Talk:Mercator projection/Archive 2

Aspect ratio of unity
I have come to find that this means a 1:1 aspect ratio. However, searching "aspect ratio of unity" didn't provide any answers (this Wikipedia article being the first hit) and so I had to go through the calculations myself to verify this. Is this really a commonly used/understood phrase in English or should it be changed to "a 1:1 aspect ratio" or something similar? — Preceding unsigned comment added by TheOnlyRealEditor (talk • contribs) 14:56, 6 July 2020 (UTC)

"Unity" is another word for "one"; "an aspect ratio of unity" just means "an aspect ratio of one" or "an aspect ratio that is one". I understood it well enough, but if it's confusing to some, I don't see any reason not to rephrase it. Justin Kunimune (talk) 15:02, 6 July 2020 (UTC)


 * mathematicians and physicists use the word "unity" to mean "1". It's so common a useage that I wouldn't even notice it, but you may be right that non-mathematicians aren't familiar with this. I'd say go ahead and change it if you think it's confusing. Geoffrey.landis (talk) 13:01, 17 August 2020 (UTC)
 * Width vs height being important, shouldn’t those aspect ratios be, for example, 1:1? And in this case, just make it “square”, I’d say. Strebe (talk) 17:47, 17 August 2020 (UTC)

Constant bearing
If we're going to state "A course of constant bearing... is used in marine navigation because ships can sail in a constant compass direction for long stretches, reducing the difficult, error-prone course corrections that otherwise would be needed frequently when sailing other kinds of courses" I would say this needs a citation (or more than one). Mariners don't travel long distances on a constant compass heading because this isn't efficient and mariners did indeed know the Earth was round (or at least they all did by Mercator's time)(*).

But mariners did travel SHORT distances on a constant compass heading, and the remarkable thing about Mercator (and no other projection) is that LOCALLY, every spot is accurate in shape and correctly oriented north/south. Globally, it may be wrong and distorted, but in any given place, every piece is right and undistorted.

I moved this statement out of the lede (it is in the "properties" section).

(*in any case, back in Mercator's time, winds and currents determined the route a ship would choose). Geoffrey.landis (talk) 13:01, 17 August 2020 (UTC)

"…Mid-latitude or middle latitude sailing was often used to convert a departure into a difference in longitude. Since the ship is not sailing at a constant latitude, the average of the initial and final latitude for the course was defined as the mid-latitude. The departure was divided by the cosine of the mid-latitude to provide an estimate of the difference in longitude. This technique is reasonably accurate for short distances, particularly near the equator where the meridians do not converge quickly as one travels North or South. For distance greater than a few hundred miles or when sailing in northern or southern waters, this method is not sufficiently accurate, and the student was advised to use the technique of Mercator Sailing…" The paper then elaborates on “Mercator Sailing”, the point of which was to estimate distances accurately provided that you sail on a rhumb. Notice that this is the recommended technique for “more than a few hundred miles”. In other words, it was common to sail long distances along rhumbs. It was far more important to get to your destination than to get get there faster but risk getting lost. Strebe (talk) 18:10, 17 August 2020 (UTC)
 * Moving the matter of rhumbs out of the lede contradicts the raison d’être of the projection and thereby does a serious disservice to the article. To Mercator, and to the generations of navigators who used it, it was all about the straight rhumbs. I don’t think Geoffrey.landis's observations here fairly characterize the practical considerations, either. I don’t want to argue over the definitions of “short” and “long” distances, but, in fact, mariners did sail “long distances” (many hundreds of nautical miles) along rhumbs. It was much too hard to frequently compute what the new course ought to be while also tacking and beating and keeping track of distance via dead reckoning. Sailors were not mathematicians. They needed failsafe ways of working under difficult conditions. Maneuvering to keep a constant bearing was plenty enough to deal with. As observed by Mercator, paraphrasing, “You will not arrive by the shortest route, but you will surely arrive”. The surely arrive was everything; ships were frequently lost and grounded because they could not figure out the right course to take because they didn’t know where they were. In order to sail a course other than a rhumb, you would have to know exactly where you are at all times. That was practically never true. Sailing a rhumb, on the other hand, meant that all you had to know or do was keep a constant course as long as you knew where you were when you started, where you intended to be when you stopped, and you had a map that correctly mapped those two coordinates. It’s also false that sailors were at the mercy of winds and currents. That was only true if there was no wind, which was a seasonal problem in the tropics but rarely any other time or place. Ships routinely sailed nearly upwind. While Mercator’s concept of rhumbs was ahead of sailing technology in his time, by the 18th century, its use was constant and celebrated. Strebe (talk) 16:50, 17 August 2020 (UTC)
 * It sounds like this could use a citation either way. I'm not sure where to look for one, though. I feel like Flattening the Earth might say something about it, but my copy is in storage right now (I assume someone else here has access to it and can check). Justin Kunimune (talk) 17:11, 17 August 2020 (UTC)
 * No end of sources about sailing specifics are available, but this is more an editorial judgment: Do rhumbs belong in the lede or not? For an introduction to the complexities of sailing, see, for example, . Excerpting, "These sin(α) sin(β) sin(γ) values can be used to determine the initial course when departing and the final course when arriving for a ship sailing a great circle course, but does not tell the sailor what his course should be at any other time on the journey. Thus this sailing is more of academic interest, rather than of practical use, and is absent in many manuscripts."

