Given a family of sets on the plane, we say that the family is intersecting if for any two sets from the family their interiors intersect. In this paper, we study intersecting families of triangles with vertices in a given set of points. In particular, we show that if a set P of n points is in convex position, then the largest intersecting family of triangles with vertices in P contains at most \(({1}/{4}+o(1))\left( {\begin{array}{c}n\\ 3\end{array}}\right) \) triangles.

中文翻译：

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三角形的交定理

给定飞机上的一组家具，我们说如果该家具中的任何两套家具的内部相交，则该家具是相交的。在本文中，我们研究了在给定点集中具有三角形的相交三角形族。特别是，我们表明，如果一组P的Ñ点是在凸起位置，那么三角形的最大交叉家族与顶点P含有至多\（（{1} / {4} + O（1））\左（{\ begin {array} {c} n \\ 3 \ end {array}} \ right）\）三角形。