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     A map is a transformation between the curved surface of the earth and the flat plane of the map. Distortions always result from this transformation. They may affect conformality, distance, direction, scale, or area  
     When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps;  scale may change from point-to-point.
     A map is equidistant when it accurately portrays great circle distances from the center of the projection to any other place on the map. An equidistant map cannot accurately show great circle distances from all points to all other points.
     A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions. 
     Scale is the relationship between a distance portrayed on a map and the same distance on the Earth. Azimuthal maps accurately show true directions from one point to all other points on the map. Azimuthal maps accurately show directions  accurately only from a single central point (or sometimes two central points).
     When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map.
      Projections seek to minimize distortions of one or more of these factors, but they do so only at the expense of distortions of other factors. For example, in Mercator's projection, a course from one point to another can be represented as a straight line between the two points, which makes the projection very useful for navigation. But it does not preserve the relationship of areas, so that the size of Greenland is much larger on the map than in reality. 

Azimuthal Equidistant   Butterfly Projection
Cordiform   Dymaxion Map
Equatorial Stereographic Gall Projection Globular Projection
Equal Area Projection Interrupted Projections Mercator's Projection
Oblique Projection   Oval Projections
Polar Projection Unusual Van der Grinten