Ah; I wouldn't have considered a few hundred miles as "long distance" on a global scale. That's short enough that there is negligible deviation from a great circle (unless you're nearly at the pole); it doesn't matter whether you take a constant bearing or a great circle.

But, the discussion here is good, some of it should go into the article, and a citation or three would be good. The material is mostly already there, but since Strebe calls marine navigation the raison d’être of the projection, it could be helpful to label it such. I suggest adding a subheading under "uses" titled "Marine Navigation" Geoffrey.landis (talk) 23:18, 17 August 2020 (UTC)


 * OK, done: I added a section "Marine navigation" under "Uses" that basically states what was discussed here. Check it and rewrite as needed (and, add a citation if you can. Is there a source for that quote paraphrased above?
 * -- The "uses" section also had a lot of text devoted to critics of the projection. That seemed out of place, so I moved it to a more appropriate heading. Geoffrey.landis (talk) 23:55, 17 August 2020 (UTC)

Image not showing poles
That is really bad, because you cannot really see the properties of the Mercator-projection on a incomplete map. — Preceding unsigned comment added by Chricho (talk • contribs) 22:53, 12 April 2011 (UTC)
 * Probably you are kidding, but did you care to read the first paragraph? Alvesgaspar (talk) 23:06, 12 April 2011 (UTC)
 * No, I am not kidding, I know about Mercator projection (it is trivial). E.g. there should be a much bigger gap between Greenland and the pole. Look at the image below, that one is showing the poles, it is much better. --Chricho ∀ (talk) 11:45, 17 August 2011 (UTC)
 * The Mercator projection does not show the poles as their distance from the equator is infinite. In the image below the largest latitude shown is 85º. -- Alvesgaspar (talk) 12:21, 17 August 2011 (UTC)
 * Oh sorry, you are right, I confused it and talked nonsense. However, the image should show a bit more to make it obvious. --Chricho ∀ (talk) 12:36, 17 August 2011 (UTC)

I think I get it now. Chricho, apparently, wanted 2 patches which would go like this:
 * !85-90 degree area cannot be shown!
 * *map itself goes here*
 * !85-90 S area cannot be shown!

Uchyotka (talk) 10:40, 21 August 2020 (UTC)

Article needs to explain difference between Mercator and central cylindrical projections
Almost every source I've seen on the internet about map projections confuses the Mercator and central cylindrical projections. We would be doing the world a huge favor by concisely and clearly explaining the differences in this article. Perhaps it could be a paragraph or subsection under the Properties section. Nosferattus (talk) 03:01, 18 August 2022 (UTC)


 * I think you might be the best candidate for this heroic task! Nosferattus (talk) 03:03, 18 August 2022 (UTC)
 * Lol sure, I can do that. I added a note to the bottom of Properties as you suggested; what do you think?  It could also go in the Mathematics section, but that section is pretty long and structured so I didn't see a good spot for it. Justin Kunimune (talk) 11:34, 18 August 2022 (UTC)
 * That’s a good observation. Strebe (talk) 05:29, 18 August 2022 (UTC)

y(φ) "must" be antisymmetric
A note at the bottom of the page says, "The function y(φ) is not completely arbitrary: it must be monotonic increasing and antisymmetric (y(−φ) = −y(φ), so that y(0)=0): it is normally continuous with a continuous first derivative."

Why must it be antisymmetric? I see no reason why it must be so. 31.52.108.53 (talk) 20:56, 21 November 2022 (UTC)


 * That’s just the conventional definition of cylindric projection. Strebe (talk) 04:08, 22 November 2022 (UTC)

As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other.


The article contains the claim "As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other."

Really? What about "Cylindrical equal-area projection with oblique orientation"?

