The geometry of numbers (Q2715710)

This expository booklet is a self-contained introduction to the geometry of numbers. Most of the material is investigated in the plane; only a few results are in general dimension. Nevertheless Minkowski's ingenious idea, the interplay between number theory and geometry, can be pursued throughout the booklet. So it is a good appetizer for students. The book starts with elementary problems on lines, polygons and lattice points around Pick's theorem, followed by Minkowski's and Blichfeldt's fundamental theorems in the plane. The last 3 chapters consider applications, e.g. to diophantine approximations, Gaussian integers and packings of circles and spheres.