Dimensions, a Math Movie

Abstract

Dimensions is a 2-h animated movie, aimed at a broad audience, produced by Jos Leys, Étienne Ghys and Aurélien Alvarez. The notion of "dimension" in the mathematical sense is explained in nine chapters: "Dimension 2" talks about location on a sphere and stereographic projection. "Dimension 3" explains how 2-dimensional creatures can imagine 3-dimensional objects, which is an introduction to "Dimension 4" where we show how we, as 3-dimensional creatures, can imagine 4-dimensional objects. Next is a visual introduction to complex numbers, leading in to the Hopf fibration as an example of 4-dimensional math. As an epilogue we show a formal proof of a geometric theorem related to stereographic projection. Through this film, the authors wanted to show that math does not need to be "dry", but that math can produce beautiful imagery. In order to reach as wide an audience as possible, the film is a non-profit project. The DVD has a low price, and the films can be downloaded free of charge from an internet site featuring additional information on the subjects of the film. Furthermore, the film has a "Creative Commons" license, which allows copying of the film (provided there is no commercial gain). The film is available in 8 commentary languages and 20 languages for the subtitles. © Springer-Verlag Berlin Heidelberg 2012.