Any convex, symmetric region in the plane (or higher-dimensional space) with area greater than four times the area of a fundamental lattice domain must contain a nonzero lattice point. It founded the geometry of numbers, a bridge between number theory and convex geometry.
Facts
StatementIf a convex region symmetric about the origin in n-dimensional space has volume greater than 2 to the power of n times the covolume of a lattice, it must contain a nonzero point of that lattice. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Minkowski's Theorem (Wikipedia)
Wikimedia FoundationFormulation section
Minkowski's theorem states that if the volume of S is strictly greater than 2n d(L), then S must contain at least one lattice point other than the origin.
lead paragraph, second sentence
The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers.
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