Response from Prof. B.

For some reason that I don not completely comprehend, I am not able to open your file for week 9 so that I can drop my comments into the end of it. If I could, I would insert a line


Prof. Banchoff's response
and that would refer to these comments. If you can get into your file and put that in, then we should be linked up.

Your comments about perspective are well taken and I hope that we will get into some good discussion about them in class this week. I too find it fascinating that there is a unique point in three- space where a viewer can stand to get the full effect of a picture in three-point perspective, but it is still true that there are group tours in most galleries, so I'm not sure how many viewers get the full effect. I do find it interesting when a gallery sets you up so that you almost automatically find yourself drawn to the right position, and I find it frustrating when the opposite happens (as it does often in the Hirschorn (sp?) Museum in Washington DC, with its curved walls.)

It is possible to make a four-point perspective view of a hypercube, but it is as difficult to imagine what it would be like to see it really as it is to think of the effect on a Flatlander of viewing a perspec- tive painting while being on the plane of the painting. I wonder if the effect, whatever it is, is more pronounced if the flat viewer is situated directly below the optimum point in three-space?

Good questions.

Prof. B.