Minimal requirements for Minkowski's theorem in the plane I
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Let K be a closed convex set in the Euclidean plane, with area A(K), which contains in its interior only one point 0 of the integer lattice. If K has other than one or three chords bisected by 0, it is shown that A(K) ≤ 4. Also, if K has three such chords, A(K) ≤ 4.5. The results are generalised to any lattice in the plane.
[1] H. G. Eggleston. Convexity by H. G. Eggleston , 1958 .
[2] On three sets with no point in common , 1978 .
[3] P. Scott. On Minkowski's Theorem , 1974 .
[4] H. Minkowski,et al. Geometrie der Zahlen , 1896 .
[5] P. R. Scott,et al. Convex Bodies and Lattice Points , 1975 .
[6] P. Scott. Area-Diameter Relations for Two-Dimensional Lattices , 1974 .