2 citations · 7 across the 20 of their papers we have counts for
22 papers
Platonic geodesic trees in the Space
Anastasios N. Zachos
In this paper, We prove that: (A) If there exists a Platonic geodesic tree having edges (geodesic segments), which form platonic angles with measure and…
A class of explicit solutions for the Fermat problem for tetrahedra
Anastasios N. Zachos
We present a class of explicit solutions for the problem of minimization of the function which gives the locati…
When do Fermat constants completely determine Clairaut constants for branching geodesics on a surface of revolution?
Anastasios N. Zachos
We prove that Fermat constants do not completely determine Clairaut constants for three branching geodesics that meet at the weighted Fermat-Torricelli point on a surface of revolu…
D'Alembert-Lagrange principle for point masses yields a system of weighted balancing unit vectors in the three dimensional Euclidean Space
Anastasios N. Zachos
In this paper, we prove that D'Alembert-Lagrange principle for point masses using Lagrange-Mach's mechanical construction yields a weighted balancing condition of unit vectors in $…
A fundamental property of the Fermat-Torricelli point for tetrahedra in the three dimensional Euclidean Space
Anastasios N. Zachos
We prove the following fundamental property for the Fermat-Torricelli point for four non-collinear and non-coplanar points forming a tetrahedron in which states t…
Isometric embedding of a weighted Fermat-Frechet multitree for isoperimetric deformations of the boundary of a simplex to a Frechet multisimplex in the -Space
Anastasios N. Zachos
In this paper, we study the weighted Fermat-Frechet problem for a tuple of positive real numbers determining -simplexes in the dimensional -Space (…
A Lagrangian program detecting the Weighted Fermat-Steiner-Frechet multitree for a Frechet multisimplex in the dimensional Euclidean Space
Anastasios N. Zachos
In this paper, we introduce the Fermat-Steiner-Frechet problem for a given tuple of positive real numbers determining the edge lengths of an simplex in $\mat…
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…
An oscillatory Fermat-Torricelli tree in R^2
Anastasios N. Zachos
We obtain an important generalization of the mechanical solution given by S. Gueron and R. Tessler w.r. to the weighted Fermat-Torricelli problem which derives a new structure of s…
The plasticity of non-overlapping convex sets in R^{2}
Anastasios Zachos
We study a generalization of the weighted Fermat-Torricelli problem in the plane, which is derived by replacing vertices of a convex polygon by 'small' closed convex curves with we…
The plasticity of some mass transportation networks in the three dimensional Euclidean Space
Anastasios Zachos
We obtain an important generalization of the inverse weighted Fermat-Torricelli problem for tetrahedra in R^3 by assigning at the corresponding weighted Fermat-Torricelli point a r…
Solving a problem of angiogenesis of degree three
Anastasios N. Zachos
An absorbing weighted Fermat-Torricelli tree of degree four is a weighted Fermat-Torricelli tree of degree four which is derived as a limiting tree structure from a generalized Gau…
An analytical solution of the weighted Fermat-Torricelli problem on the unit sphere
Anastasios N. Zachos
We obtain an analytical solution for the weighted Fermat-Torricelli problem for an equilateral geodesic triangle A_1A_2A_3 which is composed by three equal geodesic arcs (sides) of…
Analytical solution of the weighted Fermat-Torricelli problem for tetrahedra: The case of two pairs of equal weights
Anastasios N. Zachos
The weighted Fermat-Torricelli problem for four non-collinear and non-coplanar points in the three dimensional Euclidean Space states that: Given four non-collinear and non-coplana…
Two new analytical solutions and two new geometrical solutions for the weighted Fermat-Torricelli problem in the Euclidean plane
Anastasios N. Zachos
We obtain two analytic solutions for the weighted Fermat-Torricelli problem in the Euclidean Plane which states that: Given three points in the Euclidean plane and a positive real…
Analytical solution of the weighted Fermat-Torricelli problem for convex quadrilaterals in the Euclidean plane: The case of two pairs of equal weights
Anastasios N. Zachos
The weighted Fermat-Torricelli problem for four non-collinear points in R^2 states that: Given four non-collinear points A_1, A_2, A_3,A_4 and a positive real number (weight) B_i w…
A plasticity principle of convex quadrilaterals on a convex surface of bounded specific curvature
Anastasios Zachos
We derive the plasticity equations for convex quadrilaterals on a complete convex surface with bounded specific curvature and prove a plasticity principle which states that: Given…