Like shadows, the denizens of Flatland flit about freely on the surface of their two-dimensional world. All Flatland's inhabitantsstraight lines, triangles, squares, pentagons, and other figuresare trapped in their planar geometry. They lack the power (and the imagination) to rise above or sink below the flat surface of their strictly limited realm.
That's the idea behind a remarkable book called Flatland: A Romance of Many Dimensions, written in 1884 by Edwin A. Abbott (1838–1926), the head of a school for boys in London. Conceived as a satire, this slim volume has long served as a gateway to the fourth dimension and beyond for many explorers of geometry.
Still available in a variety of editions, Flatland has attracted all sorts of attention over the years. Mathematician Thomas F. Banchoff of Brown University has looked extensively into Abbott's life and background, pursuing the question of how Abbott came to write this book. Banchoff himself provides some insights in the introduction to a Princeton University Press edition of Flatland.
Mathematician Ian Stewart of the University of Warwick produced not only an annotated edition of Flatland but also an entertaining sequel that he titled Flatterland: Like Flatland, Only More So.
Now, two teams of filmmakers have created colorful animated versions of Abbott's classic.
One production is the work of filmmakers Jeffrey Travis (director) and Seth Caplan (producer). About 30 minutes long, it features the voices of Martin Sheen (Arthur Square) and Kristen Bell (Square's granddaughter, Hex). The movie is slated to be part of an educational DVD that also includes the original text of the book, teacher notes, games, and quizzes. You can find out more about this production at http://www.flatlandthemovie.com/.
The movie will make its Mathematical Association of America debut in August at MathFest 2007 in San Jose, Calif. After the showing, Banchoff will lead a discussion about Flatland and its use in the classroom. Banchoff was on the film's advisory board, along with Jon Farley, Sarah Greenwald, and John Benson.
The second production comes from independent filmmaker Ladd Ehlinger Jr., of Huntsville, Ala. Working with Tom Whalen (writer) and Mark Slater (composer), Ehlinger created an 83-minute, wide-screen epic that fleshes out Abbott's tale into a dramatic political fable that hinges on the invasion of Flatland by three-dimensional beings. It echoes with commentary on racism, social rigidity, political manipulation, and challenges to accepted belief. For more details, including film clips and music samples, see http://www.flatlandthefilm.com/.
To be able to afford to bring his feature to film festivals and to the attention of film distributors, Ehlinger is currently selling a special "collector's edition" DVD of the production.
It'll be interesting to see what comes out of these ventures, but, whatever the result, the original Flatland is as accessible as ever—in print.
Flatland: The Movie.
Flatland: The Film.
Abbott, E.A. 2005. Flatland: A Romance of Many Dimensions, with an introduction by Thomas F. Banchoff. Princeton, N.J.: Princeton University Press.
______. 2002. The Annotated Flatland: A Romance of Many Dimensions, with introduction and notes by Ian Stewart. Cambridge, Mass.: Perseus.
______. 1992. Flatland: A Romance of Many Dimensions. Dover.
Banchoff, T.F. 1990. From Flatland to hypergraphics. Interdisciplinary Science Reviews 15(No. 4):364-372.
Peterson, I. 2000. Views from Flatland. Muse 4(October):26-27.
______. 2000. A stranger from Spaceland. MAA Online (Dec. 20).
The full text of Flatland is available at http://www.geom.uiuc.edu/~banchoff/Flatland/.