通过包围许多点的点的线段和圆的深度：一个注释
Depth of segments and circles through points enclosing many points: a note
摘要：
Neumann-Lara和Urrutia在1985年证明了在平面上任意n个点的集合中总有一对点使得通过它们的任意圆至少包含（n-2）/60个点。在一系列论文中，这个结果随后被改进到n/4.7，这是目前最知名的下界。在本文中，我们提出了一种新的方法来解决这个问题，使我们能够通过使用已知的结果，j方面的点集在$R^3$，给一个简单的证明某种程度上更强的结果：总是有一对点，使任何圆通过他们，无论是内部和外部，至少有n/4.7点。
英文摘要：
Neumann-Lara and Urrutia showed in 1985 that in any set of n points in the plane in general positionthere is always a pair of points such that any circle through them contains at least (n-2)/60 points. In a series of papers, this result was subsequently improved till n/4.7, which is currently the best known lower bound. In this paper we propose a new approach to the problem that allows us, by using known results about j-facets of sets of points in $R^3$, to give a simple proof of a somehow stronger result: there is always a pair of points such that any circle through them has, both inside and outside, at least n/4.7 points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
