Format:
Online-Ressource (XII, 860p. 666 illus, digital)
ISBN:
9783540709978
Series Statement:
SpringerLink
Content:
Points and lines in the plane -- Circles and spheres -- The sphere by itself: can we distribute points on it evenly? -- Conics and quadrics -- Plane curves -- Smooth surfaces -- Convexity and convex sets -- Polygons, polyhedra, polytopes -- Lattices, packings and tilings in the plane -- Lattices and packings in higher dimensions -- Geometry and dynamics I: billiards -- Geometry and dynamics II: geodesic flow on a surface.
Content:
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.
Note:
Includes bibliographical references and indexes
,
About the Author; Introduction; Table of Contents; I Points and lines in the plane; II Circles and spheres; III The sphere by itself: can we distribute points on it evenly?; IV Conics and quadrics; V Plane curves; VI Smooth surfaces; VII Convexity and convex sets; VIII Polygons, polyhedra, polytopes; IX Lattices, packings and tilings in the plane; X Lattices and packings in higher dimensions; XI Geometry and dynamics I: billiards; XII Geometry and dynamics II: geodesic flow on a surface; Selected Abbreviations for Journal Titles; Name Index; Subject Index; Symbol Index;
Additional Edition:
ISBN 9783540709961
Additional Edition:
Buchausg. u.d.T. Berger, Marcel, 1927 - 2016 Geometry revealed Berlin : Springer, 2010 ISBN 9783540709961
Additional Edition:
ISBN 3540709967
Language:
English
Subjects:
Mathematics
Keywords:
Geometrie
;
Geometrie
DOI:
10.1007/978-3-540-70997-8
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Berger, Marcel 1927-2016
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