The number of halving circles

Details The number of halving circles The number of halving circles

2004-08-25

arxiv.org/abs/math/0408354v1

American Mathematical Monthly 111 (2004), 586-591

Mathematics

Combinatorics

7 pages, 3 figures

Scientific paper

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, n-1 points in its interior, and n-1 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.

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