Beyond 3-D, Chapter 6

David Akers

Perspective Illusions

When I first looked at the picture of the 5-cell on page 118, I interpreted it incorrectly. I saw the "middle point" of the tetrahedron as being a fourth vertex on the base of the figure, and wondered why that funny line divided the base. Of course, I was able to see it the correct way when I read the caption, but without this caption the image is ambiguous. The lines from the far left and far right vertices appear to be vanishing to the middle point, which makes the middle point seem farther away than all the others.

It actually reminded me of an amazing illusion I encountered as part of a Psychology 3 lab last semester. Here's how it worked: A two dimensional projection of a cube (about 2 feet per side) was modeled using wood. After we had established the illusion of three dimensions, we were instructed to close one eye and then move around the room while still looking at the two dimensional projection. The illusion of a three dimensional cube could be maintained the whole time, with strange effects on perception. Everything looked okay, but the rotation was not correct. Since the cube was not actually three dimensional, the rotation which we perceived was somehow backwards. I'm still not exactly sure how to explain it, but I thought it was an interesting demonstration of the way the mind perceives depth.

Prof. Banchoff's response.

More on rotating figures

I've updated my page on rotations, having added all of the regular 3-d polyhedra. Check it out if you're curious. I guess since I've run out of 3-D polyhedra to spin, I'll have to move on to 4-d figures now. If I only knew what I was doing . . .


Dan Margalit's week 9 paper.

Michael Matthews' week 8 paper. (Nice scanned images!)

David Akers