Another applet demonstrates parallel transport on spheres by letting the user drag a tangent vector around.
I also supervised the construction of a number of other applets for the EggMath project at UIUC, demonstrating for instance the Ham Sandwich Theorem.
A newer applet (2003) demonstrates the tight clasp, a topic of my joint research with Jason Cantarella, Joe Fu, Rob Kunser and Nancy Wrinkle.
I have versions of these applets, modified to use the new Java 1.2 API, but they don't seem to work with Microsoft's IE unless you install Sun's JRE. (Why not just consider upgrading to Mozilla?)
They are here: stereographic projection and parallel transport.