Angular eccentricity
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Angular_eccentricity_and_linear_eccentricity.svg/200px-Angular_eccentricity_and_linear_eccentricity.svg.png)
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.
- ^ a b Rapp, Richard H. (1991). Geometric Geodesy, Part I, Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio.[1]
External links
- Toby Garfield's APPENDIX A: The ellipse [Archived copy].
- Map Projections for Europe (pg.116)