The **Robinson projection** is a map projection of a world map which 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.^{ [1] }

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.^{ [2] } In 1998 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".^{ [3] }^{ [4] }

The Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt that this produced a better overall view than could be achieved by adhering to either. The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points.^{ [1] }

Hence, distortion close to the poles is severe but quickly declines to moderate levels moving away from them. The straight parallels imply severe angular distortion at the high latitudes toward the outer edges of the map – a fault inherent in any pseudocylindrical projection. However, at the time it was developed, the projection effectively met Rand McNally's goal to produce appealing depictions of the entire world.^{ [5] }^{ [6] }

I decided to go about it backward. … I started with a kind of artistic approach. I visualized the best-looking shapes and sizes. I worked with the variables until it got to the point where, if I changed one of them, it didn't get any better. Then I figured out the mathematical formula to produce that effect. Most mapmakers start with the mathematics.

The projection is defined by the table:^{ [7] }^{ [8] }^{ [9] }

Latitude *X**Y*0° 1.0000 0.0000 5° 0.9986 0.0620 10° 0.9954 0.1240 15° 0.9900 0.1860 20° 0.9822 0.2480 25° 0.9730 0.3100 30° 0.9600 0.3720 35° 0.9427 0.4340 40° 0.9216 0.4958 45° 0.8962 0.5571 50° 0.8679 0.6176 55° 0.8350 0.6769 60° 0.7986 0.7346 65° 0.7597 0.7903 70° 0.7186 0.8435 75° 0.6732 0.8936 80° 0.6213 0.9394 85° 0.5722 0.9761 90° 0.5322 1.0000

The table is indexed by latitude at 5-degree intervals; intermediate values are calculated using interpolation. Robinson did not specify any particular interpolation method, but it is reported that he used Aitken interpolation himself.^{ [10] } The *X* column is the ratio of the length of the parallel to the length of the equator; the *Y* column can be multiplied by 0.2536^{ [11] } to obtain the ratio of the distance of that parallel from the equator to the length of the equator.^{ [7] }^{ [9] }

Coordinates of points on a map are computed as follows:^{ [7] }^{ [9] }

where *R* is the radius of the globe at the scale of the map, *λ* is the longitude of the point to plot, and *λ _{0}* is the central meridian chosen for the map (both

Simple consequences of these formulas are:

- With
*x*computed as constant multiplier to the meridian across the entire parallel, meridians of longitude are thus equally spaced along the parallel. - With
*y*having no dependency on longitude, parallels are straight horizontal lines.

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 **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 in marine navigation because ships can sail in a constant compass direction for long stretches, reducing the difficult, error-prone course corrections that otherwise would be needed frequently when sailing other kinds of courses. 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 is very small near the equator but accelerates with increasing 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 **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.

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. 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 **transverse Mercator** map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.

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.

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.

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 **Winkel tripel projection**, a modified azimuthal map projection of the world, is one of three projections proposed by German cartographer Oswald Winkel in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection: The name *tripel* refers to Winkel's goal of minimizing three kinds of distortion: area, direction, and distance.

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 **Kavrayskiy VII projection** is a map projection invented by Soviet cartographer Vladimir V. Kavrayskiy in 1939 for use as a general-purpose pseudocylindrical projection. Like the Robinson projection, it is a compromise intended to produce good-quality maps with low distortion overall. It scores well in that respect compared to other popular projections, such as the Winkel tripel, despite straight, evenly spaced parallels and a simple formulation. Regardless, it has not been widely used outside the former Soviet Union.

**Wagner VI** is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of ^{}⁄_{}. This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s equator to any meridian.

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

The **Eckert IV projection** is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, meridians are the same whereas parallels differ. Odd-numbered projections have parallels spaced equally, whereas even-numbered projections have parallels spaced to preserve area. Eckert IV is paired with Eckert III.

The **Eckert II projection** is an equal-area pseudocylindrical map projection. In the equatorial aspect the network of longitude and latitude lines consists solely of straight lines, and the outer boundary has the distinctive shape of an elongated hexagon. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert II is the Eckert I projection.

The **central cylindrical projection** is a perspective cylindrical map projection. It corresponds to projecting the Earth's surface onto a cylinder tangent to the equator as if from a light source at Earth's center. The cylinder is then cut along one of the projected meridians and unrolled into a flat map.

The **natural Earth projection** is a pseudocylindrical map projection designed by Tom Patterson and introduced in 2012. It is neither conformal nor equal-area.

- 1 2 3 John Noble Wilford (October 25, 1988). "The Impossible Quest for the Perfect Map".
*The New York Times*. Retrieved 1 May 2012. - ↑ Snyder, John P. (1993).
*Flattening the Earth: 2000 Years of Map Projections*. University of Chicago Press. p. 214. ISBN 0226767469. - ↑ "National Geographic Maps – Wall Maps – World Classic (Enlarged)". National Geographic Society. Retrieved 2019-02-17.
This map features the Winkel Tripel projection to reduce distortion of land masses as they near the poles.

- ↑ "Selecting a Map Projection". National Geographic Society. Retrieved 2019-02-17.
- ↑ Myrna Oliver (November 17, 2004). "Arthur H. Robinson, 89; Cartographer Hailed for Map's Elliptical Design".
*Los Angeles Times*. Retrieved 1 May 2012. - ↑ New York Times News Service (November 16, 2004). "Arthur H. Robinson, 89 Geographer improved world map".
*Chicago Tribune*. Retrieved 1 May 2012. - 1 2 3 Ipbuker, C. (July 2005). "A Computational Approach to the Robinson Projection".
*Survey Review*.**38**(297): 204–217. doi:10.1179/sre.2005.38.297.204 . Retrieved 2019-02-17. - ↑ "Table for Constructing the Robinson Projection". RadicalCartography.net. Retrieved 2019-02-17.
- 1 2 3 Snyder, John P.; Voxland, Philip M. (1989). "An Album of Map Projections". (PDF). U.S. Geological Survey Professional Paper 1453. Washington, D.C.: U.S. Government Printing Office. pp. 82–83, 222–223. doi:10.3133/pp1453 http://pubs.usgs.gov/pp/1453/report.pdf . Retrieved 2019-02-18.Missing or empty
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(help) - ↑ Richardson, R. T. (1989). "Area deformation on the Robinson projection".
*The American Cartographer*.**16**(4): 294–296. doi:10.1559/152304089783813936. - ↑ From the formulas below, this can be calculated as .

- Arthur H. Robinson (1974). "A New Map Projection: Its Development and Characteristics". In:
*International Yearbook of Cartography*. Vol 14, 1974, pp. 145–155. - John B. Garver Jr. (1988). "New Perspective on the World". In:
*National Geographic*, December 1988, pp. 911–913. - John P. Snyder (1993).
*Flattening The Earth—2000 Years of Map Projections*, The University of Chicago Press. pp. 214–216.

Wikimedia Commons has media related to . Maps with Robinson projection |

- Table of examples and properties of all common projections, from radicalcartography.net
- Numerical evaluation of the Robinson projection, from Cartography and Geographic Information Science, April, 2004 by Cengizhan Ipbuker

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