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Angular eccentricity
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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.
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