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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
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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 Three times Π²/6
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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 On a lemma of Littlewood and Offord
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    Chapter 25 Cotangent and the Herglotz trick
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    Chapter 26 Buffon’s needle problem
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    Chapter 27 Pigeon-hole and double counting
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    Chapter 28 Tiling rectangles
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    Chapter 29 Three famous theorems on finite sets
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    Chapter 30 Shuffling cards
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    Chapter 31 Lattice paths and determinants
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    Chapter 32 Cayley’s formula for the number of trees
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    Chapter 33 Identities versus bijections
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    Chapter 34 The finite Kakeya problem
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    Chapter 35 Completing Latin squares
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    Chapter 36 The Dinitz problem
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    Chapter 37 Permanents and the power of entropy
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    Chapter 38 Five-coloring plane graphs
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    Chapter 39 How to guard a museum
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    Chapter 40 Turán’s graph theorem
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    Chapter 41 Communicating without errors
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    Chapter 42 The chromatic number of Kneser graphs
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    Chapter 43 Of friends and politicians
  45. Altmetric Badge
    Chapter 44 Probability makes counting (sometimes) easy
Overall attention for this book and its chapters
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Title
Proofs from THE BOOK
Published by
Springer-Verlag Berlin Heidelberg, January 2014
DOI 10.1007/978-3-662-44205-0
ISBNs
978-3-66-244205-0, 978-3-66-244204-3, 978-3-66-249592-6
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 28 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 62 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Brazil 1 2%
Unknown 61 98%

Demographic breakdown

Readers by professional status Count As %
Student > Bachelor 12 19%
Student > Master 10 16%
Student > Ph. D. Student 9 15%
Researcher 6 10%
Other 3 5%
Other 9 15%
Unknown 13 21%
Readers by discipline Count As %
Mathematics 16 26%
Computer Science 12 19%
Engineering 6 10%
Physics and Astronomy 4 6%
Agricultural and Biological Sciences 2 3%
Other 8 13%
Unknown 14 23%