Ebook: Proofs from THE BOOK

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Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Six proofs of the infinity of primes....Pages 3-6
Bertrand’s postulate....Pages 7-12
Binomial coefficients are (almost) never powers....Pages 13-16
Representing numbers as sums of two squares....Pages 17-21
Every finite division ring is a field....Pages 23-26
Some irrational numbers....Pages 27-34
Front Matter....Pages 35-35
Hilbert’s third problem: decomposing polyhedra....Pages 37-43
Lines in the plane and decompositions of graphs....Pages 45-50
The slope problem....Pages 51-55
Three applications of Euler’s formula....Pages 57-62
Cauchy’s rigidity theorem....Pages 63-66
The problem of the thirteen spheres....Pages 67-71
Touching simplices....Pages 73-76
Every large point set has an obtuse angle....Pages 77-82
Borsuk’s conjecture....Pages 83-88
Front Matter....Pages 89-89
Sets, functions, and the continuum hypothesis....Pages 91-100
In praise of inequalities....Pages 101-107
A theorem of P?lya on polynomials....Pages 109-116
On a lemma of Littlewood and Offord....Pages 117-120
Front Matter....Pages 121-121
Pigeon-hole and double counting....Pages 123-133
Front Matter....Pages 121-121
Three famous theorems on finite sets....Pages 135-139
Cayley’s formula for the number of trees....Pages 141-146
Completing Latin squares....Pages 147-152
The Dinitz problem....Pages 153-158
Front Matter....Pages 159-159
Five-coloring plane graphs....Pages 161-164
How to guard a museum....Pages 165-168
Tur?n’s graph theorem....Pages 169-172
Communicating without errors....Pages 173-182
Of friends and politicians....Pages 183-185
Probability makes counting (sometimes) easy....Pages 187-195
Back Matter....Pages 196-199

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Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Six proofs of the infinity of primes....Pages 3-6
Bertrand’s postulate....Pages 7-12
Binomial coefficients are (almost) never powers....Pages 13-16
Representing numbers as sums of two squares....Pages 17-21
Every finite division ring is a field....Pages 23-26
Some irrational numbers....Pages 27-34
Front Matter....Pages 35-35
Hilbert’s third problem: decomposing polyhedra....Pages 37-43
Lines in the plane and decompositions of graphs....Pages 45-50
The slope problem....Pages 51-55
Three applications of Euler’s formula....Pages 57-62
Cauchy’s rigidity theorem....Pages 63-66
The problem of the thirteen spheres....Pages 67-71
Touching simplices....Pages 73-76
Every large point set has an obtuse angle....Pages 77-82
Borsuk’s conjecture....Pages 83-88
Front Matter....Pages 89-89
Sets, functions, and the continuum hypothesis....Pages 91-100
In praise of inequalities....Pages 101-107
A theorem of P?lya on polynomials....Pages 109-116
On a lemma of Littlewood and Offord....Pages 117-120
Front Matter....Pages 121-121
Pigeon-hole and double counting....Pages 123-133
Front Matter....Pages 121-121
Three famous theorems on finite sets....Pages 135-139
Cayley’s formula for the number of trees....Pages 141-146
Completing Latin squares....Pages 147-152
The Dinitz problem....Pages 153-158
Front Matter....Pages 159-159
Five-coloring plane graphs....Pages 161-164
How to guard a museum....Pages 165-168
Tur?n’s graph theorem....Pages 169-172
Communicating without errors....Pages 173-182
Of friends and politicians....Pages 183-185
Probability makes counting (sometimes) easy....Pages 187-195
Back Matter....Pages 196-199
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