English: Blichfeldts theorem, in the form that every plane set of area ${\displaystyle A}$ (here, an ellipse with area ${\displaystyle \pi }$) contains at least ${\displaystyle \lceil A\rceil }$ points (here, ${\displaystyle \lceil \pi \rceil =4}$ points), all of whose coordinates differ from each other by integers. The theorem is proved by cutting the set up by squares of the integer grid (top), translating each piece by an integer translation vector into a single unit square, finding a point in that unit square that is covered by many pieces (middle), and using the preimages of this point as the desired points (bottom).