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The **two-point equidistant projection** is a map projection first described by Hans Maurer in 1919. It is a generalization of the much simpler azimuthal equidistant projection. In this two-point form, two locus points are chosen by the mapmaker to configure the projection. Distances from the two loci to any other point on the map are correct: that is, they scale to the distances of the same points on the sphere.

A **map projection** is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane. Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. 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. There is no limit to the number of possible map projections.

The **azimuthal equidistant projection** is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.

In geometry, a **locus** is a set of all points, whose location satisfies or is determined by one or more specified conditions.

The projection has been used for all maps of the Asian continent by the National Geographic Society atlases since 1959,^{ [1] } though its purpose in that case was to reduce distortion throughout Asia rather than to measure from the two loci.^{ [2] } The projection sometimes appears in maps of air routes. The Chamberlin trimetric projection is a logical extension of the two-point idea to three points, but the three-point case only yields a sort of minimum error for distances from the three loci, rather than yielding correct distances. Tobler extended this idea to arbitrarily large number of loci by using automated root-mean-square minimization techniques rather than using closed-form formulae.^{[ citation needed ]}

The **National Geographic Society** (**NGS**), headquartered in Washington, D.C., United States, is one of the largest non-profit scientific and educational organizations in the world. Founded in 1888, its interests include geography, archaeology, and natural science, the promotion of environmental and historical conservation, and the study of world culture and history. The National Geographic Society's logo is a yellow portrait frame—rectangular in shape—which appears on the margins surrounding the front covers of its magazines and as its television channel logo. Through National Geographic Partners, the Society operates the magazine, TV channels, a website, worldwide events, and other media operations.

The **Chamberlin trimetric projection** is a map projection where three points are fixed on the globe and the points on the sphere are mapped onto a plane by triangulation. It was developed in 1946 by Wellman Chamberlin for the National Geographic Society. Chamberlin was chief cartographer for the Society from 1964 to 1971. The projection's principal feature is that it compromises between distortions of area, direction, and distance. A Chamberlin trimetric map therefore gives an excellent overall sense of the region being mapped. Many National Geographic Society maps of single continents use this projection.

In mathematics and its applications, the **root mean square** is defined as the square root of the mean square . The RMS is also known as the **quadratic mean** and is a particular case of the generalized mean with exponent 2. RMS can also be defined for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle.

The **Gall–Peters projection** is a rectangular map projection that maps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes. The projection is a particular example of the cylindrical equal-area projection with latitudes 45° north and south as the regions on the map that have no distortion.

In geography, **latitude** is a geographic coordinate that specifies the north–south position of a point on the Earth's surface. Latitude is an angle which ranges from 0° at the Equator to 90° at the poles. Lines of constant latitude, or *parallels*, run east–west as circles parallel to the equator. Latitude is used together with longitude to specify the precise location of features on the surface of the Earth. On its own, the term latitude should be taken to be the *geodetic latitude* as defined below. Briefly, geodetic latitude at a point is the angle formed by the vector perpendicular to the ellipsoidal surface from that point, and the equatorial plane. Also defined are six *auxiliary latitudes* which are used in special applications.

The **Mercator projection** is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because of its unique property of representing any course of constant bearing as a straight segment. Such a course, known as a rhumb or, mathematically, a loxodrome, is preferred by navigators because the ship can sail in a constant compass direction to reach its destination, eliminating difficult and error-prone course corrections. Linear scale is constant on the Mercator in every direction around any point, thus preserving the angles and the shapes of small objects and fulfilling the conditions of a conformal map projection. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation starts infinitesimally but accelerates with latitude to reach infinite at the poles. So, for example, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.

A **geographic coordinate system** is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector. A common choice of coordinates is latitude, longitude and elevation. To specify a location on a plane requires a map projection.

The **Dymaxion map** or **Fuller map** is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes.

In astronomy, a **planisphere** is a star chart analog computing instrument in the form of two adjustable disks that rotate on a common pivot. It can be adjusted to display the visible stars for any time and date. It is an instrument to assist in learning how to recognize stars and constellations. The astrolabe, an instrument that has its origins in Hellenistic astronomy, is a predecessor of the modern planisphere. The term *planisphere* contrasts with *armillary sphere*, where the celestial sphere is represented by a three-dimensional framework of rings.

A **world map** is a map of most or all of the surface of the Earth. World maps form a distinctive category of maps due to the problem of projection. Maps by necessity distort the presentation of the earth's surface. These distortions reach extremes in a world map. The many ways of projecting the earth reflect diverse technical and aesthetic goals for world maps.

In geometry, **focuses** or **foci**, singular **focus**, are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian oval, and more than two foci are used in defining an n-ellipse.

The **scale** of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways. The first way is the ratio of the size of the **generating globe** to the size of the Earth. The generating globe is a conceptual model to which the Earth is shrunk and from which the map is projected.

In demographics, the **centre of population** of a region is a geographical point that describes a centrepoint of the region's population. There are several different ways of defining such a "centre point", leading to different geographical locations; these are often confused.

The **equirectangular projection** is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, and circles of latitude to horizontal straight lines of constant spacing. The projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.

The earliest known world maps date to classical antiquity, the oldest examples of the 6th to 5th centuries BCE still based on the flat Earth paradigm. World maps assuming a spherical Earth first appear in the Hellenistic period. The developments of Greek geography during this time, notably by Eratosthenes and Posidonius culminated in the Roman era, with Ptolemy's world map, which would remain authoritative throughout the Middle Ages.

The **General Perspective projection** is a map projection. When the Earth is photographed from space, the camera records the view as a perspective projection. When the camera is aimed toward the center of the Earth, the resulting projection is called Vertical Perspective. When aimed in other directions, the resulting projection is called a Tilted Perspective.

**Afro-Eurasia** is a landmass which comprises the continents of Africa and Eurasia. The terms are portmanteaus of the names of its constituent parts. Its mainland is the largest contiguous landmass on Earth.

The **equidistant conic projection** is a conic map projection known since Classical times, Ptolemy's first projection being derived from it.

- ↑ Snyder, J.P. (1993).
*Flattening the Earth: 2,000 years of map projections*. pp. 234–235. ISBN 0226767469. - ↑ "Portrait of Earth's largest continent",
*National Geographic Magazine*, vol. 116 no. 6, p. 751, 1959

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