Not long ago I watched the DVD of Flatland staring Martin Sheen as the voice of Arthur Square. The movie is based on Edwin Abbott Abbott’s 1884 book of the same title. Flatland is a story of polygons living in a two dimensional world and A. Square’s discovery of the third dimension. It is also a social satire about the class structure in Victorian society. The movie was very well done, and I highly recommend it.

Inspired by my viewing of Flatland, I thought I would post a few more dimension-related videos for your viewing pleasure.

Second feature: an old video of Carl Sagan discussing dimension and Flatland.

Third feature: a 2-hour video called “Dimensions.” It is available in several languages and is free to download. Here is the preview:

Fourth feature: the Geometry Center put together a beautiful video called “Outside in” (under the direction of Silvio Levy, Delle Maxwell and Tamara Munzner). “Outside In” explains and illustrates the process of sphere eversion. It is based on the theorem proved by Steve Smale (my academic grandfather) that if we are allowed to pass a sphere through itself, then it is possible to turn it inside out without creating any creases in the sphere. The video is available online in two parts:

Edwin O'Shea (on HOM listserv): Fundamental Theorem of Calc Textbooks—the nth edition of any calc text converges to Stewart as n gets large. 7 hours ago