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Proofs from THE BOOK

  • Textbook
  • © 1998

Overview

Authors:
  1. Martin Aigner

    1. Institut für Mathematik II (WE2), Freie Universität Berlin, Berlin, Germany

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  2. Günter M. Ziegler

    1. Fachbereich Mathematik, MA 7-1, Technische Universität Berlin, Berlin, Germany

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    You can also search for this author in PubMed   Google Scholar

  • An excellent, easy-to-read book for everyone with an interest in mathematics.

  • Two top researchers have made a big effort and selected a list of mathematical problems which can be solved by elegant, esthetically pleasing proofs.

  • The result is a book which will be fun for everybody with an interest in mathematics requiring only very little previous knowledge.

  • Includes supplementary material: sn.pub/extras

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Table of contents (30 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Number Theory

    1. Front Matter

      Pages 1-1
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    2. Six proofs of the infinity of primes

      • Martin Aigner, Günter M. Ziegler
      Pages 3-6

    3. Bertrand’s postulate

      • Martin Aigner, Günter M. Ziegler
      Pages 7-12

    4. Binomial coefficients are (almost) never powers

      • Martin Aigner, Günter M. Ziegler
      Pages 13-16

    5. Representing numbers as sums of two squares

      • Martin Aigner, Günter M. Ziegler
      Pages 17-21

    6. Every finite division ring is a field

      • Martin Aigner, Günter M. Ziegler
      Pages 23-26

    7. Some irrational numbers

      • Martin Aigner, Günter M. Ziegler
      Pages 27-34

  3. Geometry

    1. Front Matter

      Pages 35-35
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    2. Hilbert’s third problem: decomposing polyhedra

      • Martin Aigner, Günter M. Ziegler
      Pages 37-43

    3. Lines in the plane and decompositions of graphs

      • Martin Aigner, Günter M. Ziegler
      Pages 45-50

    4. The slope problem

      • Martin Aigner, Günter M. Ziegler
      Pages 51-55

    5. Three applications of Euler’s formula

      • Martin Aigner, Günter M. Ziegler
      Pages 57-62

    6. Cauchy’s rigidity theorem

      • Martin Aigner, Günter M. Ziegler
      Pages 63-66

    7. The problem of the thirteen spheres

      • Martin Aigner, Günter M. Ziegler
      Pages 67-71

    8. Touching simplices

      • Martin Aigner, Günter M. Ziegler
      Pages 73-76

    9. Every large point set has an obtuse angle

      • Martin Aigner, Günter M. Ziegler
      Pages 77-82

    10. Borsuk’s conjecture

      • Martin Aigner, Günter M. Ziegler
      Pages 83-88

  4. Analysis

    1. Front Matter

      Pages 89-89
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    2. Sets, functions, and the continuum hypothesis

      • Martin Aigner, Günter M. Ziegler
      Pages 91-100
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Keywords

About this book

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.

Reviews

"...a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another." - Notices of the AMS

Authors and Affiliations

  • Institut für Mathematik II (WE2), Freie Universität Berlin, Berlin, Germany

    Martin Aigner

  • Fachbereich Mathematik, MA 7-1, Technische Universität Berlin, Berlin, Germany

    Günter M. Ziegler

Bibliographic Information

  • Book Title: Proofs from THE BOOK

  • Authors: Martin Aigner, Günter M. Ziegler

  • DOI: https://doi.org/10.1007/978-3-662-22343-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • eBook ISBN: 978-3-662-22343-7Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: VIII, 199

  • Topics: Number Theory, Geometry, Analysis, Combinatorics

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