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# The Number of Halving Circles

@article{Ardila2004TheNO, title={The Number of Halving Circles}, author={Federico Ardila}, journal={The American Mathematical Monthly}, year={2004}, volume={111}, pages={586-591} }

- Published 2004 in The American Mathematical Monthly

1. INTRODUCTION. We say that a set S of 2n + 1 points in the plane is in general position if no three of the points are collinear and no four are concyclic. We call a circle halving with respect to S if it has three points of S on its circumference, n − 1 points in its interior, and n − 1 in its exterior. The goal of this paper is to prove the following surprising fact: any set of 2n + 1 points in general position in the plane has exactly n 2 halving circles. Our starting point is the following… CONTINUE READING