Editing Latitude (section)

===The geometry of the ellipsoid===
[[File:Ellipsoid parametric euler mono.svg|thumb|A sphere of radius ''a'' compressed along the ''z'' axis to form an oblate ellipsoid of revolution.]]

The shape of an ellipsoid of revolution is determined by the shape of the [[ellipse]] which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the [[ellipse|semi-major axis]], {{mvar|a}}. The other parameter is usually (1)&nbsp;the polar radius or [[ellipse|semi-minor axis]], {{mvar|b}}; or (2)&nbsp;the (first) [[flattening]], {{mvar|f}}; or (3)&nbsp;the [[ellipse|eccentricity]], {{mvar|e}}. These parameters are not independent: they are related by

:<math>f=\frac{a-b}{a}, \qquad e^2=2f-f^2,\qquad b=a(1-f)=a\sqrt{1-e^2}\,.</math>
Many other parameters (see [[ellipse]], [[ellipsoid]]) appear in the study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set {{mvar|a}}, {{mvar|b}}, {{mvar|f}} and {{mvar|e}}. Both {{mvar|f}} and {{mvar|e}} are small and often appear in series expansions in calculations; they are of the order {{sfrac|1|298}} and 0.0818 respectively. Values for a number of ellipsoids are given in [[Figure of the Earth]]. Reference ellipsoids are usually defined by the semi-major axis and the ''inverse'' flattening, {{math|{{sfrac|1|''f''}}}}. For example, the defining values for the [[WGS84]] ellipsoid, used by all GPS devices, are<ref>{{cite web|author=National Imagery and Mapping Agency|url=https://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf|title=Department of Defense World Geodetic System 1984|date=23 June 2004|publisher=National Imagery and Mapping Agency|id=TR8350.2 |page=3{{hyphen}}1|access-date=25 April 2020|df=dmy}}</ref>
* {{mvar|a}} (equatorial radius): {{val|6378137.0|u=m}} exactly
* {{math|{{sfrac|1|''f''}}}} (inverse flattening): {{val|298.257223563}} exactly
from which are derived
* {{mvar|b}} (polar radius): {{val|6356752.31425|u=m}}
* {{math|''e''<sup>2</sup>}} (eccentricity squared): {{val|0.00669437999014}}
The difference between the semi-major and semi-minor axes is about {{convert|21|km|0|abbr=in}} and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from a 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening.