The Geometry of Numbers
Olds, Carl D, Davidoff, Giuliana
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.
Categories:
Volume:
41
Year:
2001
Publisher:
Mathematical Association of America (MAA)
Language:
english
ISBN 10:
0883859556
ISBN 13:
9780883859551
Series:
Anneli Lax New Mathematical Library
File:
PDF, 939 KB
IPFS:
,
english, 2001
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