The number of point-splitting circles
Combinatorics
2007-05-23 v1
Abstract
Let S be a set of 2n+1 points in the plane such that no three are collinear and no four are concyclic. A circle will be called point-splitting if it has 3 points of S on its circumference, n-1 points in its interior and n-1 in its exterior. We show the surprising property that S always has exactly n^2 point- splitting circles, and prove a more general result.
Keywords
Cite
@article{arxiv.math/0110209,
title = {The number of point-splitting circles},
author = {Federico Ardila M},
journal= {arXiv preprint arXiv:math/0110209},
year = {2007}
}
Comments
12 pages, 4 figures