Non-Euclidean Geometries

János Bolyai Memorial Volume

  • András Prékopa
  • Emil Molnár

Part of the Mathematics and Its Applications book series (MAIA, volume 581)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. History

    1. Front Matter
      Pages 1-1
    2. András Prékopa
      Pages 3-59
    3. Jeremy Gray
      Pages 61-80
    4. Elemér Kiss
      Pages 81-93
  3. Axiomatical and Logical Aspects

    1. Front Matter
      Pages 95-95
    2. Walter Benz
      Pages 97-107
    3. Asia Ivic Weiss, William Weiss
      Pages 115-118
    4. Hajnal Andréka, Judit X. Madarász, István Németi
      Pages 155-185
  4. Polyhedra, Volumes, Discrete Arrangements, Fractals

    1. Front Matter
      Pages 187-187
    2. Robert Connelly
      Pages 189-196
    3. Charles Radin
      Pages 197-207
    4. Hellmuth Stachel
      Pages 209-225
    5. Bernd O. Stratmann
      Pages 227-247
  5. Tilings, Orbifolds and Manifolds, Visualization

    1. Front Matter
      Pages 267-267
    2. A.D. Mednykh, V.S. Petrov
      Pages 307-319
  6. Differential Geometry

    1. Front Matter
      Pages 365-365
    2. Sigurdur Helgason
      Pages 367-384
    3. Neda Bokan, Paola Matzeu, Zoran Rakić
      Pages 385-405
    4. János Szenthe
      Pages 427-444
    5. Lajos Tamássy
      Pages 445-461
  7. Physics

About this book


"From nothing I have created a new different world,” wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture.

The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.


This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information.


Applications in physics Axiomatics History of Mathematics History of geometry János Bolyai Non-Euclidean Geometry Relativity Special relativity Volume

Editors and affiliations

  • András Prékopa
    • 1
  • Emil Molnár
    • 2
  1. 1.Rutgers Center for Operations ResearchPiscatawayUSA
  2. 2.Budapest University of Technology and EconomicsHungary

Bibliographic information