Talk:Mercator projection

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[edit] Image about relationship between latitude and position on map

I think the image that relates latitude on globe to vertical position on map could be improved in two ways. 1. Make it show the complete graph. Neither latitude or vertical position on map are defined to infinity; both are limited. The current image conveys the idea that vertical position on map approaches a limit as latitude tends towards infinity. 2. Change the distance between "ticks" on the vertical axis so that the graph reaches +90 and -90 degrees, instead of current half-pi. Since in navigation, degrees are practicaly ubiquitous, it makes little sense to me to use radians here. I'd be grateful if someone who has software that can make that kind of proffesional looking graph would deal with this. --85.224.196.223 23:02, 16 November 2006 (UTC)

[edit] Headline text

One of the reasons I can rationalize proposing using a Mercator Projection in a recent proposal to map the fields of views that the Hubble Space Telescope has seen is that Mercator projections were used to navigate travel to a point. Faced with the question of how our earth interacts with other planets, galaxies, galaxy clusters, superclusters, asteroids and other objects in its travel around the universe, solar system and galaxy, a map which sees us as navigating our path through the universe is a useful image.


The Mercator Projection is a useful image or story then to assist with navigation, but as this article points out does not accurately reflect the size of areas on earth or on space. It should be said that Mercator had a similar focus to me later in his life. He focused on ideas about the development of everything..I vaguely recall from reading just now at the Univeristy of Chicago Regenstein Library.

James Timothy Struck - moved from the main page.


[edit] Just a question

Sir,

      I have longitude and latitude value and just find co-ordinates value in two dimension (x,y). I get one formula but i do not get h or ln value.

formula available in this hyperlink

               "http://en.wikipedia.org/wiki/Mercator_Projection"

[edit] That rv might need explanation

Regarding this edit of mine: formula did look wrong, but not because of erroneous input -- "My preferences/[Math] (•) HTML if very simple or else PNG" was at fault. —Preceding unsigned comment added by Saimhe (talk • contribs) 2006-09-28T00:09:21

[edit] Main Picture

I'm putting forth the suggestion that the main example of the projection used at the top of the page should be changed to something more modern. While the historical map is endearing, it makes it much harder for the reader to quickly absorb the distortions instituted by the mercator projecition.


>>> You might use World Map flat Mercator.png. I uploaded it together with World Map flat Gall-Peters.png because I wanted some clean maps. Nutzelfutz (talk) 18:33, 17 May 2008 (UTC)

[edit] Scale

This statement doesn't seem to me to be accurate: "Being a conformal projection, the linear scale does not vary with direction and the angles are preserved around all locations." As I understand it, the only lines of constant scale on a Mercator projection are the parallels. Any line which isn't parallel to the equator varies in scale (the representative fraction gets larger as the latitude gets higher). If I'm missing something, is there a clear way to explain what is meant by "scale does not vary with direction"? - Justin (Authalic) 22:22, 20 February 2007 (UTC)

The statement means that scale near any one point is the same in all directions. As you said, it's true (indeed, it has to be true for every flat map projection) that scale is not constant in all directions over any signficant distance.
Consider a counterexample: the plate carree projection. Its horizontal scale changes as you move away from the equator but its vertical scale doesn't. So at 60 degrees latitute, the horizontal scale is twice the vertical scale -- which means that shapes are distorted (stretched horizontally by a factor of 2). In the Mercator projection, and in any other conformal projection, the horizontal and vertical scales change by the same amount as you move around the map. Paul Koning 14:39, 30 May 2007 (UTC)

[edit] Why the vertical distortion?

