The Eckert-Greifendorff projection is an equal-area

map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...

described by

Max Eckert-Greifendorff Max Eckert (after 1934, Max Eckert-Greifendorff: 10 April 1868 in Chemnitz, Kingdom of Saxony – 26 December 1938, in Aachen) was a German geographer. Biography He received his education in Löbau and Berlin, and taught for some time at Löba ...

in 1935. Unlike his previous six projections, it is not pseudocylindrical.

Development

Directly inspired by the

Hammer projection 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 ...

, Eckert-Greifendorff suggested the use of the equatorial form of the

Lambert azimuthal equal-area projection The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, but it does not accurately represent angles. It is named for the Swiss mathematician Johan ...

instead of Aitoff's use of the

azimuthal equidistant projection 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 azimut ...

: :

\begin x &= 2\operatorname_x\left(\frac, \varphi\right) \\
y &= \tfrac12 \operatorname_y\left(\frac, \varphi\right) \end

where laea and laea are the ''x'' and ''y'' components of the equatorial Lambert azimuthal equal-area projection. Written out explicitly: :

\begin x &= \frac \\
y &= \frac \end

The inverse is calculated with the intermediate variable :

z \equiv \sqrt

The longitude and latitudes can then be calculated by :

\begin
\lambda &= 4 \arctan \frac \\
\varphi &= \arcsin zy
\end

where ''λ'' is the

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...

from the central meridian and ''φ'' is the

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north po ...

.Weisstein, Eric W
"Hammer–Aitoff Equal-Area Projection." From MathWorld—A Wolfram Web Resource
/ref>

References

{{Map projections Map projections Equal-area projections

Development

See also

References