This is the summary of a presentation given at the Joint Mathematics
Meetings, January 1013, 1996, Orlando, Florida.
Explorations in Geometry:
A Course for the Liberal Arts
Using materials developed under an NSF grant awarded to Mount
Holyoke College, a terminal course in geometry is taught for majors in the
humanities and social sciences divisions at Lewis & Clark College. The
only prerequisite is high school algebra. Topics covered include:
geodesics, distances, circles, and disks on surfaces; curvature; surfaces
of constant curvature (plane, cylinders, spheres, and hyperbolic planes);
GaussBonnet Theorem for polygons on surfaces of constant curvature;
generalized GaussBonnet Theorem; Euler characteristic; GaussBonnet
formula; higher dimensions; and the universe. This is a handson course
with extensive use of models, e.g., globes and balls for spheres; cans and
cardboard tubes for cylinders; inner tubes for tori; paper models of
hyperbolic planes; stretched string and rubber bands for geodesic arcs;
etc. Students learn how mathematics evolves from vague ideas and
imprecise terminology into rigorous definitions and theorems. Mathematics
is a language  and so much more! This course is especially beneficial to
students who are more talented at visualization than at algebraic
manipulations. Similar materials have been used in a course at Mount
Holyoke College to attract students to minor or major in mathematics.
Gregory A. Fredricks, Lewis & Clark College