I can see why at the polar regions there would be a horizontal distortion, but why is there also a vertical one? Ajuk 12:30, 1 May 2007 (UTC)

Because the scale changes for both. It's a conformal projection -- it preserves (small scale) shape. So if the horizontal scale has to change, as of course it has to, then the vertical scale changes by the same amount. Paul Koning 15:52, 1 May 2007 (UTC)

Is there a projection that doesn't have the horizontal distortion?Ajuk 21:30, 6 May 2007 (UTC)

No. All flat maps are distorted; only a globe has an undistorted picture. With maps, your only choice is what distortion you choose (or tolerate), given the purpose of the map. For example, on a Mercator projection, headings are true. On a gnomonic projection, great circles are straight lines. Pick your goal, and deal with whatever distortion that produces. Paul Koning 00:41, 7 May 2007 (UTC)

Sorry my mistake, I know that. Is there a map that doesn't have the vertical distortion, just the horizontal? Ajuk 20:17, 7 May 2007 (UTC)

Equirectangular projection, also known as Plate carrée projection. Paul Koning 20:26, 7 May 2007 (UTC)

[edit] su song map

The Su Song star map picture is labeled as being Mercator projection. How is that supported? It looks like a cylindrical projection of some sort, all right, but it's not obvious from inspection whether it's plate carree, Mercator, or something else. Paul Koning 16:09, 14 August 2007 (UTC) If you open up the image, this is the description provided:

This is a star map for the celestial globe of Su Song (1020-1101), a Chinese scientist and mechanical engineer of the Song Dynasty (960-1279). It was first published in the year 1092, in Su's book known as the Xin Yi Xiang Fa Yao (Wade-Giles: Hsin Yi Hsiang Fa Yao). On this star map there are 14 xiu (lunar mansions) on Mercator's projection. The equator is represented by the horizontal straight line running through the star chart, while the ecliptic curves above it. Note the unequal breadth of the lunar mansions on the map. Su Song's star maps had the hour circles between the xiu (lunar mansions) forming the astronomical meridians, with stars marked in quasi-orthomorphic cylindrical projection on each side of the equator, and thus was in accordance to their north polar distances. Not until the work of Gerard Mercator in 1569 was a celestial map of this projection created in the Western world (Needham, Volume 4, Part 3, 569). This picture appears on page 277 of Joseph Needham's book Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth.

I hope this clears up anything about the image.--Pericles of AthensTalk 01:21, 11 February 2008 (UTC)

No, it doesn't. I saw the description but it gives good reason to argue that the chart is not a Mercator projection. For one thing, the description says "quasi-orthomorphic". I'm not sure what that is but it doesn't sound like "Mercator". Furthermore, the article on Su Song claims that the map show the pole star. So by definition the projection cannot be Mercator. Paul Koning (talk) 15:32, 11 February 2008 (UTC)
  • From the map file : Su Song's star maps had the hour circles between the xiu (lunar mansions) forming the astronomical meridians, with stars marked in quasi-orthomorphic cylindrical projection on each side of the equator, and thus was in accordance to their north polar distances. Not until the work of Gerard Mercator in 1569 was a celestial map of this projection created in the Western world (Needham, Volume 4, Part 3, 569)

These two properties are contraditory. Either the projection is "quasi-conformal" (i.e., quasi-Mercator) or the distances along the meridians are conserved. It is impossible to have both things. If the projection were indeed conformal then the scale along the meridians would grow with declination, becoming infinite at the celestial pole. -- Alvesgaspar (talk) 16:23, 11 February 2008 (UTC)

[edit] Continued

I'll admit, I'm a layman when it comes to specifics in astronomy and cartography; let me present what Joseph Needham says in full and in his own writing:

. . .Lastly, the projection of Gerard Mercator in 1569 was a great advance, but he never knew that he was preceded by Su Song five centuries earlier in a celestial atlas, in which the hour circles between the hsiu (lunar mansions) formed the meridians, with the stars marked in quasi-orthomorphic cylindrical projection on each side of the equator according to their north polar distances (Needham, Science and Civilization in China, Volume 4, Part 3, 568–569.)

Ok, and in Needham's 3rd volume on page 278:

If the maps incorporated in the Hsin I Hsiang Fa Yao (New Description of an Armillary Clock) by Su Sung really date from the time when the book was written, they must be the oldest printed Chinese star-charts which we possess. Begun in 1088, it was finished in 1094, and the maps which it contain are remarkable in several ways. They are five in number, one of the north polar region, two cylindrical orthomorphic 'Mercator' projections of the regions of declination about 50° N and 60° S, and two polar projections, one of the northern hemisphere and one of the south. The space where the southern circumpolars should be is left blank. The drawing of stars is much more carefully done than on the MS map of rather more than a century earlier, but this also had the 'Mercator' projection...Close examination reveals that while the first of these maps accepts the pole-star of -350° as the position of the true pole, the fourth places this position half-way between Thien shu and our Polaris. This would suggest that Su Song must have taken advantage of the observations of his contemporary Shen Kua, already referred to.

