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.
The position of a sphere refers to its location in three-dimensional space, usually described by its coordinates or distance from a reference point.
The coordinates of a sphere can vary depending on the reference system used. In a Cartesian coordinate system, the coordinates are typically given as (x,y,z) where x is the horizontal position, y is the vertical position, and z is the depth or distance from the reference point.
The center of a sphere is located at the midpoint of its diameter, which can be found by measuring the distance between any two points on the surface of the sphere and dividing it by two.
The radius of a sphere is the distance from its center to any point on its surface. It can be calculated using the Pythagorean theorem or by measuring the diameter and dividing it by two.
To convert between different coordinate systems for a sphere, you can use mathematical equations or transformation matrices specific to each system. Alternatively, there are online conversion tools available that can do the calculations for you.