On the Number of D-Points on a Line in the Tiling (3.6.3.6)
琳 彭 · Advances in Applied Mathematics · 2017
阿基米德铺砌(3.6.3.6)的顶点称为D-点。论文首先研究了平面内任意给定直线上的D-点数，证明了所有直线按其所含D-点数可分为三类，即不含D-点、含且仅含一个D-点与含无穷多个D-点，同时给出了刻画这三类直线的充要条件，进而探讨了 方向上内部不含D-点的最宽路径问题。 A vertex of the Archimedean tiling (3.6.3.6) is called a D-point. In this paper, we first investigate the number of D-points lying on any given line in the plane, and prove that all the lines can be classified into three categories according to the numbers of D-points lying on them, namely, no D-point, one and only one D-point and an infinitely many D-points. We also give the whole characterizations of those three types of lines by some necessary and sufficient conditions. Furthermore, we consider the broadest paths that contain no D-points in their interiors in any given direction .