SpaceCurve

A free OS X application for exploring parametric curves.
(Download, Documentation)

Features

• Full-fledged formula parser with exponential, trig, hyperbolic trig functions and their inverses
• Instantly-updating curvature and torsion calculations
• Arc length between any two points on the curve
• Draggable, resizable tangent line, moving frame, osculating plane and osculating circle.
• Draggable 3D viewpoint selection and zoom

Screenshots (click for full-size version):

Spivak

A free OS X application for exploring parametrized surfaces.
(Download Regular version, G5-Optimized version; Documentation)

Features

• Same formula parser as SpaceCurve
• Instantly-updating calculations of minimum, maximum, Gaussian, and mean curvatures
• Draggable tangent lines and tangent planes
• Geodesics at any point, in any direction
• Solid or wireframe rendering
• Draggable 3D viewpoint selection and zoom

Screenshots (click for full-size version):

Tangent plane to a torus	Geodesic on a stretched wireframe torus	Geodesic segment and principal curvatures on a pseudosphere	Tangent plane on an annular section of a saddle surface

Mathematica notebooks

	2xN-adjacency-free.nb, PDF Enumerating selections from a 2xN grid with no horizontal or vertical adjacency.
	cpanimate.nb A notebook for demonstrating how the critical point structure of a 1-parameter family of functions changes as you vary the parameter. You get an animation showing the graph of the function beside its contour map; the zero sets of the partials are color-coded, and critical points are identified, classified by the 2nd derivative test, and displayed both on the contour map and the graph of the function. Watch critical points appear, split, merge, and disappear as the parameter changes. I really like this one.
	levelsets.nb Level sets of a function of a function of two variables shown on the graph of the function and in a contour map simultaneously; step through the animation and watch the topology of the level sets change as you pass through critical heights.
	osculating3d.nb Moving frame and osculating circle animations for space curves.
	osculating2d.nb Moving frame and osculating circle animations for plane curves.

Perl

registrar.pl	Downloads my class rolls from the registrar's site into Excel-readable files.
sneeze.pl	Generates this important table of data.
arxiv-keywords.pl	Generates selective RSS feeds from the arXiv What's New page