Editing 2911: Greenland Size
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==Explanation== | ==Explanation== | ||
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Because the {{w|Earth}} is {{w|Empirical evidence for the spherical shape of Earth|curved}}, all flat maps have some distortion. (A common comparison is flattening an orange peel, which cannot be done without tearing or stretching or wrinkling parts of it). Different {{w|map projection}}s can distort different {{w|Map projection#Metric properties of maps|metric properties}}, such as distances, areas, and angles, while leaving others intact. It can be desirable to preserve different metrics in different applications. | Because the {{w|Earth}} is {{w|Empirical evidence for the spherical shape of Earth|curved}}, all flat maps have some distortion. (A common comparison is flattening an orange peel, which cannot be done without tearing or stretching or wrinkling parts of it). Different {{w|map projection}}s can distort different {{w|Map projection#Metric properties of maps|metric properties}}, such as distances, areas, and angles, while leaving others intact. It can be desirable to preserve different metrics in different applications. | ||
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The title text is about the fact that regardless of the size of the map there ''is'' a certain point where the area on the map is equal to the area at the actual pole at that latitude. This is because a horizontal line on a worldwide Mercator projection corresponds to a line of latitude. While most lines of latitude are thousands of miles (kilometers) long, they become smaller and smaller approaching the poles. As long as the projection (and choice of how much map to print) includes the pole (a point of zero length) expanded out as a measurable edge of the map, there will be a line of latitude around each pole whose length would equal the width of the map that Cueball is looking at (though the specific line would be different depending on the size and precise geometry of the map). If Cueball's map were 1 m wide, then this line of latitude would be at 89.999998568° N or S - that is, the line of latitude there would be a circle with a circumference of 1 m around each of the poles. Of course, in order for the map to actually include (say) the northern of those latitude lines as well as the equator, it would have to be over 3 meters tall. | The title text is about the fact that regardless of the size of the map there ''is'' a certain point where the area on the map is equal to the area at the actual pole at that latitude. This is because a horizontal line on a worldwide Mercator projection corresponds to a line of latitude. While most lines of latitude are thousands of miles (kilometers) long, they become smaller and smaller approaching the poles. As long as the projection (and choice of how much map to print) includes the pole (a point of zero length) expanded out as a measurable edge of the map, there will be a line of latitude around each pole whose length would equal the width of the map that Cueball is looking at (though the specific line would be different depending on the size and precise geometry of the map). If Cueball's map were 1 m wide, then this line of latitude would be at 89.999998568° N or S - that is, the line of latitude there would be a circle with a circumference of 1 m around each of the poles. Of course, in order for the map to actually include (say) the northern of those latitude lines as well as the equator, it would have to be over 3 meters tall. | ||
| − | + | A map at a scale of 1:1 was discussed in {{w|Lewis Carroll}}'s "{{w|Sylvie and Bruno Concluded}}": | |
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| + | <blockquote> | ||
| + | ''"What a useful thing a pocket-map is!" I remarked.''<br> | ||
| + | ''"That's another thing we've learned from ''your'' Nation," said Mein Herr, "map-making. But we've carried it much further than ''you''. What do you consider the ''largest'' map that would be really useful?"''<br> | ||
| + | ''"About six inches to the mile."''<br> | ||
| + | ''"Only ''six inches''!" exclaimed Mein Herr. "We very soon got to six ''yards'' to the mile. Then we tried a ''hundred'' yards to the mile. And then came the grandest idea of all! We actually made a map of the country, on the scale of ''a mile to the mile''!"''<br> | ||
| + | ''"Have you used it much?" I enquired.''<br> | ||
| + | ''"It has never been spread out, yet," said Mein Herr: "the farmers objected: they said it would cover the whole country, and shut out the sunlight! So we now use the country itself, as its own map, and I assure you it does nearly as well."'' | ||
| + | </blockquote> | ||
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| + | The same idea was expanded in {{w|Jorge Luis Borges}}'s "{{w|On Exactitude in Science}}". | ||
Mercator projections have been mentioned previously in [[977: Map Projections]], [[2082: Mercator Projection]], and [[2613: Bad Map Projection: Madagascator]]. The misleading size of Greenland on the Mercator projection is also the object of [[2489: Bad Map Projection: The Greenland Special]]. | Mercator projections have been mentioned previously in [[977: Map Projections]], [[2082: Mercator Projection]], and [[2613: Bad Map Projection: Madagascator]]. The misleading size of Greenland on the Mercator projection is also the object of [[2489: Bad Map Projection: The Greenland Special]]. | ||
