# MATHEMATICA PACKAGES

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Differential Geometry and Topology of Curves and Surfaces (Math 497C)

Spring 2004, Penn State

- CrossProducts.nb

How to prove various identities involving dot product and cross products, including the three dimensional version of the Pythagorean theorem.

- GraysProgs.nb

This notebook loads up all the miniprograms written by Alfred Gray to accompany his book on Curves and Surfaces.

- PlanarCurves.nb

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.

- SpaceCurves.nb

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.

- Surfaces.nb

Dozens of parametrizations for various surfaces; programs for computing Gauss and mean curvature; programs for coloring a surface by its Gauss or mean curvature.