Differential Geometry and Topology of Curves and Surfaces (Math 497C)
Spring 2004, Penn State
How to prove various identities involving dot product and cross products, including the three dimensional version of the Pythagorean theorem.
This notebook loads up all the miniprograms written by Alfred Gray to accompany his book on Curves and Surfaces.
Dozens of parametrizations for various curves; programs for computing curvature, length, and winding number; plotting programs for coloring a curve according to its curvature, and programs for plotting curves determined by a given curvature function; several animation programs including cycloid, tractrix and trochoids.
Dozens of parametrizations for various curves; programs for computing curvature, torsion and length; programs for coloring a curve by its curvature or torsion; programs for plotting the tangential, normal, and binormal, spherical images.
Dozens of parametrizations for various surfaces; programs for computing Gauss and mean curvature; programs for coloring a surface by its Gauss or mean curvature.