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Geometry Revealed

A Jacob's Ladder to Modern Higher Geometry

  • Marcel Berger

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Marcel Berger
    Pages 1-59
  3. Marcel Berger
    Pages 61-139
  4. Marcel Berger
    Pages 181-247
  5. Marcel Berger
    Pages 249-340
  6. Marcel Berger
    Pages 341-407
  7. Marcel Berger
    Pages 409-504
  8. Marcel Berger
    Pages 505-561
  9. Marcel Berger
    Pages 563-622
  10. Marcel Berger
    Pages 623-674
  11. Marcel Berger
    Pages 675-737
  12. Back Matter
    Pages 785-831

About this book

Introduction

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.

Keywords

Lattice contemporary geometry differential geometry mathematical tools and concepts polygon polytope unsolved and recently solved problems

Authors and affiliations

  • Marcel Berger
    • 1
  1. 1.Études ScientifiquesInstitut des HautesBures-sur-YvetteFrance

Bibliographic information