Steiner point

Meanings

1. One vertex of a Steiner tree.
2. An extra vertex that is not a member of the input.
3. The point on the circumcircle of a triangle that lies at the intersection of three lines through the vertices of the triangle, where those lines are parallel to the corresponding sides of the first Brocard triangle.
4. The geometric centroid of the system obtained by placing a mass equal to the magnitude of the exterior angle at each vertex of the system.
5. Any of the 20 points located at the 3 by 3 intersections of the 60 Pascal lines which are produced by extending the triplets on opposite sides of a conic section in Pascal's theorem for all permutations of verices.

Etymology

Named after Jakob Steiner.