About: Minkowski's theorem

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In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin). The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. It can be extended from the integers to any lattice and to any symmetric convex set with volume greater than , where denotes the covolume of the lattice (the absolute value of the determinant of any of its bases).

Attributes	Values
rdfs:label	Minkowski's theorem (en)
rdfs:comment	In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin). The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. It can be extended from the integers to any lattice and to any symmetric convex set with volume greater than , where denotes the covolume of the lattice (the absolute value of the determinant of any of its bases). (en)
sameAs	Minkowski's theorem Minkowski's theorem
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Subject	Articles containing proofs Convex analysis Theorems in number theory Hermann Minkowski Geometry of numbers
gold:hypernym	Statement
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Minkowski's_theorem?oldid=1053790896&ns=0
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Wikipage revision ID	1053790896 (xsd:integer)
Link from a Wikipage to another Wikipage	Fractional ideal Number theory TFNP Algebraic number field Area Blichfeldt's theorem Volume Articles containing proofs Convex analysis Theorems in number theory Geometry of numbers Hermann Minkowski Dirichlet's approximation theorem Dirichlet's unit theorem Dual lattice Lenstra–Lenstra–Lovász lattice basis reduction algorithm Pick's theorem Wolfgang M. Schmidt Hypercube List of mathematical jargon Plane (geometry) Convex set Hermann Minkowski Hermite constant Minkowski's bound Minkowski's second theorem Origin (mathematics) Geometry of numbers Danzer set Ideal class group Determinant Thue's lemma Field norm Injective function Integer Integer lattice Lagrange's four-square theorem Vector space Lattice (group) Lattice problem Mathematics
has abstract	In mathematics, Minkowski's theorem is the statement that every convex set in which is symmetric with respect to the origin and which has volume greater than contains a non-zero integer point (meaning a point in that is not the origin). The theorem was proved by Hermann Minkowski in 1889 and became the foundation of the branch of number theory called the geometry of numbers. It can be extended from the integers to any lattice and to any symmetric convex set with volume greater than , where denotes the covolume of the lattice (the absolute value of the determinant of any of its bases). (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Minkowski's_theorem
is Wikipage redirect of	Minkowskis theorem Minkowsky's theorem Minkowski's convex body theorem Minkowski's theorem of convex bodies Minkowski constant Minkowski convex body theorem Minkowski theorem
is Link from a Wikipage to another Wikipage of	List of theorems List of things named after Hermann Minkowski Algebraic number field Basic Number Theory Blichfeldt's theorem Freiman's theorem Geometry of numbers Dirichlet's approximation theorem Dual lattice Oded Regev (computer scientist) List of eponyms (L–Z) List of geometry topics List of group theory topics List of number theory topics List of scientific laws named after people Ehrhart's volume conjecture Hermann Minkowski List of convexity topics Minkowski Minkowski's bound Minkowskis theorem Minkowsky's theorem Danzer set

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