The Geometry of Numbers

 C. D. Olds, Anneli Lax and Giuliana P. Davidoff

The Mathematical Association of America | 2000 | 193 páginas | rar - pdf | 786 kb

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This is a self-contained introduction to the geometry of numbers, beginning with easily understood questions about lattice points on lines, circles and inside simple polygons in the plane. A minimum of mathematical expertise is required beyond an acquaintance with elementary geometry. The authors gradually lead up to the theorems of Minkowski and others who succeeded him. On the way the reader will see how this powerful approach gives improved approximations to irrational numbers by rationals, simplifies arguments on ways of representing integers as sums of squares, and provides a natural tool for attacking problems involving dense packings of spheres.

Contents
Lattice Points and Number Theory
An Introduction to the Geometry of Numbers
Gaussian Integers, by Peter D. Lax
The Closest Packing of Convex Bodies
Brief Biographies
Solutions and Hints.