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 respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening is and its definition in terms of the semi-axes and of the resulting ellipse or ellipsoid is
The compression factor is in each case; for the ellipse, this is also its aspect ratio.

Definitions

There are three variants: the flattening sometimes called the first flattening, as well as two other "flattenings" and each sometimes called the second flattening, sometimes only given a symbol, or sometimes called the second flattening and third flattening, respectively.
In the following, is the larger dimension, whereas is the smaller. All flattenings are zero for a circle.

Identities

The flattenings can be related to each-other:
The flattenings are related to other parameters of the ellipse. For example,
where is the eccentricity.