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On the Number of Ordinary Circles Determined by n Points.

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Title: On the Number of Ordinary Circles Determined by n Points.
Authors: Zhang, Ruixiang1 zrx_gpx@126.com
Source: Discrete & Computational Geometry. Sep2011, Vol. 46 Issue 2, p205-211. 7p.
Subjects: Line geometry, Circle, Intersection graph theory, Euclidean algorithm, Discrete geometry
Abstract: 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]
Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: 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]
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  Data: <i>Copyright of Discrete & Computational Geometry is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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