Mathematical Models : From the Collections of Universities and Museums -- Photograph Volume and Commentary

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 Front Matter ....Pages I-XIX Front Matter ....Pages 1-1 Elementary Analytic Geometry (Gerd Fischer)....Pages 1-10 Algebraic Surfaces (Gerd Fischer)....Pages 11-56 Differential Geometry (Gerd Fischer)....Pages 57-93 Convex Bodies of Constant Width (Gerd Fischer)....Pages 95-100 Regular Star-Polyhedra (Gerd Fischer)....Pages 101-105 Models of the Real Projective Plane (Gerd Fischer)....Pages 107-115 Functions (Gerd Fischer)....Pages 117-129 Front Matter ....Pages 131-131 Elementary Analytic Geometry (Gerd Fischer)....Pages 133-137 Algebraic Surfaces (Wolf Barth, Horst Knörrer)....Pages 139-154 Differential Geometry (Manfredo P. do Carmo, Gerd Fischer, Ulrich Pinkall, Helmut Reckziegel)....Pages 155-180 Convex Bodies of Constant Width (Johannes Böhm)....Pages 181-188 Regular Star-Polyhedra (Erhard Quaisser)....Pages 189-194 Models of the Real Projective Plane (Ulrich Pinkall)....Pages 195-199 Functions (Jürgen Leiterer)....Pages 201-209 Back Matter ....Pages 211-216 Gerd Fischer, Editor ; With A Preface By Gert-martin Greuel. Includes Bibliographical References.