I found his chapter very difficult. Perhaps I didn't put in enough effort. I w as confused on many of the topics, such as geometric acoustics and geometric optics, differential topology and "horn cyclides". The film we saw at the art club helped the visualization of the ellipses and circles collapsing in on themselves and then moving outward again. I am still very unclear on what the meaning of the two interlocking tori is.

I did have a question on finding the dimensionality from the number of coordinates a figure has. If the screen saver ellipse (which you made reference to one day in class) is four dimensional because of its position on the 2D screen and the length of its major and minor axis, then this is my question: what if there were a screen saver which had a four sided figure which grew and shrank and had side lengths of x, 2x, 3x and 4x? Would that then be six dimensional? No, actually I guess it would only be three dimensional because youÕd only have to figure out x and the other two coordinates. But, is there some 2D figure that need three parts of information to create it in different sizes? hmmmmm, I guess thatÕs it.

Oh, I found something interesting using the diagram on the bottom of page 144. If you draw humans standing upright on the horizontal plane so that the plane seems to be extending towards you from the top to the bottom, it makes for a confusing perspective situation. I feel like I'm in a DeChirico painting.

Prof. Banchoff's Response