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**Gall isographic projection** is a specific instance of equirectangular projection such that its standard parallels are north and south 45°. The projection is named after James Gall, who presented it in 1855.

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.

Rev **James Gall** was a Scottish clergyman who founded the Carrubbers Close Mission. He was also a cartographer, publisher, sculptor, astronomer and author. In cartography he gives his name to three different map projections: Gall stereographic; Gall isographic; and Gall orthographic.

Gall–Peters projection Gall stereographic projection

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.

The **Gall stereographic projection**, presented by James Gall in 1855, is a cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection.

- Gall Isographic Projection, from Mathworks

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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 **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.

A **circle of latitude** on Earth is an abstract east–west circle connecting all locations around Earth at a given latitude.

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.

**Isabelle Geneviève Marie Anne Gall**, better known by her stage name **France Gall**, was a French *yé-yé* singer. In 1965, aged 17, she won the Eurovision Song Contest. Between 1973 and 1992, she collaborated with singer-songwriter Michel Berger.

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.

**Arno Peters** developed the Peters world map, based on the Gall–Peters projection.

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.

The **Hobo–Dyer** map projection is a cylindrical equal-area projection, with standard parallels at 37.5° north and south of the equator. The map was commissioned in 2002 by Bob Abramms and Howard Bronstein of ODT Inc., and drafted by cartographer Mick Dyer, as a modification of the 1910 Behrmann projection. The name *Hobo–Dyer* is derived from Bronstein and Abramms' first names and Dyer's surname.

In cartography, the **Lambert cylindrical equal-area projection**, or **Lambert cylindrical projection**, is a cylindrical equal-area projection. This projection is undistorted along the equator, which is its standard parallel, but distortion increases rapidly towards the poles. Like any cylindrical projection, it stretches parallels increasingly away from the equator. The poles accrue infinite distortion, becoming lines instead of points.

The **Behrmann projection** is a cylindrical map projection described by Walter Behrmann in 1910. It is a member of the cylindrical equal-area projection family. Members of the family differ by their standard parallels, which are parallels along which the projection has no distortion. In the case of the Behrmann projection, the standard parallels are 30°N and 30°S. The projection shares many characteristics with other members of the family such as the Lambert cylindrical equal-area projection, whose standard parallel is the equator, and the Gall–Peters projection, whose standard parallels are 45°N and 45°S. While equal-area, distortion of shape increases in the Behrmann projection according to distance from the standard parallels. This projection is not equidistant.

A **Klumpenhouwer Network**, named after its inventor, Canadian music theorist and former doctoral student of David Lewin's at Harvard, Henry Klumpenhouwer, is "any network that uses T and/or I operations to interpret interrelations among pcs". According to George Perle, "a Klumpenhouwer network is a chord analyzed in terms of its dyadic sums and differences," and "this kind of analysis of triadic combinations was implicit in," his "concept of the cyclic set from the beginning", cyclic sets being those "sets whose alternate elements unfold complementary cycles of a single interval."

In cartography, the **cylindrical equal-area projection** is a family of cylindrical, equal-area map projections.

* Dasineura crataegi*, the

The **Equal Earth map projection** is an equal-area pseudocylindrical projection for world maps, invented by Bojan Šavrič, Bernhard Jenny, and Tom Patterson in 2018. It is inspired by the widely used Robinson projection, but unlike the Robinson projection, retains the relative size of areas. The projection equations are simple to implement and fast to evaluate.

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