The geometry of numbers (Q6631508)

In this interesting and well written article, the author gives a very nice introduction to the geometry of numbers in the plane, with insight accessible to general readers. The title of the article is the same as the famous book by the originator of the subject, Hermann Minkokwski, first published in 1896.\N\NThe author begins with Minkowski's theorem which states that any convex and with respect to the origin symmetric set in the plane with area greater than 4 contains a non-zero integer point. The theorem is formulated and proved using the Blichfeld's lemma.\N\NAs illustrative applications of the theorem, then the Dirichlet's approximation theorem and the Fermat-Euler theorem on sums of two squares are proved.