no stitching. How do you expect this play out? How do you tell yourself that you are following Wikipedia policy? Strebe (talk) 16:23, 7 October 2019 (UTC)
 * There seems to be a pretty solid consensus in favor of the present way of describing things, and ultimately no one is required to personally satisfy you that it is better than the previous way. Making personalized attacks on me is not going to change the situation. If you are dissatisfied you can always browse the options for dispute resolution. --JBL (talk) 01:41, 8 October 2019 (UTC)

Dispute resolution noticeboard — Preceding unsigned comment added by Strebe (talk • contribs)
 * The ping template doesn't work if you don't sign your message.  Strebe is pinging all of us to alert us to something he's opened on DRN. --JBL (talk) 21:02, 14 October 2019 (UTC)

"Flat maps"
The text now states, "Flat maps of the globe cannot be created without map projections. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent." It used to not state "flat". User:David Eppstein justifies this with, "Maps on curved paper are obviously possible, and even used (in the form of globes)". This is not correct. (A) Maps onto curved surfaces of whatever sort still require projection; (B) Globes are not made with maps projected onto "curved" paper; they are projected onto normal paper (using a projection tailored for that purpose) which is then warped onto the curved globe; (C) If the projection surface is the globe or a portion of the globe, the projection is a scaling, which is still a projection. Strebe (talk) 19:07, 30 October 2019 (UTC)
 * The physical process of constructing them is not the point. If it were, we wouldn't be talking about projection at all (no actual maps are ever made by a physical process of projecting features of the earth by some sort of earth-penetrating beam from a point within the earth to a sheet of paper well beyond the earth); we'd be talking about printing processes instead. And one could, still obviously and as both Lewis Carroll and Jorge Luis Borges famously described, make a map in the same scale and shape of the surface of the earth, with no distortion at all. So flat is necessary here to convey the correct meaning. —David Eppstein (talk) 19:21, 30 October 2019 (UTC)
 * You were the one who brought up physical construction in your justification, not I. The error is yours. You also ignored the fact that curved surfaces of other sorts also require projection, a truth that makes “flat" unnecessarily restrictive. Alternatively, it’s redundant, given that the entire previous paragraph sets the context for the article by specifically talking about maps on planes. Are we now to inject “flat” before “map” everywhere in the article? I’ll go ahead and make that edit for you. In any case, it’s pretty clear what’s going on here. Strebe (talk) 19:36, 30 October 2019 (UTC)
 * it’s pretty clear what’s going on here Yes: what's going on is that you have adopted an enormously combative and uncollegial approach to editing this article, making the usual process of discussion and consensus very difficult. If you would knock that off and try treating other editors as good-faith contributors who happen to have different views than you, life would be much better. (For example, by striking all the personalized commentary in your second comment.)
 * On the substantive question: I think there are reasonable points on both sides here about balancing clarity with irredundancy. When I read the second paragraph, I find that its first sentence is awkward.  Maybe actually the whole first sentence is redundant with the preceding paragraph (including "flat" or not) and should be removed, leaving the second paragraph to begin "All projections ...."  --JBL (talk) 19:54, 30 October 2019 (UTC)
 * I do not feel as I have been treated with good faith—not even remotely. Yes, that makes me combative. If you would like to discuss your concerns on my Talk page or preferably in a more conversational venue, then perhaps we can come to some sort of understanding that prevents the messes that recur here. As for the article, I’m losing interest. Do what you want to it; god knows it needs a lot of work—although, the ICA Commission on Map Projections may end up reworking it all out from under you anyway, since that was a topic in their last meeting, and good luck battling them. In fact, I’m losing interest in Wikipedia. It isn’t vandalism and creeping entropy that will kill Wikipedia; it’s a long, slow death from the departure of good, productive editors who get ground down by the playground bullying. Strebe (talk) 20:17, 30 October 2019 (UTC)
 * It isn't "playground bullying" for you to have to confront the fact that WP:EXPERT is no trump card, and that you cannot refute any of us (as you unsuccessfully tried to do above) with argumentum ad nauseum.
 * I don't like this statement in and of itself. I have a pair of maps at home that were clearly not produced by any map projection, as they are unphysical and without any sense of scale anywhere (hence not even diffeomorphic to any patch of the earth).--Jasper Deng (talk) 08:58, 2 November 2019 (UTC)

RfC on “geometric interpretation”

