The **Albers equal-area conic projection**, or **Albers projection** (named after Heinrich C. Albers), is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.

The Albers projection is used by the United States Geological Survey and the United States Census Bureau.^{ [1] } Most of the maps in the * National Atlas of the United States * use the Albers projection.^{ [2] } It is also one of the standard projections used by the government of British Columbia,^{ [3] } and the sole governmental projection for the Yukon.^{ [4] }

Snyder^{ [5] } describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a spherical datum can be transformed into Albers equal-area conic projection coordinates with the following formulas, where is the radius, is the longitude, the reference longitude, the latitude, the reference latitude and and the standard parallels:

where

In mathematics, a **spherical coordinate system** is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the *radial distance* of that point from a fixed origin, its *polar angle* measured from a fixed zenith direction, and the *azimuthal angle* of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system.

A **cardioid** is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse curve of the parabola with the focus as the center of inversion.

The use of **orthographic projection in cartography** dates back to antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The *point of perspective* for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges.

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 **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.

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 **Bottomley map projection** is an equal area map projection defined as:

In cartography, a **Tissot's indicatrix** is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.

The **multiple integral** is a definite integral of a function of more than one real variable, for example, *f*(*x*, *y*) or *f*(*x*, *y*, *z*). Integrals of a function of two variables over a region in **R**^{2} are called **double integrals**, and integrals of a function of three variables over a region of **R**^{3} are called **triple integrals**. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.

A **Lambert conformal conic projection** (**LCC**) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication *Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten*.

**Cylindrical multipole moments** are the coefficients in a series expansion of a potential that varies logarithmically with the distance to a source, i.e., as . Such potentials arise in the electric potential of long line charges, and the analogous sources for the magnetic potential and gravitational potential.

The **van der Grinten projection** is a compromise map projection, which means that it is neither equal-area nor conformal. Unlike perspective projections, the van der Grinten projection is an arbitrary geometric construction on the plane. Van der Grinten projects the entire Earth into a circle. It largely preserves the familiar shapes of the Mercator projection while modestly reducing Mercator's distortion. Polar regions are subject to extreme distortion.

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.

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

In optics, the **Fraunhofer diffraction equation** is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.

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. In 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 IV is the Eckert III projection.

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.

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.

The **Strebe 1995 projection**, **Strebe projection**, **Strebe lenticular equal-area projection**, or **Strebe equal-area polyconic projection** is an equal-area map projection presented by Daniel "daan" Strebe in 1994. Strebe designed the projection to keep all areas proportionally correct in size; to push as much of the inevitable distortion as feasible away from the continental masses and into the Pacific Ocean; to keep a familiar equatorial orientation; and to do all this without slicing up the map.

The **Eckert-Greifendorff projection** is an equal-area map projection described by Max Eckert-Greifendorff in 1935. Unlike his previous six projections, It is not pseudocylindrical.

- ↑ "Projection Reference". Bill Rankin. Archived from the original on 25 April 2009. Retrieved 2009-03-31.
- ↑ Snyder, John P. (1987).
*Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395*. Washington, D.C.: United States Government Printing Office. p. 2. - ↑
- ↑ "Support & Info: Common Questions".
*Geomatics Yukon*. Government of Yukon. Retrieved 15 October 2014. - ↑ Snyder, John P. (1987). "Chapter 14: ALBERS EQUAL-AREA CONIC PROJECTION".
*Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395*. Washington, D.C.: United States Government Printing Office. p. 100.

Wikimedia Commons has media related to . Albers projection |

- Mathworld's page on the Albers projection
- Table of examples and properties of all common projections, from radicalcartography.net
- An interactive Java Applet to study the metric deformations of the Albers Projection.

This cartography or mapping term article is a stub. You can help Wikipedia by expanding it. |

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.