“Sphere to Tangential Plane”: Polar (Normal) Aspect - Map Projections: Cartographic Information Systems - page 183

Fig. 5.1. Mapping the sphere to a tangential plane: polar aspect. Point-of-contact: North Pole. Parameters:
Λ 0 ∈ [0 ◦ , 360 ◦ ] ,Φ 0 =90 ◦

Note that the gnomonic projection is believed to has been
invented by Thales of Milet (1st half of sixth century B.C.),
the equiareal azimuthal projection has been invented by
J. H. Lambert ( 25

September 1777, Berlin), and G. Postel used the equidistant
azimuthal projection for a first map of France (1568, 1570).

∗ 26 August 1728, Muelhausen, Elsass; †

Fig. 5.2. The magic triangle: equiareal map, equidistant map, and conformal map

2 R with radius R are reviewed by its ID card. Such an ID
card is a list of (i) the embedding of the sphere S

The characteristics of the sphere S

2 R into a three-dimensional Euclidean space

{ R

3 , I 3 } which is equipped with a canonical metric (the matrix of the metric is the unit matrix,