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 and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is

The compression factor in each case; for the ellipse, this is also its aspect ratio.

Definitions

sometimes called the first flattening, each sometimes called the second flattening, sometimes only given a symbol, or sometimes called the second flattening and third flattening, respectively.

is the smaller (semiminor axis). All flattenings are zero for a circle ().

1. {| class="wikitable"

| style="padding-left: 0.5em " | Fundamental. Geodetic reference ellipsoids | style="padding-left: 0.5em" | Used in geodetic calculations as a small expansion parameter. |}

Identities

The flattenings can be related to each-other:

The flattenings are related to other parameters of the ellipse. For example,

is the eccentricity.

See also

• Earth flattening

• Equatorial bulge

• Ovality

• Planetary flattening

• Sphericity

• Roundness (object)

References