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 . . .
Links
Dan
Margalit's week 9 paper.
Michael
Matthews' week 8 paper. (Nice scanned images!)
David Akers