# 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?