Steiner point = bc / (b2 − c2) : ca / (c2 − a2) : ab / (a2 − b2) = the nonvertex point of intersection of the circumcircle with the Steiner ellipse.
It is also possible to formulate a version of the point set or polygon triangulation problems in which one is allowed to add Steiner points, extra vertices, in order to reduce the total edge length of the resulting triangulations.
The Fermat point of a triangle, the solution to the Steiner tree problem for the three vertices of the triangle
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Steiner tree problem, an algorithmic problem of finding extra "Steiner" points to add to a point set to reduce the cost of connecting the points
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