Differential Geometry: Meusnier, Monge, and Dupin's Work on Surfaces - Lecture 33

Explore the work of Charles Dupin and his contributions to differential geometry in this 55-minute lecture. Delve into triply orthogonal surfaces, lines of curvatures, and confocal families of ellipses and hyperbolas. Learn about conjugate directions on surfaces, the Dupin indicatrix, and its relation to normal approximating paraboloids for defining and computing curvatures. Examine topics such as lines of curvature on ellipsoids, quadric surfaces, tangent planes, and theorems of confocal systems. Gain insights into Dupin's theory, his use of the indicatrix as a visual indicator, and the concept of conjugate directions dating back to Apollonius. Conclude with a special case problem to reinforce understanding of these advanced geometric concepts.

Introduction
Overview
Lines of curvature of an Ellipsoid
Consider quadrics of the form_
Tangent plane at P
Theorem of a confocal system
Dupin theory
Why Dupin used the indicatrix as a visual indicator
Conjugate directions Back to Apollonius
Prob- For a special case