Beyond 3-D: Chapter Six

Lisa Hicks

Dali's idea for a 30-kilometer horse is fascinating. In the chapter, it says that, with computer graphics, we can see what it would look like. Has anyone designed a program for this, and, if so, can we look at it in class? I'd love to see that. I also liked the idea of an architect designing buildings and changing things around by computer. One of my favorite books is The Fountainhead (yes, I should italicize it, but I don't know how italics will work in HTML), and there is a scene in it where the main character, an architect, is using clay to visualize his prospective building. Having him tapping away at a computer might lose some of the romance, but it's so much more high-tech.

In this chapter, it is harder to find projects for lower-level students. Most of the things I'm thinking of (programs to show Dali's horse, for instance) would require more computer literacy than most middle-schoolers have. For particularly artistically talented students, creating a stereographic projection of something--the world, a tennis ball (I'd love to see this), whatever--would be a possible project. A human head isn't really spherical, but would it still work as a stereographic projection?

The projections of the Clifford torus and the explanations that went with them sort of startled me. I had always thought that the image on the cover of our book was a view of the inside of some 4-D figure, not the outside. Thinking of it as an external view is a little disorienting.

I don't understand how the grid forms a polyhedral torus.

I had never noticed before that the central projection of the hypercube and the polyhedral torus look pretty much the same in three-space if you fill in the correct sides.

Is there any etymological significance to "tesseract," or did Hinton just think it sounded cool?

I really enjoyed this chapter. It made me wish I had a stronger programming background. I'm looking forward to the next chapter.

Prof. Banchoff's Response