The number of halving circles
Abstract
A set S of 2n+1 points in the plane is said to be in general position if no three points of S are collinear and no four are concyclic. A circle is called halving with respect to S if it has three points of S on its circumference, n1 points in its interior, and n1 in its exterior. We prove the following surprising result: any set of 2n+1 points in general position in the plane has exactly n^2 halving circles.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2004
 arXiv:
 arXiv:math/0408354
 Bibcode:
 2004math......8354A
 Keywords:

 Combinatorics;
 Metric Geometry;
 52C35;
 05A15
 EPrint:
 7 pages, 3 figures