5-2 Special mapping equations 173
N
S
r
T N S
2
R
P
p
O
∆
2
=
π
4
−
Φ
2
Fig. 5.8. Spherical vertical section, equiareal mapping of the sphere to the tangential plane at the North Pole,
azimuthal projection.
Historical
aside.
The geometric construction to be considered here may have motivated J. H. Lambert (1772)
to invent such an equiareal mapping of the sphere. Due to the postulate of an equiareal
mapping, the equiareal azimuthal projection of the sphere is very popular in Geostatistics.
In order to complete the considerations, we present to you Fig. 5.9, which shows a sample of the polar
equiareal projection of the sphere.
Fig. 5.9. Equiareal map of the sphere S
2
R onto the tangent space T N S
2
R , Tissot ellipses, polar aspect, graticule
15
◦ , shorelines.
N
S
r
T N S
2
R
P
p
O
∆
2
=
π
4
−
Φ
2
Fig. 5.8. Spherical vertical section, equiareal mapping of the sphere to the tangential plane at the North Pole,
azimuthal projection.
Historical
aside.
The geometric construction to be considered here may have motivated J. H. Lambert (1772)
to invent such an equiareal mapping of the sphere. Due to the postulate of an equiareal
mapping, the equiareal azimuthal projection of the sphere is very popular in Geostatistics.
In order to complete the considerations, we present to you Fig. 5.9, which shows a sample of the polar
equiareal projection of the sphere.
Fig. 5.9. Equiareal map of the sphere S
2
R onto the tangent space T N S
2
R , Tissot ellipses, polar aspect, graticule
15
◦ , shorelines.