The GCS world map has a coordinate system based on a 3D model of the Earth. It is a conformal map in which direction, shape and angles are preserved on the map.The projection has distortions as well; Distance and Area is distorted. The distance from Washington DC and Kabul is shorter in the GCS world map. The distance between the two cities can be explained by the horizontal stretch of the map. Such a stretch is indicated by the size of Antarctica and Greenland; these two land masses appear more wider and horizontally stretched. Also The GCS world map depicts distortion of these two land masses; they are seen to be very large. Greenland looks to be comparable in size with the United States.
The Mercator map is also a conformal map because it too has meridians and parallels that intersect to form right angles. The Mercator map preserves the direction, angle, and shape as well. The Mercator map distorts distance and area too, however it distorts the map a different way. The Mercator map stretches the map vertically. The distance between Washington DC and Kabul is further away than the GCS map because the map itself is stretched in a vertical direction. Land masses are not being pushed closer together by extending horizontally as with the GCS map. The area of Antarctica and Greenland are elongated and appear to be very large. Again, Greenland looks larger than it is and even looks larger than the United States due to its vertical stretch.
These two maps are both equal area maps. The top map is called Cylindrical equal area map and the bottom is a Bonne equal area map. The areas of land masses are preserved and the shape, distance and angles are distorted in both projections. The Cylindrical map is made by the use of a cylinder. You can image a cylinder being wrapped around the Earth and then projecting onto the cylinder, and subsequently unfolding the cylinder.
The Bonne map is a pseudoconical equal area projection. All parallels are circular arcs with a common central point, and meridians are not straight lines. Parallels are equally spaced and are all standard lines. Its shape distortion is acceptable except far from the center. For construction, one parallel at the sphere is chosen, and a cone tangent at that central parallel is built. The parallel's radius at the map is the same as the radius along the cone. All other parallels's radii are marked accordingly.
Both these maps are equidistant maps. The top map is the Aitoff Equidistant map and the bottom map is the Equidistant Cylindrical map. In theory, both maps should have the same distant from Washington DC to Kabul, however they are different because it is most likely that the reduction rate, or scales, are not constant. Also the shortest distance between two points on a sphere is rarely represented by a straight line on a flat map, and measuring distances along an arbitrary, or not always marked, curve is not a straightforward procedure.
The Aitoff map is a modified azimuthal map projection in terms of its equatorial aspect of the map. There is great areal exaggeration near the map boundaries. There is equidistant only along the Equator and central meridian. Doubling longitudinal values enabled the whole world to fit in the inner disc of the map; the horizontal scale was then doubled, creating a 2 : 1 ellipse.
The Equidistant Cylindrical map is only equidistant at the meridians and at two parallels. It distorts shape and area. It is a cylindrical projection with standard meridians. All meridians are standard equally-spaced vertical lines, and all parallels are horizontal, equally-spaced, equally long lines. This map resembles the construction of tightly rolling an cylindrical sheet against the Equator and having every meridian drawn on this tube by light rays emanating from an equatorial point on the meridian directly opposite, however it not truly created by a perspective method.
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