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Julie Strandberg is a choreographer and a teacher at Brown University who incorporates dimensionality into her compositions and her teaching. In her 20 minute dance Dimensions, she has her performers experience the limitations of movement in two dimensions. One dancer is sprung into a higher dimension, to enjoy the freedom of three-dimensional space. The exhilaration tempts her to try to go on to four dimensions and higher. The attempt is too much, and the protagonist is forced to return to the plane, overcome with the sadness of loss.
You can view a slide record of the crucial scenes from the Dimensions dance. There also are some dimensional exercises that explore the dimensionality of dance.
Julie Strandberg is the Executive Director of the American Dance Legacy Institute, dedicated to preserving the legacy of dance in America.
Here is an introductory site about the notation used to record and preserve dance. Mathematics can be used to describe modern dance movements, or any kind of movement in general. See also this historical and pictorial introduction to the history of dance movement.
For another site about dance in America, see the National Museum of Dance. A site that provides images of moves from classical ballet is at the American Ballet Theatre.