Map Projections
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Map Projections
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, 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. More generally, projections are considered in several fields of pure mathematics, includin ...
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Claudius Ptolemy- The World
Tiberius Claudius Caesar Augustus Germanicus ( ; ; 1 August 10 BC – 13 October AD 54), or Claudius, was a Roman emperor, ruling from AD 41 to 54. A member of the Julio-Claudian dynasty, Claudius was born to Nero Claudius Drusus, Drusus and Antonia Minor at Lugdunum in Roman Gaul, where his father was stationed as a military legate. He was the first Roman emperor to be born outside Roman Italy, Italy. As he had a limp and slight deafness due to an illness he suffered when young, he was ostracized by his family and was excluded from public office until his consulship (which was shared with his nephew, Caligula, in 37). Claudius's infirmity probably saved him from the fate of many other nobles during the purges throughout the reigns of Tiberius and Caligula, as potential enemies did not see him as a serious threat. His survival led to him being declared emperor by the Praetorian Guard after Caligula's assassination, at which point he was the last adult male of his family. Despite ...
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Earth
Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all of Earth's water is contained in its global ocean, covering Water distribution on Earth, 70.8% of Earth's crust. The remaining 29.2% of Earth's crust is land, most of which is located in the form of continental landmasses within Earth's land hemisphere. Most of Earth's land is at least somewhat humid and covered by vegetation, while large Ice sheet, sheets of ice at Polar regions of Earth, Earth's polar polar desert, deserts retain more water than Earth's groundwater, lakes, rivers, and Water vapor#In Earth's atmosphere, atmospheric water combined. Earth's crust consists of slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's outer core, Earth has a liquid outer core that generates a ...
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Area
Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Two different regions may have the same area (as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area o ...
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Usgs Map Albers Equal Area Conic
The United States Geological Survey (USGS), founded as the Geological Survey, is an agency of the U.S. Department of the Interior whose work spans the disciplines of biology, geography, geology, and hydrology. The agency was founded on March 3, 1879, to study the landscape of the United States, its natural resources, and the natural hazards that threaten it. The agency also makes maps of planets and moons, based on data from U.S. space probes. The sole scientific agency of the U.S. Department of the Interior, USGS is a fact-finding research organization with no regulatory responsibility. It is headquartered in Reston, Virginia, with major offices near Lakewood, Colorado; at the Denver Federal Center; and in NASA Research Park in California. In 2009, it employed about 8,670 people. The current motto of the USGS, in use since August 1997, is "science for a changing world". The agency's previous slogan, adopted on its hundredth anniversary, was "Earth Science in the Public S ...
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Winkel Tripel Projection
The Winkel tripel projection (Winkel III), a modified azimuthal map projection of the world map, world, is one of Winkel projection, three projections proposed by German cartographer Oswald Winkel (7 January 1874 – 18 July 1953) in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection: The name (German language, German for 'triple') refers to Winkel's goal of minimizing three Map projection#Metric properties of maps, kinds of distortion: area, direction, and distance. Algorithm : \begin x &= \frac \left(\lambda \cos \varphi_1 + \frac\right), \\ y &= \frac \left(\varphi + \frac\right), \end where ''λ'' is the longitude relative to the central meridian of the projection, ''φ'' is the latitude, ''φ'' is the standard parallel for the equirectangular projection, sinc is the sinc function, unnormalized cardinal sine function, and : \alpha = \arccos\left(\cos\varphi \cos \frac \right). In his proposal, Winkel set : \varphi_1 ...
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Robinson Projection
The Robinson projection is a map projection of a world map that shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image. The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, which has used the projection in general-purpose world maps since that time. Robinson published details of the projection's construction in 1974. The National Geographic Society (NGS) began using the Robinson projection for general-purpose world maps in 1988, replacing the Van der Grinten projection. In 1998, the NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, as the latter "reduces the distortion of land masses as they near the poles". Strengths and weaknesses The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt that this pr ...
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National Geographic Society
The National Geographic Society, headquartered in Washington, D.C., United States, is one of the largest nonprofit scientific and educational organizations in the world. Founded in 1888, its interests include geography, archaeology, natural science, the promotion of environmental protection, environmental and historical preservation, historical conservation movement, conservation, and the study of civilization, world culture and World history (field), history. The National Geographic Society's logo is a yellow page orientation, portrait frame—rectangular in shape—which appears on the Margin (typography), margins surrounding the front covers of its magazines and as its television channel logo. Through National Geographic Partners (a joint venture with The Walt Disney Company), the Society operates the National Geographic, magazine, National Geographic Global Networks, TV channels, a website, worldwide events, and other media operations. Overview The National Geographic S ...
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Gall–Peters Projection
The Gall–Peters projection is a rectangular, Equal-area projection, equal-area map projection. Like all equal-area projections, it distorts most shapes. It is a cylindrical equal-area projection with latitudes 45° north and south as the regions on the map that have no distortion. The projection is named after James Gall and Arno Peters. Gall described the projection in 1855 at a science convention and published a paper on it in 1885. Peters brought the projection to a wider audience beginning in the early 1970s through his "Peters World Map". The name "Gall–Peters projection" was first used by Arthur H. Robinson in a pamphlet put out by the American Cartographic Association in 1986.American Cartographic Association's Committee on Map Projections, 1986. ''Which Map is Best'' p. 12. Falls Church: American Congress on Surveying and Mapping. The Gall–Peters projection achieved notoriety in the late 20th century as the centerpiece of a controversy about the political implication ...
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Sinusoidal Projection
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, using it in a world map in 1570. The projection represents the poles as points, as they are on the sphere, but the meridians and continents are distorted. The equator and the central meridian are the most accurate parts of the map, having no distortion at all, and the further away from those that one examines, the greater the distortion. The projection is defined by: :\begin x &= \left(\lambda - \lambda_0\right) \cos \varphi \\ y &= \varphi\,\end where \varphi is the latitude, ''λ'' is the longitude, and ''λ'' is the longitude of the central meridian. Scale is constant along the central meridian, and east–west scale is constant throughout the map. Therefore, the length of each parallel on the map is proportional to the cosine of the latitude, ...
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Equal-area Projection
In cartography, an equivalent, authalic, or equal-area projection is a map projection that preserves relative area measure between any and all map regions. Equivalent projections are widely used for thematic maps showing scenario distribution such as population, farmland distribution, forested areas, and so forth, because an equal-area map does not change apparent density of the phenomenon being mapped. By Carl Friedrich Gauss, Gauss's Theorema Egregium, an equal-area projection cannot be conformal map projection, conformal. This implies that an equal-area projection inevitably distorts shapes. Even though a point or points or a path or paths on a map might have no distortion, the greater the area of the region being mapped, the greater and more obvious the distortion of shapes inevitably becomes. Description In order for a map projection of the sphere to be equal-area, its generating formulae must meet this Cauchy-Riemann equations, Cauchy-Riemann-like condition: :\frac \cdo ...
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