- In the case of a segment , a circle , a sphere or in general an n-dimensional sphere , the center point is the point that has the same (minimum) distance from all points of this sphere . This definition can generally be made in (complete) metric spaces .
- In the case of conic sections and the second-order surfaces described by quadrics (e.g. ellipsoids or cones ), the center points are the fixed elements of a reflection , which transforms the given figure into itself. All conic sections with the exception of the parabolas have exactly one center; a surface of the second order can have no, exactly one or a whole straight line or plane of centers. If it has exactly one center, it is referred to as a center quadric.
Description by coordinates
Is the end point and the starting point of a route is known, it can be the coordinates of the center point on the relationships , or in addition at a distance in space with determined.
Circle / sphere
If a circular equation of the form is given, the coordinates of the center point can be specified directly via . In a ball, the equation is added to the Z-axis: . The center is thus .
- Grotemeyer, KP: Analytical Geometry, Berlin: Göschen / de Gruyter Collection (4th edition 1969)