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The **Goode homolosine projection** (or **interrupted Goode homolosine projection**) is a pseudocylindrical, equal-area, composite map projection used for world maps. Normally it is presented with multiple interruptions. Its equal-area property makes it useful for presenting spatial distribution of phenomena.

The projection was developed in 1923 by John Paul Goode to provide an alternative to the Mercator projection for portraying global areal relationships. Goode offered variations of the interruption scheme for emphasizing the world’s land and the world’s oceans. Some variants include extensions that repeat regions in two different lobes of the interrupted map in order to show Greenland or eastern Russia undivided. The homolosine evolved from Goode’s 1916 experiments in interrupting the Mollweide projection.^{ [1] }

Because the Mollweide is sometimes called the "homolographic projection", Goode fused the two names "homolographic" and "sinusoidal" to create the name "homolosine".^{ [2] } Common in the 1960s, the Goode homolosine projection is often called an "orange-peel map" because of its resemblance to the flattened rind of a hand-peeled orange. In its most common form, the map interrupts the North Atlantic, the South Atlantic, the South Pacific, the Indian Ocean, and the entire east/west meridian of the map.

Up to latitudes 40°44′11.8″N/S, the map is projected according to the sinusoidal projection’s transformation. The higher latitudes are the top sections of a Mollweide projection, grafted to the sinusoidal midsection where the scale of the two projections matches. This grafting results in a kink in the meridians along the parallel of the graft. The projection’s equal-area property follows from the fact that its source projections are themselves both equal-area.

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 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 become 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 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. 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. Every distinct map projection distorts in a distinct way, by definition. The study of map projections is the characterization of these distortions. There is no limit to the number of possible map projections. 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.

The **Mollweide projection** is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the **Babinet projection**, **homalographic projection**, **homolographic projection**, and **elliptical projection**. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.

**John Paul Goode**, a geographer and cartographer, was one of the key geographers in American geography’s Incipient Period from 1900 to 1940. Goode was born in Stewartville, Minnesota on November 21, 1862. Goode received his bachelor's degree from the University of Minnesota 1889 and his doctorate in economics from the University of Pennsylvania in 1903. Later on in 1903, he was offered a position as a professor in the Geography Department at the University of Chicago.

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 **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 **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, appearing in a world map of 1570.

The **Bonne projection** is a pseudoconical equal-area map projection, sometimes called a **dépôt de la guerre**, **modified Flamsteed**, or a **Sylvanus** projection. Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter’s usages were approximate, however, and it is not clear they intended to be the same projection.

The **Aitoff projection** is a modified azimuthal map projection proposed by David A. Aitoff in 1889. Based on the equatorial form of the azimuthal equidistant projection, Aitoff first halves longitudes, then projects according to the azimuthal equidistant, and then stretches the result horizontally into a 2:1 ellipse to compensate for having halved the longitudes. Expressed simply:

The **Hammer projection** is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide.

The **Tobler hyperelliptical projection** is a family of equal-area pseudocylindrical projections that may be used for world maps. Waldo R. Tobler introduced the construction in 1973 as the *hyperelliptical* projection, now usually known as the Tobler hyperelliptical projection.

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

The **Waterman "Butterfly" World Map** is a map arrangement created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a globe treated as a truncated octahedron, evoking the *butterfly map* principle first developed by Bernard J.S. Cahill (1866–1944) in 1909. Cahill and Waterman maps can be shown in various profiles, typically linked at the north Pacific or north Atlantic oceans.

The **Eckert projections** are six pseudocylindrical map projections devised by Max Eckert-Greifendorff, who presented them in 1906. The latitudes are parallel lines in all six projections. The projections come in pairs; in the odd-numbered projections, the latitudes are equally spaced, while their even-numbered counterparts are equal-area.

The **Boggs eumorphic projection** is a pseudocylindrical, equal-area map projection used for world maps. Normally it is presented with multiple interruptions. Its equal-area property makes it useful for presenting spatial distribution of phenomena. The projection was developed in 1929 by Samuel Whittemore Boggs (1889–1954) to provide an alternative to the Mercator projection for portraying global areal relationships. Boggs was geographer for the United States Department of State from 1924 until his death. The Boggs eumorphic projection has been used occasionally in textbooks and atlases.

In map projections, an **interruption** is any place where the globe has been split. All map projections are interrupted at at least one point. Typical world maps are interrupted along an entire meridian. In that typical case, the interruption forms an east/west boundary, even though the globe has no boundaries.

In map projection, **equal-area maps** preserve area measure, generally distorting shapes in order to do that. Equal-area maps are also called **equivalent** or **authalic**.

- ↑ Snyder, John Parr (1993).
*Flattening the earth : two thousand years of map projections*. Chicago: University of Chicago Press. pp. 167–168. ISBN 9780226767475. OCLC 26764604. - ↑ Monmonier, Mark S. (2015).
*Mapping It Out: Expository Cartography for the Humanities and Social Sciences*. University of Chicago Press. p. 40. ISBN 9780226217857. OCLC 905918505.

- Goode, J.P. (1925). "The Homolosine projection – a new device for portraying the Earth's surface entire".
*Annals of the Association of American Geographers*.**15**(3): 119–125. doi:10.2307/2560812. JSTOR 2560812. - Susan., Schulten (2001).
*The geographical imagination in America, 1880–1950*. Chicago: University of Chicago Press. ISBN 9780226740553. OCLC 44578714.

- Table of examples and properties of all common projections, from radicalcartography.net.
- Non-interrupted Goode Homolosine example (PDF)

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