International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 283846, 16 pages
The Weighted Fermat Triangle Problem
Natural Sciences and Mathematics, The Richard Stockton College of New Jersey, Pomona, NJ 08240, USA
Received 29 June 2007; Accepted 13 September 2007
Academic Editor: Marco Squassina
Copyright © 2008 Yujin Shen and Juan Tolosa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We completely solve the generalized Fermat problem: given a triangle , , and
three positive numbers , , , find a point for which the sum
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.