I will try to scoop up more about this, but I think this is all Needham has to say, since right after this paragraph he switches topic.--Pericles of AthensTalk 06:52, 15 February 2008 (UTC)

Found some more; on page 208 of Needham's 3rd Volume of Science and Civilization in China, he says this after introducing Su Song's astronomical book and atlas:

The second chapter describes a celestial globe and includes star-maps in which the central palace (circumpolar region) and south polar region are planispheres, while the stars of the more equatorial-ecliptic regions are arranged on a cylindrical projection very similar to Mercator's.

More coming...--Pericles of AthensTalk 06:57, 15 February 2008 (UTC)

Needham talks of an earlier Tang Dynasty precedent of the Dunhuang map from the 8th century (Needham says the 10th century):

It will be remembered that already for the 10th century documentary evidence exists [footnote "h" here: Cf. pp. 264, 276 above regarding the Tunhuang manuscript star map] that a projection analogous to that of Mercator was used, the hsiu being represented as long rectangles centered on the equator and of course very distorted towards the poles.

Still looking for more...--Pericles of AthensTalk 07:04, 15 February 2008 (UTC)

On Islamic astronomy, Needham states on page 563 of Volume 3:

In comparing the scientific cartography of the Muslims with the Chinese, there are three chief maps to keep in mind. The first and most famous of these was the world map of Abu Abdallah al-Sharif al-Idrisi (1099 to 1166), made about 1150 for Roger II, the Norman king of Sicily, and often reproduced in modern works. This was fully in the Ptolemaic tradition, using nine parallels of latitude (climates) and eleven meridians of longitude, but arranged on a projection like Mercator's and making no attempt to allow for the earth's curvature.

Needham cites Kimble (I), p. 57 on this. Still looking for more...--Pericles of AthensTalk 07:09, 15 February 2008 (UTC)

Unfortunately, these quotes aren't precise enough to tell us what we need to know. I suspect the authors quoted do not understand projections that well. The most that one can conclude from them is that these old charts are cylindrical projections. But Mercator is not any old cylindrical projection, it's cylindrical conformal. That means the scale changes in a specific way (the distortion going towards the poles changes in a specific way). All flat maps have distortion, so all cylindrical projections have distortion, but that doesn't make them Mercator. And earlier cylindrical projections do not deserve credit as anticipating Mercator because it is precisely that conformality property that is essential and valuable in the Mercator projection.
Given an accurate image of one of these old maps and identifications of some of the stars, it would be possible to reverse-engineer the projection. I have been wondering if the Su Song map image in that article is good enough to do this; I haven't tried yet. (In this process one would have to account for precession of the equinox, of course.)
One thing I'm still wondering about, and the imprecise terminology of the authors quoted doesn't help dispel the uncertainty, is whether these old charts are projections at all. In other words, are they more than just sketches -- can you take the coordinates of a star on the chart and run it through a reverse projection transform -- any single fixed transform -- to arrive at the correct position of that star in the sky? If yes then it is a chart; if not then it's only a sketch. The quotes say the former, but their wording doesn't convince me that the authors actually fully understand the difference.
Paul Koning (talk) 22:40, 15 February 2008 (UTC)

[edit] Accessibility

It should be noted that the sections "Derivation of the projection" and "Mathematics of the projection" have no value to the majority of readers because there is little to no clear explanation other than the mathematic equations. This is a huge problem across Wikipedia. While the equations are surely important, we mustn't use them as the only point of reference when explaining the concepts (in most cases). It seems as though it would not be hard to put the concept in black & white terms. I'd do it, but I don't understand the math in this case.-DMCer (talk) 19:38, 24 November 2007 (UTC)

What sort of other points would you add? The defining property of the Mercator projection is that it is conformal; the math follows from that. The intro paragraph states what Mercator is all about (straight rhumb lines, in particular). Mercator is not a geometric projection -- as indeed is true for most map projections. So you can't talk about it informally in geometric terms, as you might do for, say, gnomonic projection. Paul Koning (talk) 16:33, 27 November 2007 (UTC)

