Overview
Description
Geometry of curves and surfaces in space; Frenet’s formulas; Cartan’s frame fields, Gaussian curvature; intrinsic geometry of surface; congruence of surfaces; the Gauss-Bonnet theorem.
Units
Lecture3
Catalog Details
Offering
Offered: Every Fall - Odd Years
Terms
fall
Attributes
Standard
Learning Outcomes
- analyze the intrinsic geometry of curves in space, such as arclength and curvature.
- analyze the intrinsic geometry of surfaces in space, such as surface area, Gaussian curvature.
- determine whether two surfaces cannot be related by an isometric bijection, due to different intrinsic geometry.
- use the Gauss-Bonnet theorem to relate the geometry of an oriented surface without boundary to its topology.