Abstract
1. Let Λ denote any plane lattice of determinant Δ ╪ 0. Then it is well known that the regioncontains a pair of generating points of Λ; and that, unless the lattice Λ is of the special formwhere both α│β, γ│δ are rational, there are an infinity of such pairs in the interior of the region. Minkowski (4) obtained this result by considering the ‘tangent’ parallelogram Пλ,inscribed in the region (1). With simple geometrical arguments, he showed that(i) Пλ always contains a point of Λ, other than 0,(ii) if Пλ contains two primitive points of Λ then these generate Λ, except possibly when Λ has points, other than 0, on both coordinate axes.
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