Mercator projection Guide, Meaning , Facts, Information and Description
The Mercator projection is a map projection devised by Gerardus Mercator in 1569.
It is a conformal map, that is, it preserves angle. Any straight line on a Mercator map is a line of constant bearing, a loxodrome or rhumb line. This makes it particularly useful to navigators, even though the plotted route is usually not a great circle (shortest distance) route. In the era of sailing ships, time of travel was subject to the elements, hence the distance traveled was not as important as the direction taken—especially since longitude was hard to determine accurately.
To achieve this effect, the Mercator projection projects Earth's surface on a cylinder tangent to Earth at the equator. This way, East-West distances are stretched by an increasing amount as the distance from the equator increases. The extreme case of distorted area is at the poless, where the two geographical points have become lines at the top and bottom of the map.
The following equations determine the x and y coordinates of a point on a Mercator map from its latitude φ and longitude λ (with λ0 being the longitude in the center of map):
And the inverse:
Controversy
Like all map projections attempting to fit a curved surface onto a flat sheet, the shape of the map is a distortion of the true layout of the Earth's surface. The Mercator projection exaggerates the size (and to a lesser extent, the shape) of areas far from the equator. For example, Greenland is presented as being roughly as large as Africa, when in fact Africa's area is approximately 13 times that of Greenland.Although the Mercator projection is still in common use for navigation, critics argue that is not suited to representing the entire world in publications and wall maps due to its distortion of land area—particularly, the exaggeration of the size of Europe and North America compared with South America and Africa. Some Mercator maps omit most or all of Antarctica, with the effect of placing Europe at the center of the map; these peculiarities are considered by some to perpetuate the idea of the inferiority of the Third World.
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. The Mercator projection is still commonly used for areas near the equator, however.
The equal-area Gall-Peters projection has also been proposed as an alternative to address these concerns. This presents a very different view of the world: the shape, rather than the size of areas is distorted. Areas near the equator are stretched vertically; areas far from the equator are squashed. A 1989 resolution by seven North American Geographical groups decried the use of all rectangular coordinate world maps, including the Gall-Peters.
Derivation of the projection
Assume a spherical Earth. (It is actually slightly flattened, but for small-scale maps the difference is immaterial. For more precision, interpose conformal latitude.) We seek a transform of longitude-latitude (λ,φ) to Cartesian (x,y) that is "a cylinder tangent to the equator" (i.e. x=λ) and conformal (i.e. with and .)
From x=λ come
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