与格点可视性相关的几个问题的结论

Some Results of Questions Related to Visibility of Lattice Points

格点即二维空间中坐标为整数的点 .设 Δ2n={ ( x,y) :x,y∈ Z,1≤ x≤n,1≤ y≤ n} ,对于 Δ2n 中的两点 P,Q,称P与 Q相互可视是指 P=Q或者在连接 P与 Q的线段上没有其他任何格点 .本文讨论了几个与格点可视性相关的问题 ,并给出了相应的结果 .

Lattice points are the integer points in two dimensions. Let Δ 2 n={(x,y):x,y∈Z, 1≤x≤n, 1≤y≤n} be the set of integer lattice points .If P and Q are two points in Δ 2 n , we say that P and Q are visible from each other if P=Q or there is no any other lattice point of Δ 2 n on the line segment joining P and Q . In this paper, some relative problems are discussed and some relevent results obtained.