Open any atlas of world maps and you will see the adjectives
"conformal", "equal area", and "equidistant". What is the mathematics
behind these terms? Can undergraduate students understand the math?
In this presentation, we will discuss an interdisciplinary
math/geography course that addressed these questions. The course,
designed and taught by myself and the late Dr. Elaine F. Bosowski
at Villanova University, was powered by our belief that an exploration
of the mathematical ideas involved in creating and analyzing
maps would show students how mathematics could help them to understand and
explain their world. At the same time, by actually creating maps of
their own, students could develop the skills needed to accurately
evaluate the quality of graphic images they encounter on a
routine basis. In the class, the students explored the shape of the earth, the
determination of latitude and longitude, elementary spherical geometry,
the uses and computation of scale factors, the design of optimal routes
for air or sea navigation, Gaussian curvature, the reasons why we can't
make a perfect flat map of the earth, how to evaluate from a critical
and analytical viewpoint maps that we encounter every day, and
how to design atlas maps using both hand-drawn techniques and computer
graphics software. Since Dr. Bosowski's untimely death in 1998,
variants of this course have been taught in a
distance-learning format and as a senior mathematics seminar.
The talk will also demonstrate how mathematical notions such as conformal
mappings and Gaussian curvature can be introduced and explained at an
elementary level.