Flattening

There are three variants: the flattening f, sometimes called the first flattening, as well as two other "flattenings" f' and n, each sometimes called the second flattening, sometimes only given a symbol, or sometimes called the second flattening and third flattening, respectively. In the following, a is the larger dimension (e.g. semimajor axis), whereas b is the smaller (semiminor axis). All flattenings are zero for a circle (). :: ==Identities==

The flattenings can be related to each-other: :\begin{align} f = \frac{2n}{1 + n}, \\[5mu] n = \frac{f}{2 - f}. \end{align} The flattenings are related to other parameters of the ellipse. For example, :\begin{align} \frac ba &= 1-f = \frac{1-n}{1+n}, \\[5mu] e^2 &= 2f-f^2 = \frac{4n}{(1+n)^2}, \\[5mu] f &= 1-\sqrt{1-e^2}, \end{align} where e is the eccentricity. == See also ==