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An characterization of the vertices of tetrahedra in the three dimensional Euclidean Space
Anastasios Zachos
We determine a positive real number (weight), which corresponds to a vertex of a tetrahedron and it depends on the three weights which correspond to the other three vertices and an…
An -characterization of a vertex formed by two non-overlapping geodesic arcs on surfaces with constant Gaussian curvature
Anastasios Zachos
We determine a positive real number (weight) which corresponds to the intersection point (vertex) of two non-overlapping geodesic arcs, which depends on the two weights which corre…
The twist angle of weighted Steiner minimal trees in the three dimensional Euclidean Space
Anastasios Zachos
We find the equations that allow us to compute the position of the two interior nodes (weighted Fermat-Torricelli points) w.r. to the weighted Steiner problem for four points deter…
A generalization of Pythagoras on a surface
Anastasios Zachos
We analyze Toponogov's sine theorem for an infinitesimal geodesic triangle ABC on a C^2 regular surface M, which is given in his book [6, Problem 3.7.2] and we provide a generaliza…
A generalized Fermat-Torricelli tree that has acquired a subconscious on a surface
Anastasios Zachos
We study a generalized Fermat-Torricelli (S.FT) problem for infinitesimal geodesic triangles on a C^2 complete surface M with variable Gaussian curvature a < K < b, for a, b in R,…
Some minimum networks for four points in the three dimensional Euclidean Space
Anastasios Zachos
We construct a minimum tree for some boundary symmetric tetrahedra R^3, which has two nodes (interior points) with equal weights (positive numbers) having the property that the com…