A lattice point in the plane is a point with integer coordinate... | Filo

Solid State | Concept Visualised | Crystal Lattice and Unit Cell | NEET

. A lattice point is a point (x, y) in the plane, both of whose coordinates are integers. It is easy to see that every lattice point can be surrounded by a small circle which excludes all other lattice points from its interior. It is not much harder to see that it is possible to draw a circle which has exactly two lattice points in its interior, or exactly 3, or exactly 4, as shown in the picture below. Do you think that for every positive integer n there is a circle in the plane which contains