2018/01/11 by Anastasios N. Zachos, Zachos, Anastasios N.
Engineering · #51E10 #51M04 #70B5 #70M20 #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Overview (math.HO) #Robotic Mechanisms and Dynamics #VLSI and FPGA Design Techniques
paper · pdf · doi:10.48550/arxiv.1801.08016
openalex publication_date 2018/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 solutions which may be called oscillatory Fermat-Torricelli trees. The weighted Fermat-Torricelli problem in R2 states that: Given three points in R2 and a positive real number (weight) which correspond to each point , find the point (weighted Fermat-Torricelli point) such that the sum of the weighted distances to these three points is minimized. By applying the mechanical device of Pick and Polya the oscillatory tree solution is a new solution w.r to the weighted Fermat-Torricelli problem for a given isosceles triangle with corresponding two equal weights at the vertices of the base segment. it is worth mentioning that after time t the oscillatory knot of the mechanical system passes from the weighted Fermat-Torricelli point with non zero velocity. Furthermore, we give a numerical example to verify the structure of an oscillatory Fermat-Torricelli tree for a given isosceles triangle with equal weights.