From Riemann Manifolds to Riemann Manifolds - Map Projections: Cartographic Information Systems - page 48

Left relative angular shear: Right relative angular shear:

Q l := cos Ψ r Q r := cos Ψ l

cos Ψ l =1 . cos Ψ r =1 .

(1.152)

In the following section, we consider the equivalence theorem for conformal mapping. How-
ever, in order to give you first some breathing time, please enjoy the Stab-Werner pseudo-conic
projection that is presented in Fig. 1.21 .

Fig. 1.21. Stab-Werner pseudo-conic projection, with shorelines of a spherical earth, equidistant mapping of the
Greenwich meridian, Tissot ellipses of distortion, “cordiform mapping”. (Johannes Werner: Libellus de quatuor
terrarum orbis in plane figurationibus. Nova translativ primi libri geographiae. El. Ptolemai (Latin), Nenenberg
1514, “designed after instructions by Johann Stabius”, first map by Petrus Aqianus, World Map of Ingolstadt)

1-9 Equivalence Theorem of Conformal Mapping

“Experience proves that anyone who studied geometry is infinitely
quicker to grasp di cult subjects than one who has not.”
(Plato. The Republic Book 7, 375 B. C.)

The equivalence theorem of conformal mapping from the left to the right two-dimensional
Riemann manifold (conformemorphism), generalized Korn-Lichtenstein equations.