Torricelli's Construction

Evangelista Torricelli developed the following method to find a Steiner point in a triangles where all interior angles are less than 120˚.

SHORTEST DISTANCE BETWEEN 3 POINTS

CASE 1: If the three points form a triangle such that one of the angles is equal to or greater than 120˚, then the minimum network connecting the three points will be the two shortest sides of the triangle a.k.a. the minimum spanning tree of the triangle.

CASE 2: If the three points form a triangle such that all three angles are less than 120˚, then the minimum network will be a network that uses an interior junction point called a Steiner Point.