 * The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Should the text remain “Few projections in practical use are perspective,” or should it be sourced and its scope be broadened to reflect what the sources say? Strebe (talk) 22:14, 26 October 2019 (UTC)
 * The RFC wording is misleading, and worded in a pov-pushing way to support Strebe's vague and synthesis of sources which (if meaningful at all) has proven opaque to the rest of the editors here, has already gained little support here, and little support in Strebe's previous attempt to forum-shop support at WP:DRN. Strebe should work harder to find a concrete, specific, and more clearly meaningful wording which can be properly sourced, instead of continuing to argue that their previous failed proposals should be resurrected. And this RFC should be speedily closed as not a proper question. —David Eppstein (talk) 23:28, 26 October 2019 (UTC)
 * The question of whether the phrase is sourced or not is not one of PoV. It is a matter of fact. The question of whether it ought to be sourced is not a matter of PoV. It is a question of whether Wikipedia policy on sourcing ought to apply, and if not (as at present), why not. The DNR volunteer dropped the matter without engagement on the technicality that DNR was not likely to succeed for one-against-many. It appears, as per the volunteer’s recommendation, that RfC is a correct way to proceed. Strebe (talk) 18:07, 27 October 2019 (UTC)


 * Agree with David Eppstein: not a properly posed RfC. --JBL (talk) 23:42, 26 October 2019 (UTC)
 * I stoop to concur with previous replies. JonRichfield (talk) 07:19, 27 October 2019 (UTC)
 * I agree that the prompt is vague and only half-intelligible; without digging deeper into how much of this is a reflection of bias, and whether or not the RfC itself is appropriate, I think at a minimum we may say that it needs to be reformatted before it can arrive at any productive purpose/consensus result. Snow let's rap 10:05, 27 October 2019 (UTC)
 * I am happy to help in whatever way works for you, User talk:Snow Rise. The sentence in dispute is unsourced. I would like to see it sourced, and see it reflect the consensus of the sources, as per policy. I tried to format the RfC as per the guidelines here. This is the first time I have requested an RfC, so I don’t have a nuanced notion of how respondents interpret these guidelines. Strebe (talk) 18:05, 27 October 2019 (UTC)
 * The RfC statement above is problematic in the following ways: (1) It conflates two completely different issues (sourcing and broadening scope). (2) It is not neutral; instead, it is phrased as a "push-poll" that presupposes that one version reflects the sources and the other doesn't.  (3) Answering the question posed does not resolve the issue, because it leaves completely open the question of what the second option means in practice.
 * Finally, I can't help but notice that the sentence you quote from the article in the RfC statement (which occurs in the lead section) is not the same sentence as the one that has been under discussion above (which occurs in the section Map_projection). You should remove the RfC tags and think about addressing these issues before starting another one. --JBL (talk) 13:07, 28 October 2019 (UTC)
 * (1) The RfC text does not conflate sourcing and broadening scope; it explicitly mentions them separately. It does put them in one RfC, if that is what you mean. (2) This RfC is not about two different versions. It is about the version in the article. The version of the article is not sourced, and does not reflect the breadth of the sources. (3) What is at issue in this RfC is the lack of sourcing and the mismatch of the article text to the only sources that have been proposed. Resolving the problem means sourcing the text and reconciling it with sources. (4) The statements in the lede and in Map_projection need to agree with each other and with the sources. It does not matter which it starts with.


 * I have pointed out repeatedly that the statements in the article are not sourced. That has been ignored by those who agreed to the present text with the justification that a “consensus” has been reached. Given that sourcing is required when text is under dispute, and given that Wikipedia is not a democracy where questions are policy may be resolved simply by a matter of local vote, I opened this RfC to invite comment from others about what appears to me to be an agreement among some to forego Wikipedia policy for reasons that I have been unable to extract from those involved.


 * Is it the opinion of observers that I must present alternatives to choose among for the article text in order for this to be an RfC? Strebe (talk) 23:08, 28 October 2019 (UTC)
 * You wrote This is the first time I have requested an RfC, so I don’t have a nuanced notion of how respondents interpret these guidelines. In response, I gave some constructive criticism about the formulation of this RfC.  Your response exhausts any remaining desire on my part to be helpful. --JBL (talk) 23:50, 28 October 2019 (UTC)


