The Geometry of Numbersby Carl D. Olds, Giuliana Davidoff, Anneli Lax
Pub. Date: 02/28/2001
Publisher: Mathematical Association of America
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.
Table of Contents1. Geometry and algebra; 2. Trigonometry, calculus and analytic geometry; 3. Inequalities; 4. Integer sums; 5. Sequences and series.
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