โ Scribed by C. D. Olds, Anneli Lax, Giuliana P. Davidoff
No coin nor oath required. For personal study only.
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.
๐ SIMILAR VOLUMES
This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc. T
This book presents 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. Little mathematical expertise is required beyond an acquaintance with those objects and with some b