Map projection

In <a href="/facts/Cartography/8YdDAAeX">cartography</a>, a map projection is any of a broad set of <a href="/facts/Transformation_(function)/Yr2J3o8H"> transformations</a> employed to represent the curved two-dimensional <a href="/facts/Surface_(mathematics)/whF08jvy">surface</a> of a <a href="/facts/Globe/8Pqs2IuQ">globe</a> on a <a href="/facts/Plane_(mathematics)/tAUtRFcn">plane</a>. In a map projection, <a href="/facts/Coordinates/Mtd0q4SP">coordinates</a>, often expressed as <a href="/facts/Latitude/IBYqkjhU">latitude</a> and <a href="/facts/Longitude/HsC61ML9">longitude</a>, of locations from the surface of the globe are transformed to coordinates on a plane.
Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography.
All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections.: 1 
More generally, projections are considered in several fields of pure mathematics, including <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, <a href="/facts/Projective_geometry/rHKSaEbx">projective geometry</a>, and <a href="/facts/Manifold/rXPERJtu">manifolds</a>. However, the term "map projection" refers specifically to a <a href="/facts/Cartography/8YdDAAeX">cartographic</a> projection.
Despite the name's literal meaning, projection is not limited to <a href="/facts/3D_projection/FATfGH2W">perspective projections</a>, such as those resulting from casting a shadow on a screen, or the <a href="/facts/Rectilinear_projection/YHMYNmld">rectilinear</a> image produced by a <a href="/facts/Pinhole_camera/8JmYNdeL">pinhole camera</a> on a flat film plate. Rather, any mathematical function that transforms coordinates from the curved surface distinctly and smoothly to the plane is a projection. Few projections in practical use are perspective.
Most of this article assumes that the surface to be mapped is that of a sphere. The <a href="/facts/Earth/HLLmDfj0">Earth</a> and other large <a href="/facts/Celestial_bodies/BCHLa0Q2">celestial bodies</a> are generally better modeled as <a href="/facts/Oblate_spheroid/GJyyLxQ7">oblate spheroids</a>, whereas small objects such as <a href="/facts/Asteroid/g7Ulr1VB">asteroids</a> often have irregular shapes. The surfaces of planetary bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid.
The most well-known map projection is the <a href="/facts/Mercator_projection/bYVL5bP9">Mercator projection</a>.: 45  This map projection has the property of being <a href="/facts/Conformal_map_projection/ExV5g5AL">conformal</a>. However, it has been criticized throughout the 20th century for enlarging regions further from the equator.: 156–157  To contrast, <a href="/facts/Equal-area_projection/KG2K7amk">equal-area projections</a> such as the <a href="/facts/Sinusoidal_projection/3k2F1qU5">Sinusoidal projection</a> and the <a href="/facts/Gall%25E2%2580%2593Peters_projection/5LD6oSL3">Gall–Peters projection</a> show the correct sizes of countries relative to each other, but distort angles. The <a href="/facts/National_Geographic_Society/mlx2uHa4">National Geographic Society</a> and most atlases favor map projections that compromise between area and angular distortion, such as the <a href="/facts/Robinson_projection/ennQXgMX">Robinson projection</a> and the <a href="/facts/Winkel_tripel_projection/lrp6vHsl">Winkel tripel projection</a>.

Map projection open-in-new

Map projection