The Weighted Fermat Triangle Problem. (8th October 2007) - Shen, Yujin
Abstract : We completely solve the generalized Fermat problem : given a triangleP 1, P 2, P 3 and three positive numbersλ 1, λ 2, λ 3, find a pointP for which the sumλ 1 P 1 P + λ 2 P 2 P + λ 3 P 3 P is minimal. We show that the point always exists and is unique, and indicate necessary and sufficient conditions for the point to lie inside the triangle. We provide geometric interpretations of the conditions and briefly indicate a connection with dynamical systems.