Speaker: TONY JACOBS (University of North Texas)

Title: 3D Curves: Tangent Lines, Planes, and Beyond!

Abstract: This talk is a presentation of an 1880 paper by Hermann Schwarz, a German mathematician whose work is frequently encountered in the study of functions of real and complex numbers, as well as in linear algebra. We will use basic calculus (derivatives) to describe the behavior of curves in 3-dimensional space, approximating these curves' locations by using lines, planes and spheres. Our main tool for doing this will be a generalization of the Mean Value Theorem of elementary calculus.

The presentation will be illustrated with some flashy animated graphs, and should be accessible to anyone familiar with derivatives of real-valued functions, and some elementary matrix and vector operations. To anyone not versed in these things, I encourage you to give it a shot anyway; many of the ideas are accessible to anyone with eyes and some openness to the potential beauty of mathematics.