Blichfeldt's theorem
id:
blichfeldt-s-theorem-241-2951943
title:
Blichfeldt's theorem
text:
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 , it can be translated so that it includes at least ⌈ A ⌉ points of the integer lattice. Equivalently, every bounded set of area A contains a set of ⌈ A ⌉ points whose coordinates all differ by integers. This theorem can be generalized to other lattices and to higher dimensions, and can be interpreted as a continuous version of the pigeonhole principle.
brand slug:
wiki
category slug:
encyclopedia
description:
High-area shapes can shift to hold many grid points
original url:
https://en.wikipedia.org/wiki/Blichfeldt%27s_theorem
date created:
date modified:
2022-07-17T00:31:38Z
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image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/a/a8/Blichfeldts_theorem.svg","width":306,"height":450}
fields total:
13
integrity:
15