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© 2019

Geometry in History

  • S. G. Dani
  • Athanase Papadopoulos
Book

Table of contents

  1. Front Matter
    Pages i-xvi
    PDF
  2. Plato on Geometry and the Geometers
    Stelios Negrepontis
    Pages 1-88
  3. Topology and Biology: From Aristotle to Thom
    Athanase Papadopoulos
    Pages 89-128
  4. Time and Periodicity from Ptolemy to Schrödinger: Paradigm Shifts vs Continuity in History of Mathematics
    Yuri I. Manin
    Pages 129-138
  5. Convexity in Greek Antiquity
    Athanase Papadopoulos
    Pages 139-152
  6. On the Concept of Curve: Geometry and Algebra, from Mathematical Modernity to Mathematical Modernism
    Arkady Plotnitsky
    Pages 153-212
  7. From Euclid to Riemann and Beyond: How to Describe the Shape of the Universe
    Toshikazu Sunada
    Pages 213-304
  8. A Path in History, from Curvature to Convexity
    Annette A’Campo-Neuen, Athanase Papadopoulos
    Pages 305-353
  9. The Axiomatic Destiny of the Theorems of Pappus and Desargues
    Victor Pambuccian, Celia Schacht
    Pages 355-399
  10. Projective Configuration Theorems: Old Wine into New Wineskins
    Serge Tabachnikov
    Pages 401-434
  11. Poincaré’s Geometric Worldview and Philosophy
    Ken’ichi Ohshika
    Pages 435-450
  12. Perturbing a Planar Rotation: Normal Hyperbolicity and Angular Twist
    Alain Chenciner
    Pages 451-468
  13. René Thom and an Anticipated h-Principle
    François Laudenbach
    Pages 469-491
  14. Rigid and Flexible Facets of Symplectic Topology
    Yakov Eliashberg
    Pages 493-514
  15. Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective
    William M. Goldman
    Pages 515-552
  16. Basic Aspects of Differential Geometry
    Marc Chaperon
    Pages 553-580
  17. The Global Study of Riemannian-Finsler Geometry
    Katsuhiro Shiohama, Bankteshwar Tiwari
    Pages 581-621
  18. The Poincaré Conjecture and Related Statements
    Valerii N. Berestovskii
    Pages 623-685
  19. A Glimpse into the Problems of the Fourth Dimension
    Valentin Poénaru
    Pages 687-703
  20. Memories from My Former Life: The Making of a Mathematician
    Valentin Poénaru
    Pages 705-734
  21. Back Matter
    Pages 735-750
    PDF

About this book

Introduction

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.

Keywords

58-02, 58-03, 14-02, 53-02, 77-02, 30D30 Geometry Topology Riemann surfaces projective geometry differential geometry

Editors and affiliations

  • S. G. Dani
    • 1
  • Athanase Papadopoulos
    • 2
  1. 1.University of Mumbai & Department of Atomic EnergyCentre for Excellence in Basic SciencesMumbaiIndia
  2. 2.Institut de Recherche MathématiqueUniversity of Strasbourg, CNRSStrasbourg CedexFrance

About the editors

The editors are mathematicians whose work is well known (Dani in dynamics and ergodic theory, and Papadopoulos in geometry and topology of low dimensions). They are the authors of many research articles and monographs, and they edited several books. They have a broad view on the current research on geometry, on the history of the subject and on its impact in modern research. Dani is the editor-in-chief of Ganita Bharati (Bulletin of the Indian Society for History of Mathematics). 

Bibliographic information

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