Editing Latitude (section)

===Numerical comparison of auxiliary latitudes===
[[File:Auxiliary Latitudes Difference.svg|inline|right|frameless]]
The plot to the right shows the difference between the geodetic latitude and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles) for the case of the WGS84 ellipsoid. The differences shown on the plot are in arc minutes. 
In the Northern hemisphere (positive latitudes), ''θ'' ≤ ''χ'' ≤ ''μ'' ≤ ''ξ'' ≤ ''β'' ≤ ''ϕ''; in the Southern hemisphere (negative latitudes), the inequalities are reversed, with equality at the equator and the poles. Although the graph appears symmetric about 45°, the minima of the curves actually lie between 45° 2′ and 45° 6′. Some representative data points are given in the table below. The conformal and geocentric latitudes are nearly indistinguishable, a fact that was exploited in the days of hand calculators to expedite the construction of map projections.<ref name=snyder/>{{rp|108}}

To first order in the flattening ''f'', the auxiliary latitudes can be expressed as
''ζ'' = ''ϕ'' − ''Cf'' sin 2''ϕ''
where the constant ''C'' takes on the values
[{{frac|2}}, {{frac|2|3}}, {{frac|3|4}}, 1, 1]
for
''ζ'' = [''β'', ''ξ'', ''μ'', ''χ'', ''θ''].

{| class="wikitable" style="margin: 1em auto 1em auto; text-align:right;" 
|+ Approximate difference from geodetic latitude ({{mvar|ϕ}})
! {{mvar|ϕ}}
! Parametric<br />{{math|''β'' − ''ϕ''}}
! Authalic<br />{{math|''ξ'' − ''ϕ''}}
! Rectifying<br />{{math|''μ'' − ''ϕ''}}
! Conformal<br />{{math|''χ'' − ''ϕ''}}
! Geocentric<br />{{math|''θ'' − ''ϕ''}}
|-
|  0°||  0.00′ ||  0.00′ ||  0.00′ ||   0.00′ ||   0.00′
|-
| 15°|| −2.88′ || −3.84′ || −4.32′ ||  −5.76′ ||  −5.76′
|-
| 30°|| −5.00′ || −6.66′ || −7.49′ ||  −9.98′ ||  −9.98′
|-
| 45°|| −5.77′ || −7.70′ || −8.66′ || −11.54′ || −11.55′
|-
| 60°|| −5.00′ || −6.67′ || −7.51′ || −10.01′ || −10.02′
|-
| 75°|| −2.89′ || −3.86′ || −4.34′ ||  −5.78′ ||  −5.79′
|-
| 90°||  0.00′ ||  0.00′ ||  0.00′ ||   0.00′ ||   0.00′
|}
{{clear}}