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Blichfeldt's Theorem


Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region will be at least A+1 (Blichfeldt 1914, Steinhaus 1999). The theorem can be generalized to n dimensions.


See also

Lattice Point, Minkowski Convex Body Theorem, Pick's Theorem

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References

Blichfeldt, H. F. "A New Principle in the Geometry of Numbers, with Some Applications." Trans. Amer. Math. Soc. 15, 227-235, 1914.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 97-99, 1999.

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Blichfeldt's Theorem

Cite this as:

Weisstein, Eric W. "Blichfeldt's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BlichfeldtsTheorem.html

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