An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P.
Jul 22, 2016
On Sets Defining Few Ordinary Circles | Discrete & Computational Geometry
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Mar 20, 2017 · An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is ...
An ordinary circle of a set $P$ of $n$ points in the plane is defined as a circle that contains exactly three points of $P$.
It is proved that if P is not contained in a line or a circle, then P spans at least at least n^2/4 - O(n) ordinary circles, and the exact minimum number of ...
Aug 24, 2012 · This paper asymptotically solves two old questions concerning finite configurations of points {P} in the plane {{\mathbb R}^2}.
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in ...
Aug 23, 2012 · We show that if n is large then there are at least n/2 ordinary lines, that is to say lines passing through exactly two points of P.
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Mar 20, 2017 · We show that if $P$ is not contained in a line or a circle, then $P$ spans at least $\frac{1}{4}n^2 - O(n)$ ordinary circles. Moreover, we ...
Our aim will be to prove a converse of this, that if the number of ordinary solids spanned by S is small then all but a few points of S are contained in the ...
Apr 24, 2020 · The well-known Sylvester-Gallai theorem asserts that if X is a finite set of points in the plane, then either X is contained in a line or there ...