Points defining triangles with distinct circumradii
Metric Geometry
2015-10-13 v1 Computational Geometry
Abstract
Paul Erdos asked if, among sufficiently many points in general position, there are always points such that all the circles through of these points have different radii. He later proved that this is indeed the case. However, he overlooked a non-trivial case in his proof. In this note we deal with this case using B\'ezout's Theorem on the number of intersection points of two curves and obtain a polynomial bound for the needed number of points.
Cite
@article{arxiv.1402.6276,
title = {Points defining triangles with distinct circumradii},
author = {Leonardo Martínez and Edgardo Roldán-Pensado},
journal= {arXiv preprint arXiv:1402.6276},
year = {2015}
}