# Beyond 3-D, Chapter 4

## David Akers

The chapter's discussion of "shadows" reminded me of a question I was once
asked by a math professor: What shape does one get if one spins a die on a
vertex very fast, looking at this die from the side as it spins? In
answering this question you have to think about the 2-dimensional
projection of this rotating die. . And obtain something like this:

/\
/ \
/ \
\ /
/ \
\ /
\ /
\/

Why does the middle of the die have such indentations? Well, if you
look at the cube while it is sitting symetrically on a vertex, three of
its verteces are above the center of the cube, and the other three are
below this center. Because of this, we visualize the rotation in this
strange way. My questions are: a) How does the image of the rotating cube
change as our viewpoint changes? b) What mathematical techniques can be
used to generate such rotation images? c) Could this rotation analogy be
applied to the fourth dimension?

David Akers