Chapter 8 • The Gauss-Bonnet Theorem and Geometry of Geodesics

8.1: Natural Frames

Page 275: The Darboux Frame

Page 278: Geodesic Curvature and Page 282: 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

Problem 8.1.9: Tube of a Curve on a Surface

8.2: Gauss-Bonnet Theorem, Local Form

Example 8.2.1: The Moldy Potato Chip

Example 8.2.6: The Moldy Patch

Page 297: Triangulations and Euler Characteristic

8.4: Geodesics

Example 8.4.7: Cylinder

8.6: Applications to Plane, Spherical, and Elliptical Geometry

p.337: Sum of Angles of a Triangle on a Sphere

8.7: Hyperbolic Geometry

Subsection 8.7.2: Poincaré Half-Plane

p.346: Sum of Angles of a Triangle (in the Poincaré Half-Plane)

Subsection 8.7.3: Poincaré Disk

Problem 8.7.8: Poincaré Half-Plane and the Pseudosphere


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