On the Number of Ordinary Circles Determined by n Points.

In this paper we deal with the following problem: Given a set B consisting of n points, not all on a line or a circle. A circle passes through exactly three points of B is called an ordinary circle. What is the minimal possible number of ordinary circles determined by B? In this paper we improve the best-known lower bound $\frac{22}{247}{n\choose2}$ to $\frac{1}{9}{n\choose2}$. [ABSTRACT FROM AUTHOR]