[edit] Controversy section

Most of the content in the Controversy section does not relate to controversy. I see three topics in there: limitations, applications and controversy. My inclination would be to merge all of this into the main body of the text. Wikipedia editors do love our controversy sections, though. Ronstew (talk) 15:55, 23 January 2008 (UTC)

I agree with you. After all there is no real controversy over the Mercator projection, as it is just a bunch of mathematical formulas. Perhaps it just needs a better name. But I can't think of one right now.151.200.90.2 (talk) 00:12, 26 February 2008 (UTC)
There does seem to be some controversy listed in that section, by Peters and others. Some of that is just noisemaking to promote a different projection, which simply trades one set of distortions for another, or equally simplistic noises objecting to a whole class of projections (cylindrical ones). At least the section does begin with the statement that all projections distort; you only get to choose your trade-offs. Paul Koning (talk) 19:18, 26 February 2008 (UTC)
I believe this was quite a controversial thing to be done. First of all, I agree that it's all just a bunch of mathematical equations. But you can't downplay the importance of the fact that in the United States of America and other anglo-saxon countries this specific equation is frequently selected for the confection of world maps, and it is not because of the nice characteristics of the equation, but just because the area of these imperialist countries look larger and stronger then the other countries (for example, then Brazil). While in the world we have millions of children growing up in the northern north hemisphere seeing this navigational map as a "fair" representation of the world, you can't just come here and pretend it is not happening, and be all Mr. Scientist. The controversy section is not about the equations, is about how this specific equation here is misused in USA as a rhetoric tool for imperialist policies. It's a geographical sophism.
Although all projections have their distortions, there is no other projection that would qualify to receive a controversy section, simply because they are not misused as much as Mercator. The controversy section is about this cultural aspect of the Mercator projection, the controversial way it is frequently used, and not about it being "inherently evil".
If you read the "uses" section as it is now, this title seems very naïve if not plain wrong. Why would a "uses" section of any projection start talking about the relative size of the countries depicted? And why would a "uses" section talk about institutions refusing to use it? This section should only say that "the map has nice characteristics that aid in some calculations during navigations". All the rest, regarding the controversial use of it in atlases and other places, and the Peters thing, and all the fight to stop its use in schools and any other place if not in the desk of someone doing calculations during navigations, must have at least a sub-section. There must be a "uses" and a "misuses" section. "uses" and "abuses". In fact, the best thing would be to have a separate article for this subject, and leave the page about the projection as clean and mathematical as possible (with a link to the controversy article, of course). -- NIC1138 (talk) 16:29, 20 March 2008 (UTC)
  • Agree and will support your changes. The problem is the "Peters religion" is still alive - Alvesgaspar (talk) 17:17, 20 March 2008 (UTC)
I don't think it's a good idea to get into political discussions when the subject is mathematics. Paul Koning (talk) 18:44, 20 March 2008 (UTC)

[edit] Uses

This section has the sentence Despite its relative scale distortions, the Mercator is well-suited as an interactive world map that can be panned and zoomed seamlessly to local maps. Now near as I can tell, there is nothing remarkable about the Mercator here, as just about any cylindrical projection would do this. mdf (talk) 13:49, 9 March 2008 (UTC)

  • I think I understand the sentence. Because the projection is conformal (scale does not vary with direction), angular distortions are zero everywhere. Then, and for large zooming (local representations) the grid of meridians and parallels will always look "square", independently of the geographic position. That does not happen with non-conformal cylindrical projections, as the ratio between the scales along meridians and parallels varies with location. It has never crossed my mind this kind of property, as the Mercator projection is a terrible solution for depicting the whole world (still, it was used a lot for that purpose, in the past) -- Alvesgaspar (talk) 16:57, 9 March 2008 (UTC)

[edit] India Higher than Finland?

That Comment is confusing, Finland is clearly higher on the Mercator Projection. And under no projection can think of India being higher on the map. unless it doesn't mean farther away from the equator, which if that is the case then the sentence is still confusing in that I don't understand what it means. Arkkeeper (talk) 18:39, 29 May 2008 (UTC)