The number of point-splitting circles

Details The number of point-splitting circles The number of point-splitting circles

2001-10-18

arxiv.org/abs/math/0110209v1

Mathematics

Combinatorics

12 pages, 4 figures

Scientific paper

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.

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