Isogonal Conjugacy and Fermat Problems
General Mathematics
2007-08-13 v1
Abstract
We consider three types of isogonal conjugacy of two points with respect to a given triangle and characterize any of these types by a geometric equality. As an application to the Fermat problem with positive weights, we prove that in the general case the given weights determine uniquely a point X and the solution to the Fermat problem is the point Y, which is isogonally conjugate of type I to the point X. We obtain a similar characterization of the solution to the Fermat problem in the case of mixed weights as well.
Cite
@article{arxiv.0708.1374,
title = {Isogonal Conjugacy and Fermat Problems},
author = {Georgi Ganchev and Nikolai Nikolov},
journal= {arXiv preprint arXiv:0708.1374},
year = {2007}
}
Comments
11 pages, 8 figures