 * This RFC cannot be answered in general because it does not provide specifically what the alternate wording should be. It is true that the only projections that are perspective are the general perspective projection, which corresponds to a view from space, and the orthographic projection, which corresponds to a view from further away in space, such as from the Moon.  Robert McClenon (talk) 04:39, 2 November 2019 (UTC)
 * The proponent should have asked for assistance in writing this RFC. Robert McClenon (talk) 04:39, 2 November 2019 (UTC)
 * Strebe is yet again incorrect in his belief that Wikipedia policy supports his text. It doesn't, for reasons hashed out above.--Jasper Deng (talk) 08:50, 2 November 2019 (UTC)
 * I concur with the above comments that this is not a well-formed RfC. XOR&#39;easter (talk) 21:05, 4 November 2019 (UTC)
 * (bot-summon) RfC is malformed yada yada but to be fair to the poster WP:RFC does not say one should present a choice between few well-defined options (it is in Writing_requests_for_comment though).
 * There is a point to the query though. Looking at the lead paragraph (Despite the name's literal meaning, projection is not limited to perspective projections (...) Few projections in practical use are perspective.) I would mildly support scrapping the last sentence which is not going to be easy to source without some WP:SYNTH (the closest I could find to sourcing would be this USGS report that list 16 map projections including two perspective projection - orthographic and stereographic - but maybe those two are in much bigger use than the other 14 after all). The replacements floated around by the original RfC posters in the above discussion are awful, though. Tigraan Click here to contact me 09:43, 5 November 2019 (UTC)


 * I also agree that this is a poor RfC. RockingGeo (talk) 00:21, 8 November 2019 (UTC)
 * Poor RFC. As currently worded, I do not even know what a "yes" !vote might do.  It basically says"should we say "tidbit" or something much better?"  It's not neutral, it's not complete, and ascribes faults to the current wording not in evidence.  I tried reading through the previous discussion to fill this out, but this RFC doesn't even attempt to be coherent with it.  (I'll grant that would be difficult, given the previous discussion is long and rambling, but it's still the job of this RFC to attempt that before anyone could !vote one way or another here.)  --A&#8239;D&#8239;Monroe&#8239;III(talk)  22:56, 11 November 2019 (UTC)
 * There is a third way. Just omit the sentence entirely. It's part of the WP:lead, so it should reflect what is expounded farther down in the article, which I don't believe it does. Anyway, one does not need to take sides if one can just snuff out the controversy by deleting the sentence. There's no reason to make this or any other editor jump through hoops unnecessarily. BeenAroundAWhile (talk) 22:21, 17 November 2019 (UTC)
 * Concur and even more. The whole paragraph starting "Despite  the name's literal meaning.." is bad. We all know that literal meanings of technical terms often bear little relevance to the "technical meaning", see etymological fallacy. Therefore the paragraph must be deleted in all its entirety.  In any case, it is does not belong to the lede, which must be article summary. Whole I understand the explanatory intent of this paragraph, it must be based on reputable sources (BTW, that's another reason of its deletion). Staszek Lem (talk) 19:31, 18 November 2019 (UTC)


 * The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

buckminster-fuller's projection
buckminster-fuller's projection onto the equal triangles of the icosahedron is listed under "Compromise projections" and commented by: "Compromise projections give up the idea of perfectly preserving metric properties... Most of these types of projections distort shape in the polar regions more than at the equator." if I understood everything well it was b.-m.'s intention to exactly avoid distortions where ever (especially in the polar regions of course) and to preverve metric properties as much as possible by projection onto the 20 equal (!) triangles of the icosahedron... so the only distortion one has there is the minimal one caused by flattening the spherical triangles. so please correct things in my head or the article... thanx! HilmarHansWerner (talk) 18:14, 10 January 2020 (UTC)
 * Neither your head nor the article needs correction; Fuller's projection does not do anything worse near the poles than anywhere else, and the article does not say that it does (thanks to the word "most"). --JBL (talk) 18:29, 10 January 2020 (UTC)

Hourglass Projection, and many more
There is no page or article references for the stated projection.

here is a book that has a diagram

here is a web page with links to various projections — Preceding unsigned comment added by 14.200.179.169 (talk) 12:48, 31 March 2020 (UTC)


 * Thank you, those look like useful references.
 * Alas, the Vespucci site seems to be offline today, but identical (as far as I can tell) copies of the information on that site are available at:


 * http://spatial.ucsb.edu/archive/map-projections/Miscellaneous.html
 * http://iscsi.spatial.ucsb.edu/map-projections/Miscellaneous/
 * http://www.csiss.org/map-projections/Miscellaneous.html


 * My understanding from p. 161-163 of the book you mentioned,
 * (Mark Monmonier. "Rhumb Lines and Map Wars: A Social History of the Mercator Projection".)
 * is that the Snyder "hourglass projection" was never seriously intended to be useful, but is more of a sarcastic way of pointing out that perhaps there are more important characteristics of a map projection than "equal area".


 * I feel that there are so many map projections that there's not room in this "map projection" overview article for the Snyder "hourglass projection",
 * but perhaps that projection might be relevant in the equal-area map article. --DavidCary (talk) 03:36, 24 December 2020 (UTC)