Internet-based differential geometry of surfaces in three and four-space
by
Thomas Banchoff
Brown University, USA

Plenary Lecture

Recent advances in computer graphics make it possible to revisit classical topics and to use enhanced visualization techniques to deduce new theorems. As an example, nineteenth century Laguerre Geometry, which represents oriented spheres in n-space as points in (n+1)-space, has modern applications in singularity theory, conformal geometry, total absolute curvature, and robotic motion. This presentation will feature examples from the work of Alfred Gray on the geometry of tubes and cyclides of Dupin, including new results on focal varieties of cyclides and self-linking numbers of torus knots on the 3-sphere.

Date received: June 7, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-12.