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Proofs from THE BOOK

  • Martin Aigner
  • Günter M. Ziegler

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Number Theory

    1. Front Matter
      Pages 1-1
    2. Martin Aigner, Günter M. Ziegler
      Pages 3-6
    3. Martin Aigner, Günter M. Ziegler
      Pages 7-12
    4. Martin Aigner, Günter M. Ziegler
      Pages 13-16
    5. Martin Aigner, Günter M. Ziegler
      Pages 17-21
    6. Martin Aigner, Günter M. Ziegler
      Pages 23-26
    7. Martin Aigner, Günter M. Ziegler
      Pages 27-34
  3. Geometry

    1. Front Matter
      Pages 35-35
    2. Martin Aigner, Günter M. Ziegler
      Pages 37-43
    3. Martin Aigner, Günter M. Ziegler
      Pages 45-50
    4. Martin Aigner, Günter M. Ziegler
      Pages 51-55
    5. Martin Aigner, Günter M. Ziegler
      Pages 57-62
    6. Martin Aigner, Günter M. Ziegler
      Pages 63-66
    7. Martin Aigner, Günter M. Ziegler
      Pages 67-71
    8. Martin Aigner, Günter M. Ziegler
      Pages 73-76
    9. Martin Aigner, Günter M. Ziegler
      Pages 77-82
    10. Martin Aigner, Günter M. Ziegler
      Pages 83-88
  4. Analysis

    1. Front Matter
      Pages 89-89
    2. Martin Aigner, Günter M. Ziegler
      Pages 91-100
    3. Martin Aigner, Günter M. Ziegler
      Pages 101-107
    4. Martin Aigner, Günter M. Ziegler
      Pages 109-116
    5. Martin Aigner, Günter M. Ziegler
      Pages 117-120
  5. Combinatorics

    1. Front Matter
      Pages 121-121
    2. Martin Aigner, Günter M. Ziegler
      Pages 123-133
    3. Martin Aigner, Günter M. Ziegler
      Pages 135-139
    4. Martin Aigner, Günter M. Ziegler
      Pages 141-146
    5. Martin Aigner, Günter M. Ziegler
      Pages 147-152
    6. Martin Aigner, Günter M. Ziegler
      Pages 153-158
  6. Graph Theory

    1. Front Matter
      Pages 159-159
    2. Martin Aigner, Günter M. Ziegler
      Pages 161-164
    3. Martin Aigner, Günter M. Ziegler
      Pages 165-168
    4. Martin Aigner, Günter M. Ziegler
      Pages 169-172
    5. Martin Aigner, Günter M. Ziegler
      Pages 173-182
    6. Martin Aigner, Günter M. Ziegler
      Pages 183-185
    7. Martin Aigner, Günter M. Ziegler
      Pages 187-195
  7. Back Matter
    Pages 196-199

About this book

Introduction

The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory.
Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection.
The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.

Keywords

Abzählen Beweise Combinatorics Euler's formula Eulersche Formel Polya Prime Zahlen calculus differential equation double counting graph theory number theory numbers proofs

Authors and affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Fachbereich Mathematik, MA 7-1Technische Universität BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-22343-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-22345-1
  • Online ISBN 978-3-662-22343-7
  • Buy this book on publisher's site
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