Chapter 8 • Curves on Surfaces



8.1: Natural Frames


Page 261: Darboux Frame



Page 264: Geodesic Curvature and Page 267: Geodesic Torsion



Problem 8.1.1: Curves on a Sphere




Problem 8.1.2: Cylinder Intersecting a Plane



Problem 8.1.4: Curves on a Torus





Problem 8.1.5: Curvature of Level Curves






8.2: Geodesics


Example 8.2.6: Cylinder






8.4: Gauss-Bonnet Theorem and Applications


Example 8.4.1: The Moldy Potato Chip



Example 8.4.4: The Moldy Patch



Page 307: Triangulations and Euler Characteristic






8.5: Intrinsic Geometry


Example 8.5.2: Poincaré Half-Plane





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