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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
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    Chapter 2 Bertrand’s postulate
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    Chapter 3 Binomial coefficients are (almost) never powers
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    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
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    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
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    Chapter 44 Of friends and politicians
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    Chapter 45 Probability makes counting (sometimes) easy
Overall attention for this book and its chapters
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133 X users
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18 Wikipedia pages

Citations

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Title
Proofs from THE BOOK
Published by
Springer Berlin Heidelberg, July 2018
DOI 10.1007/978-3-662-57265-8
ISBNs
978-3-66-257264-1, 978-3-66-257265-8
Authors

Martin Aigner, Günter M. Ziegler, Aigner, Martin, Ziegler, Günter M.

X Demographics

X Demographics

The data shown below were collected from the profiles of 133 X users who shared this research output. Click here to find out more about how the information was compiled.
Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 587 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 12 2%
France 3 <1%
Canada 3 <1%
Netherlands 2 <1%
Japan 2 <1%
Italy 2 <1%
Finland 2 <1%
India 2 <1%
China 2 <1%
Other 10 2%
Unknown 547 93%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 124 21%
Researcher 90 15%
Student > Master 85 14%
Student > Bachelor 52 9%
Professor 43 7%
Other 116 20%
Unknown 77 13%
Readers by discipline Count As %
Mathematics 127 22%
Computer Science 111 19%
Engineering 80 14%
Physics and Astronomy 46 8%
Social Sciences 17 3%
Other 105 18%
Unknown 101 17%