Explore the geometry of curves and surfaces through 34 interactive demonstrations featuring curvature-colored surfaces, animated geodesics, and parallel transport visualizations.
See also: Linear Algebra for tangent spaces as vector spaces, Topology for manifolds as smooth topological spaces, and Relativity for curved spacetime as a pseudo-Riemannian manifold.
Explore space curves, curvature, torsion, and moving frames
Define and explore surfaces through parametrization
Measure lengths, angles, and areas on surfaces
Capture how surfaces curve in space
The two fundamental curvature measures with stunning color-coded visualizations
The extremal curvatures and their directions
The shortest paths along curved surfaces with animated particle tracing
Moving vectors along curves and the geometry of loops
Surfaces that minimize area - soap films and beyond
Gauss's remarkable theorem about intrinsic curvature