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

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Overview

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This lecture examines Charles Dupin’s work on triply orthogonal surfaces and lines of curvature. It connects the Dupin indicatrix and conjugate directions to the study of surface curvature.

Syllabus

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

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Insights into Mathematics

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