© 2017

Mathematical Models

From the Collections of Universities and Museums – Photograph Volume and Commentary

  • Gerd Fischer
  • Plaster Models et al. in geometry

  • Reprint of the 1986 edition in one volume

  • With a new preface by Gert-Martin Greuel


Table of contents

  1. Front Matter
    Pages I-XIX
  2. Photo Collection

    1. Front Matter
      Pages 1-1
    2. Gerd Fischer
      Pages 1-10
    3. Gerd Fischer
      Pages 11-56
    4. Gerd Fischer
      Pages 57-93
    5. Gerd Fischer
      Pages 95-100
    6. Gerd Fischer
      Pages 101-105
    7. Gerd Fischer
      Pages 107-115
    8. Gerd Fischer
      Pages 117-129
  3. Commentary Volume

    1. Front Matter
      Pages 131-131
    2. Gerd Fischer
      Pages 133-137
    3. Wolf Barth, Horst Knörrer
      Pages 139-154
    4. Manfredo P. do Carmo, Gerd Fischer, Ulrich Pinkall, Helmut Reckziegel
      Pages 155-180
    5. Johannes Böhm
      Pages 181-188
    6. Erhard Quaisser
      Pages 189-194
    7. Ulrich Pinkall
      Pages 195-199
    8. Jürgen Leiterer
      Pages 201-209
  4. Back Matter
    Pages 211-216

About this book


This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry.

This book is a reprint thirty years after the original publication in 1986 with a new preface by Gert-Martin Greuel. The models have a timeless appeal and a historical value.

The Editor
Prof. Dr. Gerd Fischer
, Department of Mathematics, Technical University of Munich


Algebraische Flächen Algebraic Surfaces Kurven und Flächen Curves and Surfaces Algebraische Geometrie Algebraic Geometry Visualisierung Visualization Models of geometric surfaces

Editors and affiliations

  • Gerd Fischer
    • 1
  1. 1.Zentrum MathematikTechnische Universität MünchenGarchingGermany

About the editors

Prof. Dr. Gerd Fischer, Department of Mathematics, Technical University of Munich

Bibliographic information

  • Book Title Mathematical Models
  • Book Subtitle From the Collections of Universities and Museums – Photograph Volume and Commentary
  • Editors Gerd Fischer
  • DOI
  • Copyright Information Springer Fachmedien Wiesbaden GmbH 2017
  • Publisher Name Springer Spektrum, Wiesbaden
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-658-18864-1
  • eBook ISBN 978-3-658-18865-8
  • Edition Number 2
  • Number of Pages XIX, 216
  • Number of Illustrations 211 b/w illustrations, 9 illustrations in colour
  • Additional Information The first edition was published in 2 volumes
  • Topics Mathematics, general
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


“It features 120 photographs of mathematical models from the second half of the 19th and early 20th century. … this book has a lot to teach about aesthetics and didactics of mathematical visualization – two aspects that will retain their importance in our times and in future.” (Hans-Peter Schröcker, zbMATH 1386.00007, 2018)