Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It may be defined in terms of the eccentricity, e, or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis):
Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature. [1]
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. [2] in terms of the semi-axes. The notation for these parameters varies. Here we follow Rapp: [2]
(first) eccentricity | ||||
second eccentricity | ||||
third eccentricity | ||||
(first) flattening | ||||
second flattening | ||||
third flattening |
The alternative expressions for the flattenings would guard against large cancellations in numerical work.