Videos

You can find all my videos on YouTube, including the videos I made for my Calculus MOOCs; many of my videos are also on iTunes U.

Animations

Möbius strip as a configuration space

A Möbius strip can be regarded as the configuration space of pairs of (indistinguishable!) points on a circle.

Percolation

A dot is drawn at a random location; if it does not overlap any previous dots, it gets a new color. Otherwise, the dot takes the color of the component it touches. Sometimes a new dot connects many components, and in this case, the new component takes on the color of the largest among the old components.

After drawing dots, how many components should we expect to see? When you draw only a few dots, most of those dots are isolated and have their own color; but after drawing a ridiculously large number of dots, they are all connected and the same color.

Reflecting triangles in the plane

Start with a triangle in the plane; reflect that triangle across its three sides; repeat, reflecting the resulting triangles through their sides, over and over again.

Observe how, for only four shapes of triangles, the resulting set of triangle vertices is discrete. You can watch the same thing with more triangles.