A regularly spaced array of points in a square array, i.e., points with coordinates (m, n, ...), where m, n, ... are integers. Such an array is often called a grid or mesh, and is a special case of a point lattice. The fraction of lattice points visible from the origin, as derived in Castellanos, is (N'(r))/(N(r)) | = | (24/π^2 r^2 + O(r ln r))/(4r^2 + O(r)) | = | (6/π^2 + O((ln r)/r))/(1 + O(1/r)) | = | 6/π^2. Therefore, this is also the probability that two randomly picked integers will be relatively prime to one another.

lattice | no-three-in-a-line-problem | point lattice