Geography/Geometry -- Visual Unity

Abstract

In 1986, an essay appeared couched in the language of projective geometry in which a theorem, linking harmonic conjugacy to perspective map projection, was proved to show the following (Harmonic Map Projection Theorem):

Centers of map projection that are geometric inverses in relation to the poles of a sphere are harmonic conjugates in the projection plane in relation to the projected images of the poles of the sphere. As a special case of the observation above, it follows that gnomonic and orthographic projections, with inverse centers of projection in the sphere, are composed of points that are harmonic conjugates of each other in the plane [Arlinghaus, 1986].