Aitoff projection
Encyclopedia
The Aitoff projection is a modified azimuthal map projection
. Proposed by David A. Aitoff in 1889, it is the equatorial form of the azimuthal equidistant projection
, but stretched into a 2:1 ellipse while halving the longitude from the central meridian:
where
and 
are the x and y components of the equatorial azimuthal equidistant projection. Written out explicitly, the projection is:
where
and
is the unnormalized sinc function with the discontinuity removed. In all of these formulas, 
is the longitude from the central meridian and 
is the latitude.
Three years later, Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal-area projection
in the same manner as Aitoff, producing the Hammer projection. While Hammer was careful to cite Aitoff, there has been some confusion since, wherein Aitoff has been attributed to Hammer's projection.
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
. Proposed by David A. Aitoff in 1889, it is the equatorial form of the azimuthal equidistant projection
Azimuthal equidistant projection
The azimuthal equidistant projection is a type of map projection.A useful application for this type of projection is a polar projection in which all distances measured from the center of the map along any longitudinal line are accurate; an example of a polar azimuthal equidistant projection can be...
, but stretched into a 2:1 ellipse while halving the longitude from the central meridian:
where
and are the x and y components of the equatorial azimuthal equidistant projection. Written out explicitly, the projection is:where
and
is the unnormalized sinc function with the discontinuity removed. In all of these formulas, is the longitude from the central meridian and is the latitude.Three years later, Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal-area projection
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...
in the same manner as Aitoff, producing the Hammer projection. While Hammer was careful to cite Aitoff, there has been some confusion since, wherein Aitoff has been attributed to Hammer's projection.