Euro2023 (talk) 03:26, 10 January 2023 (UTC)


 * Sounds like you have identified an issue with the description. Was this my fault? did you want to fix it? GeogSage  ( ⚔Chat?⚔ ) 04:21, 10 January 2023 (UTC)
 * This description seems entirely fine to me. I believe Euro2023 wants to change this to “As in all cylindrical projections in equatorial aspect, ...” (or perhaps “normal aspect”, “direct aspect”, or another synonym) for precision. I think this is unnecessarily pedantic but don’t really care strongly either way. –jacobolus (t) 04:28, 10 January 2023 (UTC)
 * Where are the straight lines in the file to the right? Euro2023 (talk) 04:29, 10 January 2023 (UTC)
 * Wikipedia readers are neither robots nor idiots. They are entirely capable of figuring out for themselves that the term “cylindrical projection” when not otherwise qualified refers to a cylindrical projection in equatorial aspect (otherwise as you point out the claim about a rectangular graticule would be entirely nonsensical). Thus the qualification is not really necessary. Adding extra qualifiers to already functionally unambiguous terms is cumbersome and distracting and can even cause more confusion than it prevents. But in this particular case I wouldn’t care strongly enough to object if someone wanted to add the qualifier to this sentence. –jacobolus (t) 04:35, 10 January 2023 (UTC)
 * Please refrain from using attack language e.g. "Wikipedia readers are neither robots nor idiots.". It has nothing to do with the observation that I made and the questions I wrote down here. If you cannot find the claimed straight lines in the image and you are correct, i.e. they don't exist, then the statement is simply wrong. Euro2023 (talk) 04:56, 10 January 2023 (UTC)
 * Setting some baseline for a presumed Wikipedia reader’s basic level of literacy / mental competence is not “attack language”. For an analogous assumption in another field, cf. reasonable person. –jacobolus (t) 05:14, 10 January 2023 (UTC)
 * The topic of this section aren't Wikipedia readers, nor their "basic level of literacy / mental competence" but the topic is a false claim. Instead of talking about the false claim, you start talking about who is not idiots. What does that help to get rid of the false claim? Did anyone claim that Wikipedia readers are idiots? If not, why did you write it? Did you intend to spread the impression that someone claimed they are idiots. Yes, you did so. You wanted to portray me as a person that did so and needs to be told that "Wikipedia readers are neither robots nor idiots.". Euro2023 (talk) 05:23, 10 January 2023 (UTC)
 * There is no "false claim" here. The claim is entirely fine. The phrase "all cylindrical projections" implicitly means "all cylindrical projections in equatorial aspect", and this is obvious to any ordinary reader (a presumed character of basic literacy and mental competence). If you strongly care about being pedantically precise in this specific case because you are worried hypothetical robot-minded readers might be confused, you can explicitly add "in equatorial aspect" (or if you prefer, "in normal aspect") to the end of the phrase, and I doubt any other editors will care strongly enough to hassle you about the change, unless you start trying to enforce the same over-qualification all across every Wikipedia article, in which case people will be annoyed, revert your changes, and ask you to stop. –jacobolus (t) 06:07, 10 January 2023 (UTC)
 * While I provided evidence that the claim is false, you don't provide evidence that it is true nor evidence that a majority of Wikipedia readers want to see claims presented as true that are false.
 * Is it true that the claim is "As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other." - YES
 * Is it true, that that the claim can be either false or true but not true and false - YES
 * Is it true, that that if the claim is not true, it is false - YES
 * Are there "cylindrical projections" for which "parallels and meridians" are not "straight and perpendicular to each other" - YES
 * Does "all cylindrical projections" include "all" (cf. wikt:all) projections that are "cylindrical projections" - YES
 * Does "all cylindrical projections" include those for which "parallels and meridians" are not "straight and perpendicular to each other" - YES
 * Are there "cylindrical projections" for which "parallels and meridians" are "straight and perpendicular to each other" and at the same time NOT "straight and perpendicular to each other" - NO
 * Is it true for "all cylindrical projections" that "parallels and meridians" are "straight and perpendicular to each other" - NO
 * Is the claim true? - NO
 * Is there evidence that a majority of readers of Wikipedia want to see claims presented as true that are false - NO
 * Euro2023 (talk) 14:32, 10 January 2023 (UTC)
 * Again, if you want to change the phrase "as in all cylindrical projections" to instead say "as in all cylindrical projections in equatorial aspect" or "as in all cylindrical projections in normal aspect" in this specific example, you can go ahead and make that edit. I doubt anyone is going to mind enough to fight about it unless you start trying to enforce the same terminology broadly. Please do not try to change this to the phrase "as in all normal cylindrical projections", because this is non-standard terminology not supported by reliable sources and likely to confuse readers.
