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Figure 10.9 Join B to the opposing pole (stereographic center of projection) and label
the point of intersection of the sphere and the line as the point P. The point P proj-
ects to B under the transformation of stereographic projection. Source: Arlinghaus,
S. L. 2007. Geometery/Geography—Visual Unity. Solstice: An Electronic Journal
of Geography and Mathematics. Volume XVIII, No. 2. Ann Arbor: Institute of
solstice/win07/hyperbolicgeometry.html
for other centers of projection within the sphere and their counterparts out-
side the sphere. Thus, the entire unbounded class of perspective projections
becomes bounded and subject to its own principle of duality. The infinite and
unbounded set of centers of projection is now completely characterized as the
bounded set within the sphere.
In the next section, you will have the opportunity to practice the concepts
that have been discussed. Beginning with the geographic analysis of a world
population data set, you will consider selected map projection issues from this
chapter, but also keep in mind themes that have permeated this entire book,
including data sources and scale.
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