The number of pointsplitting circles
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 pointsplitting if it has 3 points of S on its circumference, n1 points in its interior and n1 in its exterior. We show the surprising property that S always has exactly n^2 point splitting circles, and prove a more general result.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110209
 Bibcode:
 2001math.....10209A
 Keywords:

 Combinatorics;
 52C99;
 05A99
 EPrint:
 12 pages, 4 figures