
Angular eccentricity is one of many parameters which arise in the study of the
ellipse or
ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...
. It is denoted here by α (alpha). It may be defined in terms of the
eccentricity
Eccentricity or eccentric may refer to:
* Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal"
Mathematics, science and technology Mathematics
* Off- center, in geometry
* Eccentricity (graph theory) of a ...
, ''e'', or the aspect ratio, ''b/a'' (the ratio of the
semi-minor axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the lon ...
and the
semi-major axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the lo ...
):
:
Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature.
Any non-dimensional parameter of the ellipse may be expressed in terms of the angular eccentricity. Such expressions are listed in the following table after the conventional definitions.
[Rapp, Richard H. (1991). ''Geometric Geodesy, Part I'', Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohi]
/ref> in terms of the semi-axes. The notation for these parameters varies. Here we follow Rapp:
::
The alternative expressions for the flattenings would guard against large cancellations in numerical work.
References
{{Reflist
External links
Toby Garfield's APPENDIX A: The ellipse
[Archived copy
/nowiki>.">rchived copy">[Archived copy
/nowiki>.br>Map Projections for Europe (pg.116)
Geodesy
Conic sections