Blichfeldt's theorem is a mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area A {\displaystyle A} , it can be translated so that it includes at least ⌈ A ⌉ {\displaystyle \lceil A\rceil } points of the integer lattice. Equivalently, every bounded set of area A {\displaystyle A} contains a set of ⌈ A ⌉ {\displaystyle \lceil A\rceil } points whose coordinates all differ by integers.
Blichfeldt's theorem is a mathematical theorem in the geometry of numbers, stating that whenever a bounded set in the Euclidean plane has area A {\displaystyle A} , it can be translated so that it includes at least ⌈ A ⌉ {\displaystyle \lceil A\rceil } points of the integer lattice. Equivalently, every bounded set of area A {\displaystyle A} contains a set of ⌈ A ⌉ {\displaystyle \lceil A\rceil } points whose coordinates all differ by integers.
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