2010

Proofs from THE BOOK

Authors:

ISBN: 978-3-642-00855-9 (Print) 978-3-642-00856-6 (Online)

Table of contents (40 chapters)

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  1. Front Matter

    Pages I-VIII

  2. Number Theory

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-6

      Six proofs of the infinity of primes

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      Book Chapter

      Pages 7-12

      Bertrand’s postulate

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      Book Chapter

      Pages 13-16

      Binomial coefficients are (almost) never powers

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      Book Chapter

      Pages 17-22

      Representing numbers as sums of two squares

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      Book Chapter

      Pages 23-30

      The law of quadratic reciprocity

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      Book Chapter

      Pages 31-34

      Every finite division ring is a field

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      Book Chapter

      Pages 35-41

      Some irrational numbers

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      Book Chapter

      Pages 43-50

      Three times Π²/6

  3. Geometry

    1. Front Matter

      Pages 51-51

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      Book Chapter

      Pages 53-61

      Hilbert’s third problem: decomposing polyhedra

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      Book Chapter

      Pages 63-67

      Lines in the plane and decompositions of graphs

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      Book Chapter

      Pages 69-73

      The slope problem

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      Book Chapter

      Pages 75-80

      Three applications of Euler’s formula

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      Book Chapter

      Pages 81-84

      Cauchy’s rigidity theorem

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      Book Chapter

      Pages 85-88

      Touching simplices

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      Book Chapter

      Pages 89-94

      Every large point set has an obtuse angle

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      Book Chapter

      Pages 95-100

      Borsuk’s conjecture

  4. Analysis

    1. Front Matter

      Pages 101-101

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      Book Chapter

      Pages 103-118

      Sets, functions, and the continuum hypothesis

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      Book Chapter

      Pages 119-125

      In praise of inequalities

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      Book Chapter

      Pages 127-129

      The fundamental theorem of algebra

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      Book Chapter

      Pages 131-138

      One square and an odd number of triangles

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