Write about the history of map projection
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Answer:
Map projections appeared more than two millennia ago, when ancient Greek scientists started applying mathematical principles to studying and representing the celestial sphere. Hundreds of map projections have been invented since. There is no limit to the number of possible map projections and their usefulness motivates scientists to develop new ones. Map projections have recently been developed to represent planets or asteroids which are too irregular to be modelled with a sphere or a rotational ellipsoid. In general, map projections are a field of mathematics, just like differential or projective geometry. Few map projections are based on perspective, while all other are some sort of mapping a continuous curved surface into a plane. Famous mathematician Leonhard Euler provided the first proof that a sphere’s surface can not be mapped onto a plane without distortion in 1777. Considering each map projection includes certain distortion, map projection theory primarily deals with researching map projection distortions. Most map projections can not be interpreted in a simple geometrical or physical manner and they are defined by mathematical formulae. Each map projection provides an image distorted in a different way. Studying map projections yields those distortions’ characteristics. Therefore, a cartographer should apply a map projection according to desired and arbitrary properties or conditions. Map projections have developed concurrently with development of map production and cartography in general. This chapter provides a brief overview of map projection development from their beginnings to the present days, mentioning famous names such as Gerhard Mercator, Johann Heinrich Lambert, Carl Friedrich Gauß, Nicolas Auguste Tissot, John Parr Snyder and many others.
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Explanation:
In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane.[1] All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. 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 the characterization of the distortions. There is no limit to the number of possible map projections.[2]:1 Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. However, "map projection" refers specifically to a cartographic projection.
Despite 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. 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.[citation needed]
Most of this article assumes that the surface to be mapped is that of a sphere. The Earth and other large celestial bodies are generally better modeled as oblate spheroids, whereas small objects such as asteroids 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.[3] Therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane.[citation needed]
A 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. These useful traits of maps motivate the development of map projections.
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