Teragon wrote:Interesting question. It would take six dimensions to depict the path as it is. In 2D and 3D the path is 2D, in 4D and 5D (double rotation) the path is already embedded in 4D. In 6D the path of the sun lies on the 6D equivalent of a Clifford torus (which has a 3D surface). Projected to 3D you can think of it as a spiral closed to a spiral closed to a circle. In reality the three planes of the three loops do not change their orientation in the course of the path. Every loop plane is entirely perpendicular to the other two planes. It must be so much more beautiful in 6D!
What I'm interested in is how the path would appear to an observer on the surface of a planet. On our Earth the path of every star appears roughly to be a circle. It appears to be a curve embedded in a 2D space.
In 4D the case where the two periods differ is the more interesting. At each pole one sees stars moving in great circles. Close to a pole it would be a helix with its axis that great circle. A 3D observer would presumably see its projection, which could be a great circle modulated by a sine wave. At the equator I'm not sure what the observed path is.
The circle modulated by a sine wave is obtainable with the 3D lissajous figures. That gave me an idea. Two of the dimensions are making a circle, so they are actually a single complex dimension. A second complex dimension would give paths on a torus. A third complex dimension perpendicular to the first two would give as good of a projection of a 6D orbit as one could hope for, I would think.