Because the Earth's curved surface is not isometric to a plane, preservation of shapes inevitably requires a variable scale and, consequently, non-proportional presentation of areas. Map projections can be constructed to preserve some of these properties at the expense of others. Many properties can be measured on the Earth's surface independently of its geography: ДЄn Albers projection shows areas accurately, but distorts shapes. The National Geographic Society and most atlases favor map projections that compromise between area and angular distortion, such as the Robinson projection and the Winkel tripel projection. :вЂЉ156вЂ“157 To contrast, equal-area map projections such as the Sinusoidal projection and the GallвЂ“Peters projection show the correct sizes of countries relative to each other, but distort angles. :вЂЉ45 Despite its important conformal properties, it has been criticized throughout the 20th century for enlarging regions further from the equator. The best known map projection is the Mercator projection. These useful traits of maps motivate the development of map projections. ДЄ model globe does not distort surface relationships the way maps do, but maps can be more useful in many situations: they are more compact and easier to store they readily accommodate an enormous range of scales they are viewed easily on computer displays they can be measured to find properties of the region being mapped they can show larger portions of the Earth's surface at once and they are cheaper to produce and transport. Therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane. The surfaces of planetary bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid. The Earth and other large celestial bodies are generally better modeled as oblate spheroids, whereas small objects such as asteroids often have irregular shapes. Most of this article assumes that the surface to be mapped is that of a sphere. Few projections in practical use are perspective. Rather, any mathematical function that transforms coordinates from the curved surface distinctly and smoothly to the plane is a projection. However, 'map projection' refers specifically to a cartographic projection.Дespite the name's literal meaning, projection is not limited to perspective projections, such as those resulting from casting a shadow on a screen, or the rectilinear image produced by a pinhole camera on a flat film plate. Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. There is no limit to the number of possible map projections. The study of map projections is primarily about the characterization of their distortions.

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.

ДЄll projections of a sphere on a plane necessarily distort the surface in some way and to some extent. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane. In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. A medieval depiction of the Ecumene (1482, Johannes Schnitzer, engraver), constructed after the coordinates in Ptolemy's Geography and using his second map projection

Perspective grid mapping