Jung's theorem

The set of Jung ( named after Heinrich Jung) makes a statement about how big does a ball in a -dimensional space that includes a predetermined amount of points.

Formulation

It had finally been many points, and it is the maximum Euclidean distance between two points.

The set of Jung says that there is a -dimensional sphere with a radius such that all points lie within the sphere ( the boundary included).

Furthermore, the center of the sphere with the smallest possible radius is uniquely determined.

Special case of a plane

Best known is the case of points in the plane, that is,. In this case, the set of Young states that the radius.

For the three corners of an equilateral triangle is exactly needed this radius.