Flattening

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is
The "compression factor" is formula_2 in each case; for the ellipse, this is also its aspect ratio.
Definitions.
There are three variants of flattening; when it is necessary to avoid confusion, the main flattening is called the first flattening. and online web texts
In the following, is the larger dimension (e.g. semimajor axis), whereas is the smaller (semiminor axis). All flattenings are zero for a circle ().
Identities.
The flattenings are related to other parameters of the ellipse. For example:
where formula_4 is the eccentricity.