Gauss's View of Curvature and the Theorema Egregium - Differential Geometry Lecture 35
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The lecture examines Gauss’s view of curvature through the Gauss–Rodrigues map and its expression using the fundamental forms, including a paraboloid example. It also connects curvature on smooth surfaces with a discrete analog for polyhedra and discusses the Gauss–Bonnet theorem.
Syllabus
Introduction
Overview
Gauss-Rodrigues map
Computation to justify the view
Paraboloid is a normal level surface
Curvature of a curve fit
Smooth DG-discrete DG
Vertex of a polyhedron
Computations
Taught by
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