Orlando Meetings: Presentation Summary

Back to Orlando: College Standards

This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 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); Gauss-Bonnet Theorem for polygons on surfaces of constant curvature; generalized Gauss-Bonnet Theorem; Euler characteristic; Gauss-Bonnet formula; higher dimensions; and the universe. This is a hands-on 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

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