Prof Banchoff--some questions. This chapter was interesting, but raised some questions for me as to the usefulness of fourth dimensional graphing. Although theoretically a stage technician or a dancer may be working with higher dimensional concepts, how do four dimensional shapes and graphs come in handy for them? Could a dancer, for example, discover all possible configuration spaces for a body in a plane, or in space, using higher dimensional coordinates?

You mention that the speed of light uses other units that make it "special" and non applicable to Euclidean geometry? Also the atomic structure. Are there other examples of "special" units and what makes them this way? Are they just different in higher dimensional geometry, or are they different in one and two dimensional geometry as well?

Why is the hyperbolic paraboloid "familiar" to architects? Certainly it is not used for any structural purpose, as it doesn't look very sturdy. On that note, are there many architects who employ higher dimensional concepts in their creations? Who would they be?

Do you have any films of the waves? The static representations are hard to visualize. In the pictures, I cannot imagine the movement and translation of the colors.

Another question: my friend at the art high school came up this weekend. I have been corresponding with her about this class, and she in turn went to her teacher, who became very excited and wants to communicate with you. Is this okay? Can I give him your email number? If you remember, he is a high school math teacher at an art school, teaching higher dimensional math and fractals in an art context, as you are (excluding the fractals.)