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