Rotation of a square
Click on this picture to see a movie of two segments
rotating in four dimensions.
These segments are opposite sides of
a square.
Click on this picture to see a movie of a square
rotating in four dimensions.
This square extends in the Y and Z directions only,
so it still looks like a point in the X_W_plane.
The square can be looked at as two segments, joined at
the ends.
You can look at these two segments
individually, by going back to the 2 segments.
Up till now, the rotations we've been seeing
look sort of like normal rotations,
with the object viewed edge on. For example,
if we imagine a planet orbiting the sun
and we look at it from the side (not from
above), from very far away,
the planet may look like its just going
back and forth along a line. But
the square extends
in the y and z directions, and its rotation
involves the x and w directions, so the
animation seen in the X_Y_Z_hyperplane
is not simply a 3d rotation viewed from
a particular angle.
Rotation of a cube
Olaf Holt 3/14/94