Tags
Topology
Nov 11, 2021
Differential Geometry
62 min readDifferential Geometry (6): Smooth Manifolds — Geometry Beyond Embedded Surfaces
Manifolds free geometry from ambient space — charts, atlases, and smooth structure let us do calculus on spaces that don't live in R^n.
Nov 9, 2021
Differential Geometry
62 min readDifferential Geometry (5): The Gauss-Bonnet Theorem — Where Geometry Meets Topology
The Gauss-Bonnet theorem connects total Gaussian curvature to the Euler characteristic — a stunning bridge between local differential geometry and global topology.