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


figure8-63




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