The Geometry of Numbers, Volume 41

Couverture
Cambridge University Press, 22 févr. 2001 - 174 pages
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 des matières

Lattice Points and Straight Lines
3
Counting Lattice Points
25
Lattice Points and the Area of Polygons
37
Lattice Points in Circles
47
Minkowskis Fundamental Theorem
65
Applications of Minkowskis Theorems
77
Linear Transformations and Integral Lattices
89
Geometric Interpretations of Quadratic Forms
103
A New Principle in the Geometry of Numbers
117
A Minkowski Theorem Optional
129
Gaussian Integers by Peter D
139
The Closest Packing of Convex Bodies
151
Brief Biographies
157
Index 172
Droits d'auteur

Expressions et termes fréquents

Informations bibliographiques