# Angular eccentricity

**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.

## References

- Haswell, Charles Haynes (1920).
*Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas*. Harper & Brothers. Retrieved 2007-04-09. - Rapp, Richard H. (1991).
*Geometric Geodesy, Part I*, Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio.