4 papers
Minimal Perimeter Triangle in Nonconvex Quadrangle: Generalized Fagnano Problem
Triloki Nath, Manohar Choudhary
In 1775, Fagnano introduced the following geometric optimization problem: inscribe a triangle of minimal perimeter in a given acute-angled triangle. A widely accessible solution is…
A Generalized Heron-Waist Problem: Optimality Conditions and Convergence Analysis
Manohar Choudhary, Triloki Nath, Ram K. Pandey
This paper introduces and solves the Generalized Heron-Waist Problem (GHWP), that integrates the classical Heron problem of optimal hub location and the waist problem of minimal-pe…
A Generalized Heron Problem:Optimality Conditions and Algorithm
Triloki Nath, Manohar Choudhary, Ram K. Pandey
This paper presents a new extension of the classical Heron problem, termed the generalized -Heron problem, which seeks an optimal configuration among feasible and ta…
A Generalized Waist Problem: Optimality Condition and Algorithm
Triloki Nath, Manohar Choudhary, Ram K. Pandey
Many years ago John Tyrell a lecturer at King's college London challenged his Ph.D. students with the following puzzle: show that there is a unique triangle of minimal perimeter wi…