$R^2$中多边形的相似系的线横截
Line transversals for homothetical systems of polygons in $R^2$
摘要：
对于给定的平面上没有断面的有限凸多边形系统，求出具有最小相似比c>1的多边形（在给定多边形内有固定中心）的仿射变换，使得变换后的系统有断面.我们证明，在这个最小的配置，我们总是可以找到三个多边形（其中两个躺在不同的半平面确定的横切面），横切面也是切线。
英文摘要：
For given finite system of convex polygons in the plane which have no transversal, find such homothety transformations of polygons (having fixed centres inside given polygons) with minimal similarity ratio c>1 that the transformed system has a transversal. We prove that in this minimal configuration, we can always find three polygons (two of them lying in distinct halfplanes determined by the transversal), for which the transversal is also the tangent line.
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。
