The discussion revolves around determining the number of coordinates required to specify all possible positions of a sphere, including considerations of rotation and the presence of distinguished points on the sphere's surface.
Several participants have offered different perspectives on the number of coordinates needed, suggesting that the context (distinguished points, radius) significantly influences the answer. The discussion is ongoing with multiple interpretations being explored.
There is a focus on whether the sphere is defined with specific points or is a generic sphere, as well as the implications of assuming a unit sphere for the discussion.
HallsofIvy said:Are there distinguished points on the sphere? And is the sphere of given radius?
If there are distinguished point on the sphere- that is, if you can distinguish one point from another (as on a globe of the earth), then you would require 5 coordinates: three to determine the center of the sphere, two angles to determine the rotations of the sphere in space.
If there are no distinguished points, if, say, the surface of the sphere is blank, then you would need three coordinates, to determine the center of the sphere. The rotations are irrelevant.
That is assuming that you are talking about a given sphere, with given radius. If you mean determine any (blank) sphere, then you will need four coordinates: three to determine the center of the sphere and one to determine the radius.