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math.GT2023
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…
math.GM2023
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 $…
math.MG2023
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…