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Proofs from THE BOOK

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Cover of 'Proofs from THE BOOK'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Six proofs of the infinity of primes
  3. Altmetric Badge
    Chapter 2 Bertrand’s postulate
  4. Altmetric Badge
    Chapter 3 Binomial coefficients are (almost) never powers
  5. Altmetric Badge
    Chapter 4 Representing numbers as sums of two squares
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    Chapter 5 The law of quadratic reciprocity
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    Chapter 6 Every finite division ring is a field
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    Chapter 7 The spectral theorem and Hadamard’s determinant problem
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    Chapter 8 Some irrational numbers
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    Chapter 9 Four times π 2 /6
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    Chapter 10 Hilbert’s third problem: decomposing polyhedra
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    Chapter 11 Lines in the plane and decompositions of graphs
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    Chapter 12 The slope problem
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    Chapter 13 Three applications of Euler’s formula
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    Chapter 14 Cauchy’s rigidity theorem
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    Chapter 15 The Borromean rings don’t exist
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    Chapter 16 Touching simplices
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    Chapter 17 Every large point set has an obtuse angle
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    Chapter 18 Borsuk’s conjecture
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    Chapter 19 Sets, functions, and the continuum hypothesis
  21. Altmetric Badge
    Chapter 20 In praise of inequalities
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    Chapter 21 The fundamental theorem of algebra
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    Chapter 22 One square and an odd number of triangles
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    Chapter 23 A theorem of Pólya on polynomials
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    Chapter 24 Van der Waerden’s permanent conjecture
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    Chapter 25 On a lemma of Littlewood and Offord
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    Chapter 26 Cotangent and the Herglotz trick
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    Chapter 27 Buffon’s needle problem
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    Chapter 28 Pigeon-hole and double counting
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    Chapter 29 Tiling rectangles
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    Chapter 30 Three famous theorems on finite sets
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    Chapter 31 Shuffling cards
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    Chapter 32 Lattice paths and determinants
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    Chapter 33 Cayley’s formula for the number of trees
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    Chapter 34 Identities versus bijections
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    Chapter 35 The finite Kakeya problem
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    Chapter 36 Completing Latin squares
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    Chapter 37 Permanents and the power of entropy
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    Chapter 38 The Dinitz problem
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    Chapter 39 Five-coloring plane graphs
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    Chapter 40 How to guard a museum
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    Chapter 41 Turán’s graph theorem
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    Chapter 42 Communicating without errors
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    Chapter 43 The chromatic number of Kneser graphs
  45. Altmetric Badge
    Chapter 44 Of friends and politicians
  46. Altmetric Badge
    Chapter 45 Probability makes counting (sometimes) easy
Attention for Chapter 5: The law of quadratic reciprocity
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Chapter title
The law of quadratic reciprocity
Chapter number 5
Book title
Proofs from THE BOOK
Published by
Springer, Berlin, Heidelberg, January 2018
DOI 10.1007/978-3-662-57265-8_5
Book ISBNs
978-3-66-257264-1, 978-3-66-257265-8
Authors

Martin Aigner, Günter M. Ziegler

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 3 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Unknown 3 100%

Demographic breakdown

Readers by professional status Count As %
Researcher 1 33%
Unknown 2 67%
Readers by discipline Count As %
Mathematics 1 33%
Agricultural and Biological Sciences 1 33%
Unknown 1 33%