The Spacetime Wheel

This is a wheel.

Each successive image in the movie is rotated by a small amount compared to the previous image.

As the wheel rotates, the coordinates (x, y) of a point on the wheel relative to its centre change, but the distance r between the point and the centre remains constant

r² = x² + y² = constant .

More generally, the coordinates (x, y, z) of the interval between any two points in 3-dimensional space (a vector) change when the coordinate system is rotated in 3 dimensions, but the separation r of the two points remains constant

r² = x² + y² + z² = constant .