# Constructing a Steiner Tree for Five Points

Constructing a Steiner Tree for Five Points

For a finite number of points in the plane, there is always a network of line segments connecting them with minimal total length. Finding this network is referred to as the Steiner tree problem. This optimal network can be achieved by adding some new points in the plane and connecting some of the points with line segments.

This Demonstration illustrates a construction that approximates the optimal network for five points. It works for some arrangements of the five points, but is not general enough to solve the problem in all cases. You can drag points, but sometimes a message appears that no solution is found. This does not mean that there is no optimal network; it means that the construction illustrated cannot find it.