论文标题
拉姆西理论和封闭环的几何形状
Ramsey Theory and Geometry of Closed Loops
论文作者
论文摘要
我们将拉姆西理论应用于封闭轮廓的几何特性的分析。考虑在封闭的轮廓上放置一组六个点。连接这些点的直线为y_ik（x）=α_ikx+\ b {eta} _ik（i，k = 1 ... 6），α_ik不等于0。我们为连接α_ik> 0的点的边缘涂上了α_ik> 0与红色保持的点，以及green with green with green with green。至少一个单色三角形应一定要出现在曲线内（根据Ramsey Number R（3,3）= 6）。该结果立即适用于分析动态台球。第二个定理来自约旦曲线和拉姆西定理的组合。考虑封闭曲线。我们将位于同一区域内的点与绿色链接以及带有红色链接的不同区域内的点连接。在这种情况下，应考虑这些点之间关系的传递性/不强制性。讨论了由封闭情况下的差异几何形状产生的拉姆齐结构。
We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are y_ik (x)=α_ik x+\b{eta}_ik (i,k=1...6), α_ik is not equal to 0. We color the edges connecting the points for which α_ik>0 holds with red, and the edges for which α_ik<0 with green with red. At least one monochromic triangle should necessarily appear within the curve (according to the Ramsey number R(3,3)=6). This result is immediately applicable for the analysis of dynamical billiards. The second theorem emerges from the combination of the Jordan curve and Ramsey theorem. The closed curve is considered. We connect the points located within the same region with green links and the points placed within the different regions with red links. In this case, transitivity/intransitivity of the relations between the points should be considered. Ramsey constructions arising from the differential geometry of closed contours are discussed.