 * But as for your checkmarks, your summary is just not how human language/communication works. Ordinary written/spoken language does not consist of formally defined mathematical statements expressed with complete precision, but instead saves effort by relying on conventions and writers'/readers' common sense to interpret statements and fill in implicit context. Statements that would be too underspecified or ambiguous for a computer software proof assistant to interpret can nonetheless be entirely unambiguous to ordinary human readers, because human readers are not idiots or robots. –jacobolus (t) 22:41, 10 January 2023 (UTC)
 * Stop your adhominem attacks. Euro2023 (talk) 22:53, 10 January 2023 (UTC)
 * You seem to misunderstand what ad hominem means. This is a discussion about terminology conventions, writing style for Wikipedia, and what can be expected from Wikipedia readers, not about you personally.
 * Nobody has insulted you or attacked your character, much less fallaciously used such attacks to dismiss/discredit unrelated arguments.
 * Please assume good faith and stop making yourself out to be a victim, and instead focus on the topic(s) under consideration. –jacobolus (t) 23:11, 10 January 2023 (UTC)
 * Stop your attacks and ad hominem statements. Euro2023 (talk) 23:15, 10 January 2023 (UTC)
 * You were helpful at removing "gigantic" from the article map projection, that's why I pinged you. If the image presented here shows a "Cylindrical equal-area projection" and if such a projection is a "cylindrical projection", and the blue lines in the image are not straight, then I think the statement given in the headline of this talk, is wrong. Maybe the following statement would be correct: As in all normal cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other. Euro2023 (talk) 04:28, 10 January 2023 (UTC)
 * For context we've been having a dustup over at Talk:Cylindrical equal-area projection. –jacobolus (t) 04:29, 10 January 2023 (UTC)
 * Again an attack? Can't you stop that? Why would that what you call a "dustup" be a context for the question here? Euro2023 (talk) 04:31, 10 January 2023 (UTC)
 * I can only assume you pinged me here based on our discussion over there. Other editors coming to our in-progress conversation without context are going to be confused, so sending them to see the context is a service. Characterizing our conversation as a dustup is not an “attack”; dustup is a light-hearted synonym for “argument”. –jacobolus (t) 04:33, 10 January 2023 (UTC)
 * "I can only assume you pinged me here based on our discussion over there." - And if so? "Other editors coming to our in-progress conversation without context are going to be confused" - which "in-progress conversation"? Here the topic is clearly defined. I just spotted yet another bug. The attack lies in the fact that you point to the other place where you attacked me over and over again. Euro2023 (talk) 05:00, 10 January 2023 (UTC)
 * I appreciated the context. Since these discussions are closely related, many points made there apply here. Justin Kunimune (talk) 14:41, 10 January 2023 (UTC)
 * "Since these discussions are closely related, many points made there apply here." - Which made there applies to the statement from 03:26, 10 January 2023 (UTC)? Euro2023 (talk) 22:52, 10 January 2023 (UTC)
 * I suppose mostly the point that "equatorial aspect" is usually implied when one mentions a cylindrical projection, and the counterpoint that WP should precisely state when nonequatorial aspects are included and when they aren’t. Those were my two main takeaways from that discussion. Justin Kunimune (talk) 23:46, 10 January 2023 (UTC)

Lack of Sources
I'm reading through the "History" section of this article and there's a whole string of paragraphs with a lot of different information and assessments and not one citation in sight. Can someone address this? 104.181.215.171 (talk) 18:21, 15 April 2023 (UTC)


 * I didn’t write any of this, but I notice Monmonier is cited in there. Pretty well everything in that section is covered in his book. Feel free to go track down more sources though, or skim through that book looking for specific pages covering particular sentences. –jacobolus (t) 18:45, 15 April 2023 (UTC)

In the main article, the claim "As a result of these criticisms, modern atlases no longer use the Mercator projection for world maps or for areas distant from the equator, preferring other cylindrical projections, or forms of equal-area projection." has zero sources. Without evidence I think it reasonable to delete such a definitive claim about the entire world's atlas makers. — Preceding unsigned comment added by VilaRest (talk • contribs) 14:49, 11 May 2023 (UTC)


 * Chapter 9 of Monmonier, "Wall Maps and Worldviews", attests to the latter part of the claim, though Monmonier argues that the cause was anti-isolationist sentiments in the US and the availability of better equal-area and compromise projections, not criticisms from academic circles. Justin Kunimune (talk) 17:54, 11 May 2023 (UTC)