What is recorded here?
Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.
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Scientific scope
The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.
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People and systems
Hermann Minkowski
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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English catalogue narrative
Minkowski: volume forces a nonzero integer lattice point
Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.
Scientific scope
The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Hermann Minkowski
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.